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Long-term monitoring of the ANTARES optical module efficiencies using \(^{40}\)K decays in sea water
(2018)
Cherenkov light induced by radioactive decay products is one of the major sources of background light for deep-sea neutrino telescopes such as ANTARES. These decays are at the same time a powerful calibration source. Using data collected by the ANTARES neutrino telescope from mid 2008 to 2017, the time evolution of the photon detection efficiency of optical modules is studied. A modest loss of only 20% in 9 years is observed. The relative time calibration between adjacent modules is derived as well.
One of the main objectives of the ANTARES telescope is the search for point- like neutrino sources. Both the pointing accuracy and the angular resolution of the detector are important in this context and a reliableway to evaluate this performance is needed. In order to measure the pointing accuracy of the detector, one possibility is to study the shadow of the Moon, i. e. the deficit of the atmospheric muon flux from the direction of the Moon induced by the absorption of cosmic rays. Analysing the data taken between 2007 and 2016, theMoon shadow is observed with 3.5s statistical significance. The detector angular resolution for downwardgoing muons is 0.73. +/- 0.14.. The resulting pointing performance is consistent with the expectations. An independent check of the telescope pointing accuracy is realised with the data collected by a shower array detector onboard of a ship temporarily moving around the ANTARES location.
Since the prediction of the quantum spin Hall effect in graphene by Kane and Mele, \(Z_2\) topology in hexagonal monolayers is indissociably linked to high-symmetric honeycomb lattices. This thesis breaks with this paradigm by focusing on topological phases in the fundamental two-dimensional hexagonal crystal, the triangular lattice. In contrast to Kane-Mele-type systems, electrons on the triangular lattice profit from a sizable, since local, spin-orbit coupling (SOC) and feature a non-trivial ground state only in the presence of inversion symmetry breaking. This tends to displace the valence charge form the atomic position. Therefore, all non-trivial phases are real-space obstructed. Inspired by the contemporary conception of topological classification of electronic systems, a comprehensive lattice and band symmetry analysis of insulating phases of a \(p\)-shell on the triangular lattice is presented. This reveals not only the mechanism at the origin of band topology, the competition of SOC and symmetry breaking, but sheds also light on the electric polarization arising from a displacement of the valence charge centers from the nuclei, i. e., real-space obstruction. In particular, the competition of SOC versus horizontal and vertical reflection symmetry breaking gives rise to four topologically distinct insulating phases: two kinds of quantum spin Hall insulators (QSHI), an atomic insulator and a real-space obstructed higher-order topological insulator. The theoretical analysis is complemented with state-of-the-art first principles calculations and experiments on trigonal monolayer adsorbate systems. This comprises the recently discovered triangular QSHI indenene, formed by In atoms, and focuses on its topological classification and real-space obstruction. The analysis reveals Kane-Mele-type valence bands which profit from the atomic SOC of the triangular lattice. The realization of a HOTI is proposed by reducing SOC by considering lighter adsorbates. Further the orbital Rashba effect is analyzed in AgTe, a consequence of mirror symmetry breaking, the formation of local angular momentum polarization and SOC. As an outlook beyond topology, the Fermi surface and electronic susceptibility of Group V adsorbates on silicon carbide are investigated.
In summary, this thesis elucidates the interplay of symmetry breaking and SOC on the triangular lattice, which can promote non-trivial insulating phase.
The ANTARES neutrino telescope has an energy threshold of a few tens of GeV. This allows to study the phenomenon of atmospheric muon neutrino disappearance due to neutrino oscillations. In a similar way, constraints on the 3+1 neutrino model, which foresees the existence of one sterile neutrino, can be inferred. Using data collected by the ANTARES neutrino telescope from 2007 to 2016, a new measurement of m 2 and (23) has been performed which is consistent with world best-fit values and constraints on the 3+1 neutrino model have been derived.
We consider the process of muon-electron elastic scattering, which has been proposed as an ideal framework to measure the running of the electromagnetic coupling constant at space-like momenta and determine the leading-order hadronic contribution to the muon g-2 (MUonE experiment). We compute the next-to-leading (NLO) contributions due to QED and purely weak corrections and implement them into a fully differential Monte Carlo event generator, which is available for first experimental studies. We show representative phenomenological results of interest for the MUonE experiment and examine in detail the impact of the various sources of radiative corrections under different selection criteria, in order to study the dependence of the NLO contributions on the applied cuts. The study represents the first step towards the realisation of a high-precision Monte Carlo code necessary for data analysis.
KM3NeT will be a network of deep-sea neutrino telescopes in the Mediterranean Sea. The KM3NeT/ARCA detector, to be installed at the Capo Passero site (Italy), is optimised for the detection of high-energy neutrinos of cosmic origin. Thanks to its geographical location on the Northern hemisphere, KM3NeT/ARCA can observe upgoing neutrinos from most of the Galactic Plane, including the Galactic Centre. Given its effective area and excellent pointing resolution, KM3NeT/ARCA will measure or significantly constrain the neutrino flux from potential astrophysical neutrino sources. At the same time, it will test flux predictions based on gamma-ray measurements and the assumption that the gamma-ray flux is of hadronic origin. Assuming this scenario, discovery potentials and sensitivities for a selected list of Galactic sources and to generic point sources with an E-2 spectrum are presented. These spectra are assumed to be time independent. The results indicate that an observation with 3 sigma significance is possible in about six years of operation for the most intense sources, such as Supernovae Remnants RX J1713.7-3946 and Vela Jr. If no signal will be found during this time, the fraction of the gamma-ray flux coming from hadronic processes can be constrained to be below 50% for these two objects. (C) 2019 The Authors. Published by Elsevier B.V.
We consider the computation of volumes contained in a spatial slice of AdS(3) in terms of observables in a dual CFT. Our main tool is kinematic space, defined either from the bulk perspective as the space of oriented bulk geodesics, or from the CFT perspective as the space of entangling intervals. We give an explicit formula for the volume of a general region in a spatial slice of AdS(3) as an integral over kinematic space. For the region lying below a geodesic, we show how to write this volume purely in terms of entangling entropies in the dual CFT. This expression is perhaps most interesting in light of the complexity = volume proposal, which posits that complexity of holographic quantum states is computed by bulk volumes. An extension of this idea proposes that the holographic subregion complexity of an interval, defined as the volume under its Ryu-Takayanagi surface, is a measure of the complexity of the corresponding reduced density matrix. If this is true, our results give an explicit relationship between entanglement and subregion complexity in CFT, at least in the vacuum. We further extend many of our results to conical defect and BTZ black hole geometries.
The modular Hamiltonian of reduced states, given essentially by the logarithm of the reduced density matrix, plays an important role within the AdS/CFT correspondence in view of its relation to quantum information. In particular, it is an essential ingredient for quantum information measures of distances between states, such as the relative entropy and the Fisher information metric. However, the modular Hamiltonian is known explicitly only for a few examples. For a family of states rho(lambda) that is parametrized by a scalar lambda, the first order contribution in (lambda) over tilde = lambda-lambda(0) of the modular Hamiltonian to the relative entropy between rho(lambda) and a reference state rho(lambda 0) is completely determined by the entanglement entropy, via the first law of entanglement. For several examples, e.g. for ball-shaped regions in the ground state of CFTs, higher order contributions are known to vanish. In these cases the modular Hamiltonian contributes to the Fisher information metric in a trivial way. We investigate under which conditions the modular Hamiltonian provides a non-trivial contribution to the Fisher information metric, i.e. when the contribution of the modular Hamiltonian to the relative entropy is of higher order in (lambda) over tilde. We consider one-parameter families of reduced states on two entangling regions that form an entanglement plateau, i.e. the entanglement entropies of the two regions saturate the Araki-Lieb inequality. We show that in general, at least one of the relative entropies of the two entangling regions is expected to involve (lambda) over tilde contributions of higher order from the modular Hamiltonian. Furthermore, we consider the implications of this observation for prominent AdS/CFT examples that form entanglement plateaux in the large N limit.
We develop a joint formalism and numerical framework for analyzing the superconducting instability of metals from a weak coupling perspective. This encompasses the Kohn–Luttinger formulation of weak coupling renormalization group for superconductivity as well as the random phase approximation imposed on the diagrammatic expansion of the two-particle Green’s function. The central quantity to resolve is the effective interaction in the Cooper channel, for which we develop an optimized numerical framework. Our code is capable of treating generic multi-orbital models in two as well as three spatial dimensions and, in particular, arbitrary avenues of spin-orbit coupling.
We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice t-t' Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publish a set of recommended choices for the functional renormalization group, shown to decrease the computational cost for FRG calculations and representing a valuable basis for further investigations.
A well-known result for the interference of two single-mode fields is that the degree of coherence and the degree of indistinguishability are the same when we consider the detection of a single photon. In this article, we present the relation between the degree of coherence, path indistinguishability and the fringe visibility considering interference of multiple numbers of single-mode fields while being interested in the detection of a single photon only. We will also mention how Born’s rule of interference for multiple sources is reflected in these results.
Josephson junctions (JJs) in the presence of a magnetic field exhibit qualitatively different interference patterns depending on the spatial distribution of the supercurrent through the junction. In JJs based on two-dimensional topological insulators (2DTIs), the electrons/holes forming a Cooper pair (CP) can either propagate along the same edge or be split into the two edges. The former leads to a SQUID-like interference pattern, with the superconducting flux quantum ϕ\(_0\) (where ϕ\(_0\)=h/2e) as a fundamental period. If CPs’ splitting is additionally included, the resultant periodicity doubles. Since the edge states are typically considered to be strongly localized, the critical current does not decay as a function of the magnetic field. The present paper goes beyond this approach and inspects a topological JJ in the tunneling regime featuring extended edge states. It is here considered the possibility that the two electrons of a CP propagate and explore the junction independently over length scales comparable to the superconducting coherence length. As a consequence of the spatial extension, a decaying pattern with different possible periods is obtained. In particular, it is shown that, if crossed Andreev reflections (CARs) are dominant and the edge states overlap, the resulting interference pattern features oscillations whose periodicity approaches 2ϕ\(_0\).
The Event Horizon Telescope (EHT) has led to the first images of a supermassive black hole, revealing the central compact objects in the elliptical galaxy M87 and the Milky Way. Proposed upgrades to this array through the next-generation EHT (ngEHT) program would sharply improve the angular resolution, dynamic range, and temporal coverage of the existing EHT observations. These improvements will uniquely enable a wealth of transformative new discoveries related to black hole science, extending from event-horizon-scale studies of strong gravity to studies of explosive transients to the cosmological growth and influence of supermassive black holes. Here, we present the key science goals for the ngEHT and their associated instrument requirements, both of which have been formulated through a multi-year international effort involving hundreds of scientists worldwide.
In the past few years, the Event Horizon Telescope (EHT) has provided the first-ever event horizon-scale images of the supermassive black holes (BHs) M87* and Sagittarius A* (Sgr A*). The next-generation EHT project is an extension of the EHT array that promises larger angular resolution and higher sensitivity to the dim, extended flux around the central ring-like structure, possibly connecting the accretion flow and the jet. The ngEHT Analysis Challenges aim to understand the science extractability from synthetic images and movies to inform the ngEHT array design and analysis algorithm development. In this work, we compare the accretion flow structure and dynamics in numerical fluid simulations that specifically target M87* and Sgr A*, and were used to construct the source models in the challenge set. We consider (1) a steady-state axisymmetric radiatively inefficient accretion flow model with a time-dependent shearing hotspot, (2) two time-dependent single fluid general relativistic magnetohydrodynamic (GRMHD) simulations from the H-AMR code, (3) a two-temperature GRMHD simulation from the BHAC code, and (4) a two-temperature radiative GRMHD simulation from the KORAL code. We find that the different models exhibit remarkably similar temporal and spatial properties, except for the electron temperature, since radiative losses substantially cool down electrons near the BH and the jet sheath, signaling the importance of radiative cooling even for slowly accreting BHs such as M87*. We restrict ourselves to standard torus accretion flows, and leave larger explorations of alternate accretion models to future work.
The next-generation Event Horizon Telescope (ngEHT) will be a significant enhancement of the Event Horizon Telescope (EHT) array, with ∼10 new antennas and instrumental upgrades of existing antennas. The increased uv-coverage, sensitivity, and frequency coverage allow a wide range of new science opportunities to be explored. The ngEHT Analysis Challenges have been launched to inform the development of the ngEHT array design, science objectives, and analysis pathways. For each challenge, synthetic EHT and ngEHT datasets are generated from theoretical source models and released to the challenge participants, who analyze the datasets using image reconstruction and other methods. The submitted analysis results are evaluated with quantitative metrics. In this work, we report on the first two ngEHT Analysis Challenges. These have focused on static and dynamical models of M87* and Sgr A* and shown that high-quality movies of the extended jet structure of M87* and near-horizon hourly timescale variability of Sgr A* can be reconstructed by the reference ngEHT array in realistic observing conditions using current analysis algorithms. We identify areas where there is still room for improvement of these algorithms and analysis strategies. Other science cases and arrays will be explored in future challenges.
Strong correlations caused by interaction in systems of electrons can bring about unusual physical phenomena due to many-body quantum effects that cannot properly be captured by standard electronic structure methods like density functional theory. In this thesis, we apply the state-of-the-art continuous-time quantum Monte Carlo algorithm in hybridization expansion (CT-HYB) for the strongly correlated multi-orbital Anderson impurity model (AIM) to the solution of models of magnetic impurities on metallic surfaces and, via dynamical mean-field theory (DMFT), to the solution of a lattice model, the multi-orbital Hubbard model with Hund's coupling.
A concise introduction to the theoretical background focuses on information directly relevant to the understanding of applied models, methods, and the interpretation of results. It starts with a discussion of the AIM with its parameters and its solution in the path integral formalism, the basis of the CT-HYB algorithm. We consider its derivation and implementation in some detail before reviewing the DMFT approach to correlated lattice models and the interpretation of the single-particle Green's function.
We review two algorithmic developments for the CT-HYB algorithm that help to increase the performance of calculations especially in case of a complex structure of the interaction matrix and allow the precise calculation of self-energies and vertex functions also at intermediate and higher frequencies.
Our comparative analysis of Kondo screening in the cobalt on copper impurity system points out the importance of an accurate interaction matrix for qualitatively correct Kondo temperatures and the relevance of all d-orbitals in that case. Theoretical modeling of cobalt impurities in copper "atomic wires" fails to reproduce variations and partial absence of Kondo resonances depending on the wire size. We analyze the dependence of results on parameters and consider possible reasons for the discrepancy. Different Kondo temperatures of iron adatoms adsorbed on clean or oxygen-reconstructed niobium in the normal state are qualitatively reproduced, with the adsorption distance identified as major factor and implications for the superconducting state pointed out.
Moving on to lattice problems, we demonstrate the connection between Hund's coupling, shown to cause first-order character of the interaction-driven Mott transition at half-filling in the two-orbital Hubbard model, and a phase separation zone ending in a quantum critical point at finite doping. We touch on similarities in realistic models of iron-pnictide superconductors. We analyze the manifestation of the compressibility divergence at the finite-temperature critical points away from half-filling in the eigenbasis of the two-particle generalized susceptibility. A threshold for impurity susceptibility eigenvalues that indicates divergence of the DMFT lattice compressibility and distinguishes thermodynamic stability and instability of DMFT solutions is determined.
Next to the emergence of nearly isolated quantum systems such as ultracold atoms with unprecedented experimental tunability, the conceptualization of the eigenstate thermalization hypothesis (ETH) by Deutsch and Srednicki in the late 20th century has sparked exceptional interest in the mechanism of quantum thermalization. The ETH conjectures that the expectation value of a local observable within the quantum state of an isolated, interacting quantum system converges to the thermal equilibrium value at large times caused by a loss of phase coherence, referred to as dephasing. The thermal behavior within the quantum expectation value is traced back to the level of individual eigenstates, who locally act as a thermal bath to subsystems of the full quantum system and are hence locally indistinguishable to thermal states. The ETH has important implications for the understanding of the foundations of statistical mechanics, the quantum-to-classical transition, and the nature of quantum entanglement. Irrespective of its theoretical success, a rigorous proof has remained elusive so far. $$ \ $$
An alternative approach to explain thermalization of quantum states is given by the concept of typicality. Typicality deals with typical states \(\Psi\) chosen from a subspace of Hilbert space with energy \(E\) and small fluctuations \(\delta\) around it. It assumes that the possible microstates of this subspace of Hilbert space are uniformly distributed random vectors. This is inspired by the microcanonical ensemble in classical statistical mechanics, which assumes equal weights for all accessible microstates with energy \(E\) within an energy allowance \(\delta\). It follows from the ergodic hypothesis, which states that the time spent in each part of phase space is proportional to its volume leading to large time averages being equated to ensemble averages. In typicality, the Hilbert space of quantum mechanics is hence treated as an analogue of classical phase space where statistical and thermodynamic properties can be defined. Since typicality merely shifts assumptions of statistical mechanics to the quantum realm, it does not provide a complete understanding of the emergence of thermalization on a fundamental microscopic level. $$ \ $$
To gain insights on quantum thermalization and derive it from a microscopic approach, we exclusively consider the fundamental laws of quantum mechanics. In the joint work with T. Hofmann, R. Thomale and M. Greiter, on which this thesis reports, we explore the ETH in generic local Hamiltonians in a two-dimensional spin-\(1/2\) lattice with random nearest neighbor spin-spin interactions and random on-site magnetic fields. This isolated quantum system is divided into a small subsystem weakly coupled to the remaining part, which is assumed to be large and which we refer to as bath. Eigenstates of the full quantum system as well as the action of local operators on those can then be decomposed in terms of a product basis of eigenstates of the small subsystem and the bath. Central to our analysis is the fact that the coupling between the subsystem and the bath, represented in terms of the uncoupled product eigenbasis, is given by an energy dependent random band matrix, which is obtained from both analytical and numerical considerations. $$ \ $$
Utilizing the methods of Dyson-Brownian random matrix theory for random band matrices, we analytically show that the overlaps of eigenstates of the full quantum system with the uncoupled product eigenbasis are described by Cauchy-Lorentz distributions close to their respective peaks. The result is supported by an extensive numerical study using exact diagonalization, where the numerical parameters for the overlap curve agree with the theoretical calculation. The information on the decomposition of the eigenstates of the full quantum system enables us to derive the reduced density matrix within the small subsystem given the pure density matrix of a single eigenstate. We show that in the large bath limit the reduced density matrix converges to a thermal density matrix with canonical Boltzmann probabilities determined by renormalized energies of the small subsystem which are shifted from their bare values due the influence of the coupling to the bath. The behavior of the reduced density matrix is confirmed through a finite size scaling analysis of the numerical data. Within our calculation, we make use of the pivotal result, that the density of states of a local random Hamiltonian is given by a Gaussian distribution under very general circumstances. As a consequence of our analysis, the quantum expectation value of any local observable in the subsystem agrees with its thermal expectation value, which proves the validity of the ETH in the equilibrium phase for the considered class of random local Hamiltonians and elevates it from hypothesis to theory. $$ \ $$
Our analysis of quantum thermalization solely relies on the application of quantum mechanics to large systems, locality and the absence of integrability. With the self-averaging property of large random matrices, random matrix theory does not entail a statistical assumption, but is rather applied as a mathematical tool to extract information about the behavior of large quantum systems. The canonical distribution of statistical mechanics is derived without resorting to statistical assumptions such as the concepts of ergodicity or maximal entropy, nor assuming any characteristics of quantum states such as in typicality. In future research, with this microscopic approach it may become possible to exactly pinpoint the origin of failure of quantum thermalization, e.g. in systems that exhibit many body localization or many body quantum scars. The theory further enables the systematic investigation of equilibration, i.e. to study the time scales on which thermalization takes place.
In this thesis, I establish new relations between quantum information measures in a two-dimensional CFT and geometric objects in a three-dimensional AdS space employing the AdS/CFT correspondence. I focus on two quantum information measures: the computational cost of quantum circuits in a CFT and Berry phases in two entangled CFTs. In particular, I show that these quantities are associated with geometric objects in the dual AdS space.
The hunt for topological materials is one of the main topics of recent research in condensed matter physics. We analyze the 4-band Luttinger model, which considers the total angular momentum \(j = 3/2\) hole states of many semiconductors. Our analysis shows that this model hosts a wide array of topological phases and allows analytical calculations of the related topological surface states. The existence of these surface states is highly desired due to their strong protection against perturbations.
In the first part of the thesis, we predict the existence of either one or two two-dimensional (2D) surface states of topological origin in the three-dimensional (3D) quadratic-node semimetal phase of the Luttinger model, called the Luttinger semimetal phase. We associate the origin of these states with the inverted order of s and p-orbital states in the band structure and approximate chiral symmetry around the node. Hence, our findings are essential for many materials, including HgTe, α-Sn, and iridate compounds. Such materials are often modified with strain engineering by growing the crystal on a substrate with a different lattice constant, which adds a deformation potential to the electrons. While tensile strain is often used to drive such materials into a gapped topological insulator regime, we apply compressive strain to induce a topological semimetal regime. Here, we differentiate between Dirac and Weyl semimetals based on inversion and time-reversal symmetry being simultaneously present or not. One major part of this thesis is the theoretical study of the evolution of the Luttinger semimetal surface states in these topological semimetal phases.
The relative strength of the compressive strain and typical bulk inversion asymmetry (BIA) terms allow the definition of a symmetry hierarchy in the system. The cubic symmetric \(O_h\) Luttinger model is the highest symmetry low-energy parent model. Since the BIA terms in the Weyl semimetal phase are small in most materials, we find a narrow energy and momentum range around the Weyl points where the surface states form Fermi arcs between two Weyl nodes with opposite chirality. Consequently, we see 2D momentum planes between the Weyl points, which can be considered as effective 2D Chern insulators with chiral edge states connecting the valence and conduction band in the bulk gap. Exceeding the range of the BIA terms, the compressive strain becomes dominating, and the system behaves like a Dirac semimetal with two doubly degenerate linear Dirac nodes in the band structure. For energies larger than the compressive strain strength, the quadratic terms in the Luttinger model dominate and surface band structure is indistinguishable from an unperturbed Luttinger semimetal. To conclude this symmetry hierarchy, we analyze the limit of the Luttinger model when the remote \(j = 1/2\)
electron states show a considerable hybridization with the \(j = 3/2\) hole states around the Fermi level. Here, the Luttinger model is not valid anymore and one needs to consider more complicated models, like the 6-band Kane Hamiltonian.
In the second part of this thesis, we analyze theoretically two different setups for s-wave superconductivity proximitized \(j = 3/2\) particles in Luttinger materials under a magnetic field. First, we explore a one-dimensional wire setup, where the intrinsic BIA of inversion asymmetric crystals opens a topological gap in the bulk states. In contrast to wires, modeled by a quadratic dispersion with Rashba or Dresselhaus spin-orbit coupling, we find two topological phase transitions due to the different effects of magnetic fields to \(|j_z| = 3/2\) heavy-hole (HH) and \(|j_z| = 1/2\) light-hole (LH) states. Second, we discuss a two-dimensional Josephson junction setup, where we find Andreev-bound states inside the superconducting gap. Here, the intrinsic spin-orbit coupling of the Luttinger model is sufficient to open a topological gap even in the presence of inversion symmetry. This originates from the hybridization of the light and heavy-hole bands in combination with the superconducting pairing.
Consequently, both setups can form Majorana-bound states at the boundaries of the system.
The existence of these states are highly relevant in the scientific community due to their nonabelian braiding statistics and stability against decoherence, making them a prime candidate for the realization of topological quantum computation. Majorana-bound states form at zero energy and are protected by the topological gap. We predict that our findings of the topological superconductor phase of the Luttinger model are valid for both semimetal and metal phases. Hence, our study is additionally relevant for metallic systems, like p-doped GaAs. This opens a new avenue for the search for topological superconductivity.
Explaining the baryon asymmetry of the Universe has been a long-standing problem of particle physics, with the consensus being that new physics is required as the Standard Model (SM) cannot resolve this issue. Beyond the Standard Model (BSM) scenarios would need to incorporate new sources of \(CP\) violation and either introduce new departures from thermal equilibrium or modify the existing electroweak phase transition. In this thesis, we explore two approaches to baryogenesis, i.e. the generation of this asymmetry.
In the first approach, we study the two-particle irreducible (2PI) formalism as a means to investigate non-equilibrium phenomena. After arriving at the renormalised equations of motions (EOMs) to describe the dynamics of a phase transition, we discuss the techniques required to obtain the various counterterms in an on-shell scheme. To this end, we consider three truncations up to two-loop order of the 2PI effective action: the Hartree approximation, the scalar sunset approximation and the fermionic sunset approximation. We then reconsider the renormalisation procedure in an \(\overline{\text{MS}}\) scheme to evaluate the 2PI effective potential for the aforementioned truncations. In the Hartree and the scalar sunset approximations, we obtain analytic expressions for the various counterterms and subsequently calculate the effective potential by piecing together the finite contributions. For the fermionic sunset approximation, we obtain similar equations for the counterterms in terms of divergent parts of loop integrals. However, these integrals cannot be expressed in an analytic form, making it impossible to evaluate the 2PI effective potential with the fermionic contribution. Our main results are thus related to the renormalisation programme in the 2PI formalism: \( (i) \)the procedure to obtain the renormalised EOMs, now including fermions, which serve as the starting point for the transport equations for electroweak baryogenesis and \( (ii) \) the method to obtain the 2PI effective potential in a transparent manner.
In the second approach, we study baryogenesis via leptogenesis. Here, an asymmetry in the lepton sector is generated, which is then converted into the baryon asymmetry via the sphaleron process in the SM. We proceed to consider an extension of the SM along the lines of a scotogenic framework. The newly introduced particles are charged odd under a \(\mathbb{Z}_2\) symmetry, and masses for the SM neutrinos are generated radiatively. The \(\mathbb{Z}_2\) symmetry results in the lightest BSM particle being stable, allowing for a suitable dark matter (DM) candidate. Furthermore, the newly introduced heavy Majorana fermionic singlets provide the necessary sources of \(CP\) violation through their Yukawa interactions and their out-of-equilibrium decays produce a lepton asymmetry. This model is constrained from a wide range of observables, such as consistency with neutrino oscillation data, limits on branching ratios of charged lepton flavour violating decays, electroweak observables and obtaining the observed DM relic density. We study leptogenesis in this model in light of the results of a Markov chain Monte Carlo scan, implemented in consideration of the aforementioned constraints. Successful leptogenesis in this model, to account for the baryon asymmetry, then severely constrains the available parameter space.
Relativistic effects crucially influence the fundamental properties of many quantum materials. In the accelerated reference frame of an electron, the electric field of the nuclei is transformed into a magnetic field that couples to the electron spin. The resulting interaction between an electron spin and its orbital angular momentum, known as spin-orbit coupling (SOC), is hence fundamental to the physics of many condensed matter phenomena. It is particularly important quantitatively in low-dimensional quantum systems, where its coexistence with inversion symmetry breaking can lead to a splitting of spin degeneracy and spin momentum locking. Using the paradigm of Landau Fermi liquid theory, the physics of SOC can be adequately incorporated in an effective single particle picture. In a weak coupling approach, electronic correlation effects beyond single particle propagator renormalization can trigger Fermi surface instabilities such as itinerant magnetism, electron nematic phases, superconductivity, or other symmetry broken states of matter.
In this thesis, we use a weak coupling-based approach to study the effect of SOC on Fermi surface instabilities and, in particular, superconductivity. This encompasses a weak coupling renormalization group formulation of unconventional superconductivity as well as the random phase approximation. We propose a unified formulation for both of these two-particle Green’s function approaches based on the notion of a generalized susceptibility.
In the half-Heusler semimetal and superconductor LuPtBi, both SOC and electronic correlation
effects are prominent, and thus indispensable for any concise theoretical description. The metallic and weakly dispersive surface states of this material feature spin momentum locked Fermi surfaces, which we propose as a possible domain for the onset of unconventional surface superconductivity. Using our framework for the analysis of Fermi surface instability and combining it with ab-initio density functional theory calculations, we analyse the surface band structure of LuPtBi, and particularly its propensity towards Cooper pair formation. We study how the presence of strong SOC modifies the classification of two-electron wave functions as well as the screening of electron-electron interactions. Assuming an electronic mechanism, we identify a chiral superconducting condensate featuring Majorana edge modes to be energetically favoured over a wide range of model parameters.
The last years have witnessed an exciting scientific quest for intriguing topological phenomena in time-dependent quantum systems. A key to many manifestations of topology in dynamical systems relies on the effective dimensional extension by time-periodic drives. An archetypal example is provided by the Thouless pump in one spatial dimension, where a robust and quantized charge transport can be described in terms of an integer quantum Hall effect upon interpreting time as an extra dimension. Generalizing this fundamental concept to multifrequency driving, a variety of higher-dimensional topological models can be engineered in dynamical synthetic dimensions, where the underlying topological classification leads to quantized pumping effects in the associated lower-dimensional time-dependent systems.
In this Thesis, we explore how correlations profoundly impact the topological features of dynamical synthetic quantum materials. More precisely, we demonstrate that the interplay of interaction and dynamical synthetic dimension gives rise to striking topological phenomena that go beyond noninteracting implementations. As a starting point, we exploit the Floquet counterpart of an integer quantum Hall scenario, namely a two-level system driven by two incommensurate frequencies. In this model, the topologically quantized response translates into a process in which photons of different frequencies are exchanged between the external modes, referred to as topological frequency conversion. We extend this prototypical setup to an interacting version, focusing on the minimal case of two correlated spins equally exposed to the external drives. We show that the topological invariant determining the frequency conversion can be changed by odd integers, something explicitly forbidden in the noninteracting limit of two identical spins. This correlated topological feature may, in turn, result in an enhancement of the quantized response.
Robust response signals, such as those predicted for the topological frequency converter, are of fundamental interest for potential technological applications of topological quantum matter. Based on an open quantum system implementation of the frequency converter, we propose a novel mechanism of topological quantization coined ''topological burning glass effect''. Remarkably, this mechanism amplifies the local response of the driven two-level system by an integer that is proportional to the number of environmental degrees of freedom to which the system is strongly coupled. Specifically, our findings are illustrated by the extension of the frequency converter to a central spin model. There, the local energy transfer mediated exclusively by the central spin is significantly enhanced by the collective motion of the surrounding spins. In this sense, the central spin adopts the topological nature of the total system in its non-unitary dynamics, taking into account the correlations with the environment.
We consider a scenario inspired by natural supersymmetry, where neutrino data is explained within a low-scale seesaw scenario. We extend the Minimal Supersymmetric Standard Model by adding light right-handed neutrinos and their superpartners, the R-sneutrinos, and consider the lightest neutralinos to be higgsino-like. We consider the possibilities of having either an R-sneutrino or a higgsino as lightest supersymmetric particle. Assuming that squarks and gauginos are heavy, we systematically evaluate the bounds on slepton masses due to existing LHC data.
We calculate the next-to-leading order electroweak corrections to the production of a photon pair in association with zero, one and two jets at the LHC. We use GoSam and Sherpa to obtain the results in a fully automated way. For a typical set of fiducial cuts the electroweak corrections lead to a modification of the total cross section of up to 3%, depending on the jet multiplicity. We find substantial contributions in differential distributions, leading to tens of per cent corrections for phase space regions within the reach of the LHC. Furthermore we investigate the importance of photon induced processes as well as subleading contributions. Photon induced processes are found to be negligible, subleading contributions can have a sizeable impact however they can be removed by appropriate phase space cuts.
Chromium dioxide CrO\(_2\) belongs to a class of materials called ferromagnetic half-metals, whose peculiar aspect is that they act as a metal in one spin orientation and as a semiconductor or insulator in the opposite one. Despite numerous experimental and theoretical studies motivated by technologically important applications of this material in spintronics, its fundamental properties such as momentumresolved electron dispersions and the Fermi surface have so far remained experimentally inaccessible because of metastability of its surface, which instantly reduces to amorphous Cr\(_2\)O\(_3\). In this work, we demonstrate that direct access to the native electronic structure of CrO\(_2\) can be achieved with soft-x-ray angle-resolved photoemission spectroscopy whose large probing depth penetrates through the Cr\(_2\)O\(_3\) layer. For the first time, the electronic dispersions and Fermi surface of CrO\(_2\) are measured, which are fundamental prerequisites to solve the long debate on the nature of electronic correlations in this material. Since density functional theory augmented by a relatively weak local Coulomb repulsion gives an exhaustive description of our spectroscopic data, we rule out strong-coupling theories of CrO\(_2\). Crucial for the correct interpretation of our experimental data in terms of the valence-band dispersions is the understanding of a nontrivial spectral response of CrO\(_2\) caused by interference effects in the photoemission process originating from the nonsymmorphic space group of the rutile crystal structure of CrO\(_2\).
Magnetism is a phenomenon ubiquitously found in everyday life. Yet, together with superconductivity and superfluidity, it is among the few macroscopically realized quantum states. Although well-understood on a quasi-classical level, its microscopic description is still far from being solved. The interplay of strong interactions present in magnetic condensed-matter systems and the non-trivial commutator structure governing the underlying spin algebra prevents most conventional approaches in solid-state theory to be applied.
On the other hand, the quantum limit of magnetic systems is fertile land for the development of exotic phases of matter called spin-liquids. In these states, quantum fluctuations inhibit the formation of magnetic long-range order down to the lowest temperatures. From a theoretical point of view, spin-liquids open up the possibility to study their exotic properties, such as fractionalized excitations and emergent gauge fields. However, despite huge theoretical and experimental efforts, no material realizing spin-liquid properties has been unambiguously identified with a three-dimensional crystal structure. The search for such a realization is hindered by the inherent difficulty even for model calculations. As most numerical techniques are not applicable due to the interaction structure and dimensionality of these systems, a methodological gap has to be filled.
In this thesis, to fill this void, we employ the pseudo-fermion functional renormalization group (PFFRG), which provides a scheme to investigate ground state properties of quantum magnetic systems even in three spatial dimensions.
We report the status quo of this established method and extend it by alleviating some of its inherent approximations. To this end, we develop a multi-loop formulation of PFFRG, including hitherto neglected terms in the underlying flow equations consistently, rendering the outcome equivalent to a parquet approximation. As a necessary prerequisite, we also significantly improve the numerical accuracy of our implementation of the method by switching to a formulation respecting the asymptotic behavior of the vertex functions as well as employing state-of-the-art numerical algorithms tailored towards PFFRG. The resulting codebase was made publicly accessible in the open-source code PFFRGSolver.jl.
We subsequently apply the technique to both model systems and real materials. Augmented by a classical analysis of the respective models, we scan the phase diagram of the three-dimensional body-centered cubic lattice up to third-nearest neighbor coupling and the Pyrochlore lattice up to second-nearest neighbor. In both systems, we uncover in addition to the classically ordered phases, an extended parameter regime, where a quantum paramagnetic phase appears, giving rise to the possibility of a quantum spin liquid.
Additionally, we also use the nearest-neighbor antiferromagnet on the Pyrochlore lattice as well as the simple cubic lattice with first- and third-nearest neighbor couplings as a testbed for multi-loop PFFRG, demonstrating, that the inclusion of higher loop orders has quantitative effects in paramagnetic regimes and that the onset of order can be signaled by a lack of loop convergence.
Turning towards material realizations, we investigate the diamond lattice compound MnSc\(_2\)S\(_4\), explaining on grounds of ab initio couplings the emergence of a spiral spin liquid at low temperatures, but above the ordering transition.
In the Pyrochlore compound Lu\(_2\)Mo\(_2\)O\(_5\)N\(_2\), which is known to not magnetically order down to lowest temperatures, we predict a spin liquid state displaying a characteristic gearwheel pattern in the spin structure factor.
Atomically thin semiconductors from the transition metal dichalcogenide family are materials in which the optical response is dominated by strongly bound excitonic complexes. Here, we present a theory of excitons in two-dimensional semiconductors using a tight-binding model of the electronic structure. In the first part, we review extensive literature on 2D van der Waals materials, with particular focus on their optical response from both experimental and theoretical points of view. In the second part, we discuss our ab initio calculations of the electronic structure of MoS\(_2\), representative of a wide class of materials, and review our minimal tight-binding model, which reproduces low-energy physics around the Fermi level and, at the same time, allows for the understanding of their electronic structure. Next, we describe how electron-hole pair excitations from the mean-field-level ground state are constructed. The electron–electron interactions mix the electron-hole pair excitations, resulting in excitonic wave functions and energies obtained by solving the Bethe–Salpeter equation. This is enabled by the efficient computation of the Coulomb matrix elements optimized for two-dimensional crystals. Next, we discuss non-local screening in various geometries usually used in experiments. We conclude with a discussion of the fine structure and excited excitonic spectra. In particular, we discuss the effect of band nesting on the exciton fine structure; Coulomb interactions; and the topology of the wave functions, screening and dielectric environment. Finally, we follow by adding another layer and discuss excitons in heterostructures built from two-dimensional semiconductors.
Effective lifting of the topological protection of quantum spin Hall edge states by edge coupling
(2022)
The scientific interest in two-dimensional topological insulators (2D TIs) is currently shifting from a more fundamental perspective to the exploration and design of novel functionalities. Key concepts for the use of 2D TIs in spintronics are based on the topological protection and spin-momentum locking of their helical edge states. In this study we present experimental evidence that topological protection can be (partially) lifted by pairwise coupling of 2D TI edges in close proximity. Using direct wave function mapping via scanning tunneling microscopy/spectroscopy (STM/STS) we compare isolated and coupled topological edges in the 2D TI bismuthene. The latter situation is realized by natural lattice line defects and reveals distinct quasi-particle interference (QPI) patterns, identified as electronic Fabry-Pérot resonator modes. In contrast, free edges show no sign of any single-particle backscattering. These results pave the way for novel device concepts based on active control of topological protection through inter-edge hybridization for, e.g., electronic Fabry-Pérot interferometry.
We study the topological properties of the generalized two-dimensional (2D) Su-Schrieffer-Heeger (SSH) models. We show that a pair of Dirac points appear in the Brillouin zone (BZ), consisting a semimetallic phase. Interestingly, the locations of these Dirac points are not pinned to any high-symmetry points of the BZ but tunable by model parameters. Moreover, the merging of two Dirac points undergoes a novel topological phase transition, which leads to either a weak topological insulator or a nodal-line metallic phase. We demonstrate these properties by constructing two specific models, which we referred as type-I and type-II 2D SSH models. The feasible experimental platforms to realize our models are also discussed.
Context. In active galaxies, matter is accreted onto super massive black holes (SMBH). This accretion process causes a region roughly the size of our solar system to outshine the entire host galaxy, forming an active galactic nucleus (AGN). In some of these active galaxies, highly relativistic particle jets are formed parallel to the rotation axis of the super massive black hole. A fraction of these sources is observed under a small inclination angle between the pointing direction of the jet and the observing line of sight. These sources are called blazars. Due to the small inclination angle and the highly relativistic speeds of the particles in the jet, beaming effects occur in the radiation of these particles. Blazars can be subdivided into the high luminosity flat spectrum radio quasars (FSRQs) and the low luminosity BL Lacertae objects (BL Lacs). As all AGN, blazars are broadband emitters and therefore observable from the longest wavelengths in the radio regime to the shortest wavelengths in the gamma-ray regime. In this thesis I will analyze blazars at these two extremes with respect to their parsec-scale properties in the radio and their time evolution properties in gamma-ray flux.
Method. In the radio regime the technique of very long baseline interferometry (VLBI) can be used in order to spatially resolve the synchrotron radiation coming from those objects down to sub-parsec scales. This information can be used to observe the time evolution of the structure of such sources. This is done in large monitoring programs such as the MOJAVE (15 GHz) and the Boston University blazar monitoring program (43 GHz). In this thesis I utilize data of 28 sources from these monitoring programs spanning 10 years of observation from 2003 to 2013, resulting in over 1800 observed epochs, to study the brightness temperature and diameter gradients of these jets. I conduct a search for systematic geometry transitions in the radio jets. The synchrotron cooling time in the radio core of the jets is used to determine the magnetic field strength in the radio core. Considering the jet geometry, these magnetic field strengths are scaled to the ergosphere of the SMBH in order to obtain the distance of the radio core to the SMBH.
In the gamma-regime these blazars cannot be spatially resolved. Due to this, it is hard to put strong constrains onto where the gamma-ray emitting region is. Blazars have shown to be variable at high energies on time scales down to minutes. The nature of this variability can be studied in order to put constrains on the particle acceleration mechanism and possibly the region and size of the gamma-ray emitting region. The variability of blazars in the energy range between 0.1 GeV and 1 GeV can for example be observed with the pair-conversion telescope on board the Fermi satellite. I use 10 years of data from the Fermi-LAT (LAT: Large Area Telescope) satellite in order to study the variability of a large sample of blazars (300-800, depending on the used significance filters for data points). I quantify this variability with the Ornstein-Uhlenbeck (OU) parameters and the power spectral density (PSD) slopes. The same procedure is applied to 20 light curves available for the radio sample.
Results. The diameter evolution along the jet axis of the radio sources suggests, that FSRQs feature flatter gradients than BL Lacs. Fitting these gradients, it is revealed that BL Lacs are systematically better described by a simple single power law than FSRQs. I found 9 sources with a strongly constrained geometry transition. The sources are 0219+421, 0336-019, 0415+379, 0528+134, 0836+710, 1101+384, 1156+295, 1253-055 and 2200+420. In all of these sources, the geometry transition regions are further out in the jet than the Bondi sphere. The magnetic field strengths of BL Lacs is systematically larger than that of FSRQs. However the scaling of these fields suggest that the radio cores of BL Lac objects are closer to the SMBHs than the radio cores of FSRQs. Analyzing the variability of Fermi-LAT light curves yields consistent results for all samples. FSRQs show systematically steeper PSD slopes and feature OU parameters more favorable to strong variability than BL Lacs. The Fermi-LAT light curves of the sub-sample of radio jets, suggest an anticorrelation between the jet complexity from the radio observations and the OU-parameters as well as the PSD slopes from the gamma-ray observations.
Conclusion.
The flatter diameter gradients of FSRQs suggest that these sources are more collimated further down the jet than BL Lacs. The systematically better description of the diameter and brightness temperature gradient by a single power law of BL Lacs, suggest that FSRQs are more complex with respect to the diameter evolution along the jet and the surface brightness distribution than BL Lac objects. FSRQs often feature regions where recollimation can occur in distinct knots within the jets. For the sources where a geometry transition could be constrained, the Bondi radius, being systematically smaller than the position of the transition region along the jet axis, suggest that changing pressure gradients are not the sole cause for these systematic geometry transitions. Nevertheless they may be responsible for recollimation regions, found typically downstream the jet, beyond the Bondi radius and the transition zone. The difference in the distance of the radio cores between FSRQs and BL Lacs is most likely due to the combination of differences in SMBH masses and systematically smaller jet powers in BL Lacs. The variability in energy ranges above 100 MeV and above 1 GeV-regime suggest that many light curves of BL Lac objects are more likely to be white noise while the PSD slopes and the OU parameters of FSRQ gamma-ray light curves favor stronger variability on larger time scales with respect to the time binning of the analyzed light curve. Although the anticorrelation of the jet complexity acquired from the radio observations and the PSD slopes and OU parameters from the gamma-observations suggest that more complex sources favor OU parameters and PSD slopes resulting in more variability (not white noise) it is beyond the scope of this thesis to pinpoint whether this correlation results from causation. The question whether a complex jet causes more gamma-ray variability or more gamma-ray variability causes more complex jets cannot be answered at this point. Nevertheless the computed correlation measures suggest that this dependence is most likely not linear and therefore an indication that these effects might even interact.
The observation of electromagnetic counterparts to both high energy neutrinos and gravitational waves marked the beginning of a new era in astrophysics. The multi-messenger approach allows us to gain new insights into the most energetic events in the Universe such as gamma-ray bursts, supernovas, and black hole mergers. Real-time multi-messenger alerts are the key component of the observational strategies to unravel the transient signals expected from astrophysical sources. Focusing on the high-energy regime, we present a historical perspective of multi-messenger observations, the detectors and observational techniques used to study them, the status of the multi-messenger alerts and the most significant results, together with an overview of the future prospects in the field.
The tremendous phenomenological success of the Standard Model (SM) suggests that its flavor structure and gauge interactions may not be arbitrary but should have a fundamental first-principle explanation. In this work, we explore how the basic distinctive properties of the SM dynamically emerge from a unified New Physics framework tying together both flavor physics and Grand Unified Theory (GUT) concepts. This framework is suggested by a novel anomaly-free supersymmetric chiral E\(_6\)×SU(2)\(_F\)×U(1)\(_F\) GUT containing the SM. Among the most appealing emergent properties of this theory is the Higgs-matter unification with a highly-constrained massless chiral sector featuring two universal Yukawa couplings close to the GUT scale. At the electroweak scale, the minimal SM-like effective field theory limit of this GUT represents a specific flavored three-Higgs doublet model consistent with the observed large hierarchies in the quark mass spectra and mixing already at tree level.
The extragalactic gamma-ray sky is dominated by blazars, active galactic nuclei (AGN) with a relativistic jet that is closely aligned with the line of sight. Galaxies develop an active nucleus if the central supermassive black hole (BH) accretes large amounts of ambient matter and magnetic flux. The inflowing mass accumulates around the plane perpendicular to the accretion flow's angular momentum. The flow is heated through viscous friction and part of the released energy is radiated as blackbody or non-thermal radiation, with luminosities that can dominate the accumulated stellar luminosity of the host galaxy. A fraction of the accretion flow luminosity is reprocessed in a surrounding field of ionised gas clouds. These clouds, revolving around the central BH, emit Doppler-broadened atomic emission lines. The region where these broad-line-emitting clouds are located is called broad-line region (BLR).
About one in ten AGN forms an outflow of radiation and relativistic particles, called a relativistic jet. According to the Blandford-Znajek mechanism, this is facilitated through electromagnetic processes in the magnetosphere of a spinning BH. The latter induces a magnetospheric poloidal current circuit, generating a decelerating torque on the BH and inducing a toroidal magnetic field. Consequently, rotational energy of the BH is converted to Poynting flux streaming away mainly along the rotational axis and starting the jet. One possibility for particle acceleration near the jet base is realised by magnetospheric vacuum gaps, regions temporarily devoid of plasma, such that an intermittent electric field arises parallel to the magnetic field lines, enabling particle acceleration and contributing to the mass loading of the jets.
Magnetised structures, containing bunches of relativistic electrons, propagate away from the galactic nucleus along the jets. Assuming that these electrons emit synchrotron radiation and that they inverse-Compton (IC) up-scatter abundant target photons, which can either be the synchrotron photons themselves or photons from external emitters, the emitted spectrum can be theoretically determined. Additionally taking into account that these emission regions move relativistically themselves and that the emission is Doppler-boosted and beamed in forward direction, the typical two-hump spectral energy distribution (SED) of blazars is recovered.
There are however findings that challenge this well-established model. Short-time variability, reaching down to minute scales at very high energy gamma rays, is today known to be a widespread phenomenon of blazars, calling for very compact emission regions. In most models of such optically thick emission regions, the gamma-ray flux is usually pair-absorbed exponentially, without considering the cascade evolving from the pair-produced electrons. From the observed flux, it is often concluded that emission emanates from larger distances where the region is optically thin, especially from outside of the BLR. Only in few blazars gamma-ray attenuation associated with pair absorption in the BLR was clearly reported.
With the advent of sophisticated high-energy or very high energy gamma-ray detectors, like the Fermi Large Area Telescope or the Major Atmospheric Gamma-ray Imaging Cherenkov telescopes, besides the extraordinarily fast variability spectral features have been found that cannot be explained by conventional models reproducing the two-hump SED. Two such narrow spectral features are discussed in this work. For the nearby blazar Markarian 501, hints to a sharp peak around 3 TeV have been reported from a multi-wavelength campaign carried out in July 2014, while for 3C 279 a spectral dip was found in 2018 data, that can hardly be described with conventional fitting functions. In this work it is examined whether these spectral peculiarities of blazar jet emission can be explained, if the full radiation reprocessing through an IC pair cascade is accounted for.
Such a cascade is the multiple concatenation of IC scattering events and pair production events. In the cascades generally considered in this work, relativistic electrons and high-energy photons are injected into a fixed soft target photon field. A mathematical description for linear IC pair cascades with escape terms is delivered on the basis of preliminary works. The steady-state kinetic equations for the electrons and for the photons are determined, whereby it is paid attention to an explicit formulation and to motivating the correct integration borders of all integrals from kinematic constraints. In determining the potentially observable gamma-ray flux, both the attenuated injected flux and the flux evolving as an effect of IC up-scattering, pair absorption and escape are incorporated, giving the emerging spectra very distinct imprints.
Much effort is dedicated to the numerical solution of the electrons' kinetic equation via iterative schemes. It is explained why pointwise iteration from higher to lower Lorentz factors is more efficient than iterating the whole set of sampling points. The algorithm is parallelised at two positions. First, several workers can perform pointwise iterations simultaneously. Second, the most demanding integral is cut into a number of part integrals which can be determined by multiple workers. Through these measures, the Python code can be readily applied to simulate steady-state IC pair cascades with escape.
In the case of Markarian 501 the developed framework is as follows. The AGN hosts an advection-dominated accretion flow with a normalised accretion rate of several \(10^{-4}\) and an electron temperature near \(10^{10}\) K. On the one hand, the accretion flow illuminates the few ambient gas clouds with approximate radius \(10^{11}\) m, which reprocess a fraction 0.01 of the luminosity into hydrogen and helium emission lines. On the other hand, the gamma rays from the accretion flow create electrons and positrons in a sporadically active vacuum gap in the BH magnetosphere. In the active gap, a power of roughly 0.001 of the Blandford-Znajek power is extracted from the rotating BH through a gap potential drop of several \(10^{18}\) V, generating ultra-relativistic electrons, which subsequently are multiplied by a factor of about \(10^6\) through interaction with the accretion flow photons. This electron beam propagates away from the central engine and encounters the photon field of one passing ionised cloud. The resulting IC pair cascade is simulated and the evolving gamma-ray spectrum is determined. Just above the absorption troughs due to the hydrogen lines, the spectrum exhibits a narrow bump around 3 TeV. When the cascaded emission is added to the emission generated at larger distances, the observed multi-wavelength SED including the sharp peak at 3 TeV is reproduced, underlining that radiation processes beyond conventional models are motivated by distinct spectral features.
The dip in the spectrum of 3C 279 is addressed by a similar cascade model. Three types of injection are considered, varying in the ratio of the photon density to the electron density and varying in the spectral shape. The IC pair cascade is assumed to happen either in the dense BLR photon field with a luminosity of several \(10^{37}\) W and a radial size of few \(10^{14}\) m or in the diluted photon field outside of the BLR. The latter scenario is however rejected as the spectral slope around several 100 MeV and the dip at few 10 GeV cannot be reconciled within this model. The radiation cascaded in the BLR can explain the observational data, irrespective of the assumed injected rate. It is therefore concluded that for this period of gamma-ray emission, the radiation production happens at the edge of the BLR of 3C 279.
Both investigations show that IC pair cascades can account for fine structure seen in blazar SEDs. It is insufficient to restrict the radiation transport to pure exponential absorption of an injection term. Pair production and IC up-scattering by all generations of photons and electrons in the optically thick regime critically shape the emerging spectra. As the advent of future improved detectors will provide more high-precision spectra, further observations of narrow spectral features can be expected. It seems therefore recommendable to incorporate cascading into conventional radiation production models or to extend the model developed in this work by synchrotron radiation.
The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is only mentioned as a particular case of the confluent hypergeometric function. In order to revive our knowledge on these functions, their basic properties (recurrence functional and differential relations, series, integrals and the Laplace transforms) are presented. Some new results are also included. Special attention is directed to the Bateman and Havelock functions with integer orders, to generalizations of these functions and to the Bateman-integral function known in the literature.
We investigated emission properties of photonic structures with InAs/InGaAlAs/InP quantum dashes grown by molecular beam epitaxy on a distributed Bragg reflector. In high-spatial-resolution photoluminescence experiment, well-resolved sharp spectral lines are observed and single-photon emission is detected in the third telecommunication window characterized by very low multiphoton events probabilities. The photoluminescence spectra measured on simple photonic structures in the form of cylindrical mesas reveal significant intensity enhancement by a factor of 4 when compared to a planar sample. These results are supported by simulations of the electromagnetic field distribution, which show emission extraction efficiencies even above 18% for optimized designs. When combined with relatively simple and undemanding fabrication approach, it makes this kind of structures competitive with the existing solutions in that spectral range and prospective in the context of efficient and practical single-photon sources for fiber-based quantum networks applications.
Hard X-ray Properties of Relativistically Beamed Jets from Radio- and Gamma-Ray-Bright Blazars
(2022)
In this work I characterize the hard X-ray properties of blazars, active galactic nuclei with highly beamed emission, which are notoriously hard to detect in this energy range. I employ pre-defined samples of beamed AGN: the radio-selected MOJAVE and TANAMI samples, as well as the most recent gamma-ray-selected Fermi/LAT 4LAC catalog. The hard X-ray data is extracted from the 105-month all-sky survey maps of the Swift/BAT (Burst Alert Telescope) in the energy band of 20 keV to 100 keV. A great majority of both the MOJAVE and TANAMI samples are significantly detected, with signal-to noise ratios of the sources often just below the X-ray catalog signal thresholds. All blazar sub-types (FSRQs, BL Lacs) and radio galaxies show characteristic ranges of X-ray flux, luminosity, and photon index. Their properties are correlated with the corresponding SED's shape / peak frequency. The LogN-LogS distributions of the samples show a scarcity of blazars in the middle and lower X-ray flux range, indicating differing evolutionary paths between radio and X-ray emission, which is also suggested by the corresponding luminosity functions. Compared to the radio samples, the 4LAC sources are on average significantly less bright in the BAT band since this range often coincides with the spectral gap region between the two big SED emission bumps. Also, the spectral shapes differ notably, especially for the sub-type of BL Lacs. Using the parameter space of X-ray and gamma-ray photon indices, 35 blazar candidate sources can be assigned to either the FSRQ or BL Lac type with high certainty. The reason why many blazars are weak in this energy band can be traced back to a number of factors: the selection bias of the initial sample, differential evolution of the X-rays and the wavelengths in which the sample is defined, and the limited sensitivity of the observing instruments.
This thesis studies connections between quantum information measures and geometric features of spacetimes within the AdS/CFT correspondence. These studies are motivated by the idea that spacetime can be thought of as an effect emerging from an underlying entanglement structure in the AdS/CFT correspondence. In particular, I study generalized entanglement measures in two-dimensional conformal field theories and their holographic duals. Unlike the ordinary entanglement entropy of a spatial subregion typically used in the AdS/CFT context, the generalization considered here measures correlations between different fields as well as between spatial degrees of freedom. I present a new gauge invariant definition of the generalized entanglement entropy applicable to both mixed and pure states as well as explicit results for thermal states of the S_N-orbifold theory of the D1/D5 system. Along the way, I develop computation techniques for conformal blocks on the torus and apply them to the calculation of the ordinary entanglement entropy for large central charge CFTs at finite size and finite temperature. The generalized Ryu-Takayanagi formula arising from these studies provides further support for the idea that entanglement and geometry are intrinsically linked in AdS/CFT. The results show that the holographic dual to the generalized entanglement entropy given by the length of a geodesic winding around black hole horizons or naked singularities probes subregions of spacetime that are inaccessible to Ryu-Takayanagi surfaces, thereby solving the puzzle of how these features of the spacetime are encoded in the boundary theory. Furthermore, I investigate quantum circuits embedded in two-dimensional conformal field theories as well as computational complexity measures therein. These investigations are motivated by conjectures relating computational complexity in conformal field theories to geometric features of black hole geometries. In this thesis, I study quantum circuits built up from conformal transformations. I investigate examples of computational complexity measures in these circuits related to geometric actions on coadjoint orbits of the Virasoro group and to the Fubini-Study metric. I then work out relations between these computational complexity measures and the dual gravitational theory. Moreover, I construct a bulk dual to the circuits in consideration and use this construction to study geometric realizations of computational complexity measures from first principles. The results of this part on the one hand rule out some possibilities for dual realizations of computational complexity in two-dimensional CFTs put forward in previous work while on the other hand providing a new robust dual realization of a computational complexity measure based on the Fubini-Study distance.
The neoclassical mainstream theory of economic growth does not care about the First and the Second Law of Thermodynamics. It usually considers only capital and labor as the factors that produce the wealth of modern industrial economies. If energy is taken into account as a factor of production, its economic weight, that is its output elasticity, is assigned a meager magnitude of roughly 5 percent, according to the neoclassical cost-share theorem. Because of that, neoclassical economics has the problems of the “Solow Residual”, which is the big difference between observed and computed economic growth, and of the failure to explain the economic recessions since World War 2 by the variations of the production factors. Having recalled these problems, we point out that technological constraints on factor combinations have been overlooked in the derivation of the cost-share theorem. Biophysical analyses of economic growth that disregard this theorem and mend the neoclassical deficiencies are sketched. They show that energy’s output elasticity is much larger than its cost share and elucidate the existence of bidirectional causality between energy conversion and economic growth. This helps to understand how economic crises have been triggered and overcome by supply-side and demand-side actions. Human creativity changes the state of economic systems. We discuss the challenges to it by the risks from politics and markets in conjunction with energy sources and technologies, and by the constraints that the emissions of particles and heat from entropy production impose on industrial growth in the biosphere.
Emergent phenomena in condensed matter physics like, e.g., magnetism, superconductivity, or non-trivial topology often come along with a surprise and exert great fascination to researchers up to this day. Within this thesis, we are concerned with the analysis of associated types of order that arise due to strong electronic interactions and focus on the high-\(T_c\) cuprates and Kondo systems as two prime candidates. The underlying many-body problem cannot be solved analytically and has given rise to the development of various approximation techniques to tackle the problem.
In concrete terms, we apply the auxiliary particle approach to investigate tight-binding Hamiltonians subject to a Hubbard interaction term to account for the screened Coulomb repulsion. Thereby, we adopt the so-called Kotliar-Ruckenstein slave-boson representation that reduces the problem to non-interacting quasiparticles within a mean-field approximation. Part I provides a pedagogical review of the theory and generalizes the established formalism to encompass Gaussian fluctuations around magnetic ground states as a crucial step to obtaining novel results.
Part II addresses the two-dimensional one-band Hubbard model, which is known to approximately describe the physics of the high-\(T_c\) cuprates that feature high-temperature superconductivity and various other exotic quantum phases that are not yet fully understood. First, we provide a comprehensive slave-boson analysis of the model, including the discussion of incommensurate magnetic phases, collective modes, and a comparison to other theoretical methods that shows that our results can be massively improved through the newly implemented fluctuation corrections. Afterward, we focus on the underdoped regime and find an intertwining of spin and charge order signaled by divergences of the static charge susceptibility within the antiferromagnetic domain. There is experimental evidence for such inhomogeneous phases in various cuprate materials, which has recently aroused interest because such correlations are believed to impact the formation of Cooper pairs. Our analysis identifies two distinct charge-ordering vectors, one of which can be attributed to a Fermi-surface nesting effect and quantitatively fits experimental data in \(\mathrm{Nd}_{2-\mathrm{x}}\mathrm{Ce}_\mathrm{x}\mathrm{CuO}_4\) (NCCO), an electron-doped cuprate compound. The other resembles the so-called Yamada relation implying the formation of periodic, double-occupied domain walls with a crossover to phase separation for small dopings.
Part III investigates Kondo systems by analyzing the periodic Anderson model and its generalizations. First, we consider Kondo metals and detect weakly magnetized ferromagnetic order in qualitative agreement with experimental observations, which hinders the formation of heavy fermions. Nevertheless, we suggest two different parameter regimes that could host a possible Kondo regime in the context of one or two conduction bands. The part is concluded with the study of topological order in Kondo insulators based on a three-dimensional model with centrosymmetric spin-orbit coupling. Thereby, we classify topologically distinct phases through appropriate \(\mathbb{Z}_2\) invariants and consider paramagnetic and antiferromagnetic mean-field ground states. Our model parameters are chosen to specifically describe samarium hexaboride (\(\mbox{SmB}_6\)), which is widely believed to be a topological Kondo insulator, and we identify topologically protected surface states in agreement with experimental evidence in that material. Moreover, our theory predicts the emergence of an antiferromagnetic topological insulator featuring one-dimensional hinge-states as the signature of higher-order topology in the strong coupling regime. While the nature of the true ground state is still under debate, corresponding long-range magnetic order has been observed in pressurized or alloyed \(\mbox{SmB}_6\), and recent experimental findings point towards non-trivial topology under these circumstances. The ability to understand and control topological systems brings forth promising applications in the context of spintronics and quantum computing.
For the understanding of the variable, transient and non-thermal universe, unbiased long-term monitoring is crucial. To constrain the emission mechanisms at the highest energies, it is important to characterize the very high energy emission and its correlation with observations at other wavelengths. At very high energies, only a limited number of instruments is available. This article reviews the current status of monitoring of the extra-galactic sky at TeV energies.
The helical distribution of the electronic density in chiral molecules, such as DNA and bacteriorhodopsin, has been suggested to induce a spin–orbit coupling interaction that may lead to the so-called chirality-induced spin selectivity (CISS) effect. Key ingredients for the theoretical modelling are, in this context, the helically shaped potential of the molecule and, concomitantly, a Rashba-like spin–orbit coupling due to the appearance of a magnetic field in the electron reference frame. Symmetries of these models clearly play a crucial role in explaining the observed effect, but a thorough analysis has been largely ignored in the literature. In this work, we present a study of these symmetries and how they can be exploited to enhance chiral-induced spin selectivity in helical molecular systems.
Single-molecule super-resolution microscopy (SMLM) techniques like dSTORM can reveal biological structures down to the nanometer scale. The achievable resolution is not only defined by the localization precision of individual fluorescent molecules, but also by their density, which becomes a limiting factor e.g., in expansion microscopy. Artificial deep neural networks can learn to reconstruct dense super-resolved structures such as microtubules from a sparse, noisy set of data points. This approach requires a robust method to assess the quality of a predicted density image and to quantitatively compare it to a ground truth image. Such a quality measure needs to be differentiable to be applied as loss function in deep learning. We developed a new trainable quality measure based on Fourier Ring Correlation (FRC) and used it to train deep neural networks to map a small number of sampling points to an underlying density. Smooth ground truth images of microtubules were generated from localization coordinates using an anisotropic Gaussian kernel density estimator. We show that the FRC criterion ideally complements the existing state-of-the-art multiscale structural similarity index, since both are interpretable and there is no trade-off between them during optimization. The TensorFlow implementation of our FRC metric can easily be integrated into existing deep learning workflows.
The electric and nonvolatile control of the spin texture in semiconductors would represent a fundamental step toward novel electronic devices combining memory and computing functionalities. Recently, GeTe has been theoretically proposed as the father compound of a new class of materials, namely ferroelectric Rashba semiconductors. They display bulk bands with giant Rashba-like splitting due to the inversion symmetry breaking arising from the ferroelectric polarization, thus allowing for the ferroelectric control of the spin. Here, we provide the experimental demonstration of the correlation between ferroelectricity and spin texture. A surface-engineering strategy is used to set two opposite predefined uniform ferroelectric polarizations, inward and outward, as monitored by piezoresponse force microscopy. Spin and angular resolved photoemission experiments show that these GeTe(111) surfaces display opposite sense of circulation of spin in bulk Rashba bands. Furthermore, we demonstrate the crafting of nonvolatile ferroelectric patterns in GeTe films at the nanoscale by using the conductive tip of an atomic force microscope. Based on the intimate link between ferroelectric polarization and spin in GeTe, ferroelectric patterning paves the way to the investigation of devices with engineered spin configurations.
In this thesis, I study entanglement in quantum field theory, using methods from operator algebra theory. More precisely, the thesis covers original research on the entanglement properties of the free fermionic field. After giving a pedagogical introduction to algebraic methods in quantum field theory, as well as the modular theory of Tomita-Takesaki and its relation to entanglement, I present a coherent framework that allows to solve Tomita-Takesaki theory for free fermionic fields in any number of dimensions. Subsequently, I use the derived machinery on the free massless fermion in two dimensions, where the formulae can be evaluated analytically. In particular, this entails the derivation of the resolvent of restrictions of the propagator, by means of solving singular integral equations. In this way, I derive the modular flow, modular Hamiltonian, modular correlation function, R\'enyi entanglement entropy, von-Neumann entanglement entropy, relative entanglement entropy, and mutual information for multi-component regions. All of this is done for the vacuum and thermal states, both on the infinite line and the circle with (anti-)periodic boundary conditions. Some of these results confirm previous results from the literature, such as the modular Hamiltonian and entanglement entropy in the vacuum state. The non-universal solutions for modular flow, modular correlation function, and R\'enyi entropy, however are new, in particular at finite temperature on the circle. Additionally, I show how boundaries of spacetime affect entanglement, as well as how one can define relative (entanglement) entropy and mutual information in theories with superselection rules. The findings regarding modular flow in multi-component regions can be summarised as follows: In the non-degenerate vacuum state, modular flow is multi-local, in the sense that it mixes the field operators along multiple trajectories, with one trajectory per component. This was already known from previous literature but is presented here in a more explicit form. In particular, I present the exact solution for the dynamics of the mixing process. What was not previously known at all, is that the modular flow of the thermal state on the circle is infinitely multi-local even for a connected region, in the sense that it mixes the field along an infinite, discretely distributed set, of trajectories. In the limit of high temperatures, all trajectories but the local one are pushed towards the boundary of the region, where their amplitude is damped exponentially, leaving only the local result. At low temperatures, on the other hand, these trajectories distribute densely in the region to either---for anti-periodic boundary conditions---cancel, or---for periodic boundary conditions---recover the non-local contribution due to the degenerate vacuum state. Proceeding to spacetimes with boundaries, I show explicitly how the presence of a boundary implies entanglement between the two components of the Dirac spinor. By computing the mutual information between the components inside a connected region, I show quantitatively that this entanglement decreases as an inverse square law at large distances from the boundary. In addition, full conformal symmetry (which is explicitly broken due to the presence of a boundary) is recovered from the exact solution for modular flow, far away from the boundary. As far as I know, all of these results are new, although related results were published by another group during the final stage of this thesis. Finally, regarding relative entanglement entropy in theories with superselection sectors, I introduce charge and flux resolved relative entropies, which are novel measures for the distinguishability of states, incorporating a charge operator, central to the algebra of observables. While charge resolved relative entropy has the interpretation of being a ``distinguishability per charge sector'', I argue that it is physically meaningless without placing a cutoff, due to infinite short-distance entanglement. Flux resolved relative entropy, on the other hand, overcomes this problem by inserting an Aharonov-Bohm flux and thus passing to a variant of the grand canonical ensemble. It takes a well defined value, even without putting a cutoff, and I compute its value between various states of the free massless fermion on the line, the charge operator being the total fermion number.
Within gauge/gravity duality, we consider the local quench-like time evolution obtained by joining two 1+1-dimensional heat baths at different temperatures at time \(t\) = 0. A steady state forms and expands in space. For the 2+1-dimensional gravity dual, we find that the “shockwaves” expanding the steady-state region are of spacelike nature in the bulk despite being null at the boundary. However, they do not transport information. Moreover, by adapting the time-dependent Hubeny-Rangamani-Takayanagi prescription, we holographically calculate the entanglement entropy and also the mutual information for different entangling regions. For general temperatures, we find that the entanglement entropy increase rate satisfies the same bound as in the ‘entanglement tsunami’ setups. For small temperatures of the two baths, we derive an analytical formula for the time dependence of the entanglement entropy. This replaces the entanglement tsunami-like behaviour seen for high temperatures. Finally, we check that strong subadditivity holds in this time-dependent system, as well as further more general entanglement inequalities for five or more regions recently derived for the static case.
In the last decade continuous-time quantum Monte Carlo in the hybridization expansion (CTHYB) was one of the most successful Monte Carlo techniques to describe correlated quantum phenomena in conjunction with dynamical mean field theory (DMFT). The first part of the thesis consists of algorithmical developments regarding CTHYB and DMFT. I provide a complete derivation and an extensive discussion of the expansion formula. We generalized it to treat spin-orbit coupling, and invented the superstate sampling algorithm to make it efficient enough for describing systems with general interactions, crystal fields and spin-orbit coupling at low temperatures. But CTHYB is known to fail in the standard implementation for equal-time correlators, certain higher-order Green’s functions and the atomic limit; we discovered that its estimator for the Greens function is also inconsistent for Anderson impurities with finite, discrete baths. I focus then on further improvements of CTHYB that we have conceived and worked on, in particular for f-orbitals and for taking physical symmetries into account in the calculation of the Monte Carlo observables. The second part of the thesis presents selected physical applications of these methods. I show DMFT calculations of highest accuracy for elemental iron and nickel and discover a new mechanism of magnetic ordering in nickel: the ordering of band structure-induced local moments. Then we analyze the stability of this phenomenon under pressure and temperatures, that characterize in the Earth’s core. We find, that the mechanism survives these conditions and may give a significant contribution to the generation of the Earth’s magnetic field. The next topic is the stability of double Dirac fermions against electronic correlations. We find, that the Coulomb interaction in the corresponding material Bi2 CuO4 are strong enough to destroy the double Dirac cone, and substantial uniform pressure is necessary to restore them. In the last chapter I derive the properties of Higgs and Goldstone bosons from Ginzburg-Landau theory, and identify these excitations in a model of an excitonic magnet.
Im Rahmen eines selbst-konsistenten Outer-Gap-Modells der Pulsar-Magnetosphäre wurde die elektromagnetische sehr hochenergetische Strahlung des Crab-Pulsars simuliert. Dies wurde parallel anhand zweier verschiedener Fälle getan, die sich in den angenommenen Gleichungen für die elektrische Feldstärke und für den Krümmungsradius der magnetischen Feldlinien unterscheiden. Die Kinetik der geladenen Teilchen bei ihrer Propagation durch die Outer Gap wurde unter Einbeziehung von Krümmungsstrahlung, inverser Compton-Streuung und Triple Paarbildung betrachtet. Das theoretisch simulierte Spektrum wird mit von Fermi-LAT und von den MAGIC Teleskopen gemessenen Daten verglichen.
In this review paper, we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics. We first start with the analytical properties of the classical Wright functions of which we distinguish two kinds. We then justify the relevance of the Wright functions of the second kind as fundamental solutions of the time-fractional diffusion-wave equations. Indeed, we think that this approach is the most accessible point of view for describing non-Gaussian stochastic processes and the transition from sub-diffusion processes to wave propagation. Through the sections of the text and suitable appendices, we plan to address the reader in this pathway towards the applications of the Wright functions of the second kind.
Over the last two decades, accompanied by their prediction and ensuing realization, topological non-trivial materials like topological insulators, Dirac semimetals, and Weyl semimetals have been in the focus of mesoscopic condensed matter research. While hosting a plethora of intriguing physical phenomena all on their own, even more fascinating features emerge when superconducting order is included. Their intrinsically pronounced spin-orbit coupling leads to peculiar, time-reversal symmetry protected surface states, unconventional superconductivity, and even to the emergence of exotic bound states in appropriate setups.
This Thesis explores various junctions built from - or incorporating - topological materials in contact with superconducting order, placing particular emphasis on the transport properties and the proximity effect.
We begin with the analysis of Josephson junctions where planar samples of mercury telluride are sandwiched between conventional superconducting contacts. The surprising observation of pronounced excess currents in experiments, which can be well described by the Blonder-Tinkham-Klapwijk theory, has long been an ambiguous issue in this field, since the necessary presumptions are seemingly not met. We propose a resolution to this predicament by demonstrating that the interface properties in hybrid nanostructures of distinctly different materials yet corroborate these assumptions and explain the outcome. An experimental realization is feasible by gating the contacts. We then proceed with NSN junctions based on time-reversal symmetry broken Weyl semimetals and including superconducting order. Due to the anisotropy of the electron band structure, both the transport properties as well as the proximity effect depend substantially on the orientation of the interfaces between the materials. Moreover, an imbalance can be induced in the electron population between Weyl nodes of opposite chirality, resulting in a non-vanishing spin polarization of the Cooper pairs leaking into the normal contacts. We show that such a system features a tunable dipole character with possible applications in spintronics. Finally, we consider partially superconducting surface states of three-dimensional topological insulators. Tuning such a system into the so-called bipolar setup, this results in the formation of equal-spin Cooper pairs inside the superconductor, while simultaneously acting as a filter for non-local singlet pairing. The creation and manipulation of these spin-polarized Cooper pairs can be achieved by mere electronic switching processes and in the absence of any magnetic order, rendering such a nanostructure an interesting system for superconducting spintronics. The inherent spin-orbit coupling of the surface state is crucial for this observation, as is the bipolar setup which strongly promotes non-local Andreev processes.
Since the genesis of condensed matter physics, strongly correlated fermionic systems have shown a variety of fascinating properties and remain a vital topic in the field.
Such systems arise through electronic interaction, and despite decades of intensive research, no holistic approach to solving this problem has been found.
During that time, physicists have compiled a wealth of individual experimental and theoretical results, which together give an invaluable insight into these materials, and, in some instances, can explain correlated phenomena.
However, there are several systems that stubbornly refuse to fall completely in line with current theoretical descriptions, among them the high-\( T_c{}\) cuprates and heavy fermion compounds.
Although the two material classes have been around for the better part of the last 50 years, large portions of their respective phase diagram are still under intensive debate.
Recent experiments in several electron-doped cuprates compounds, e.g. neodymium cerium copper oxide (Nd\(_{2x}\)Ce\(_x\)CuO\(_4\)), reveal a charge ordering about an antiferromagnetic ground state.
So far, it has not been conclusively clarified how this intertwining of charge and spin polarization comes about and how it can be reconciled with a rigorous theoretical description.
The heavy-fermion semimetals, on the other hand, have enjoyed renewed scientific interest with the discovery of topological Kondo insulators, a new material class offering a unique interface of topology, symmetry breaking, and correlated phenomena. In this context, samarium hexaboride (SmB\(_6\)) has emerged as a prototypical system, which may feature a topological ground state.
In this thesis, we present a spin rotational invariant auxiliary particle approach to investigate the propensities of interacting electrons towards forming new states of order.
In particular, we study the onset of spin and charge order in high-\( T_c{}\) cuprate systems and Kondo lattices, as well as the interplay of magnetism and topology.
To that end, we use a sophisticated mean-field approximation of bosonic auxiliary particles augmented by a stability analysis of the saddle point via Gaussian fluctuations.
The latter enables the derivation of dynamic susceptibilities, which describe the response of the system under external fields and offer a direct comparison to experiments.
Both the mean-field and fluctuation formalisms require a numerical tool that is capable of extremizing the saddle point equations, on the one hand, and reliably solving a loop integral of the susceptibility-type, on the other.
A full, from scratch derivation of the formalism tailored towards a software implementation, is provided and pedagogically reviewed.
The auxiliary particle method allows for a rigorous description of incommensurate magnetic order and compares well to other established numerical and analytical techniques.
Within our analysis, we employ the two-dimensional one-band Hubbard as well as the periodic Anderson model as minimal Hamiltonians for the high-\( T_c{}\) cuprates and Kondo systems, respectively.
For the former, we observe a regime of intertwined charge- and spin-order in the electron-doped regime, which matches recent experimental observations in the cuprate material Nd\(_{2x}\)Ce\(_x\)CuO\(_4\).
Furthermore, we localize the emergence of a Kondo regime in the periodic Anderson model and establish the magnetic phase diagram of the two-band model for topological Kondo insulators.
The emerging antiferromagnetic ground state can be characterized by its topological properties and shows, for a non-trivial phase, topologically protected hinge modes.
We employ the AdS/CFT correspondence and hydrodynamics to analyze the transport properties of \(2+1\) dimensional electron fluids. In this way, we use theoretical methods from both condensed matter and high-energy physics to derive tangible predictions that are directly verifiable in experiment.
The first research topic we consider is strongly-coupled electron fluids. Motivated by early results by Gurzhi on the transport properties of weakly coupled fluids, we consider whether similar properties are manifest in strongly coupled fluids. More specifically, we focus on the hydrodynamic tail of the Gurzhi effect: A decrease in fluid resistance with increasing temperature due to the formation of a Poiseuille flow of electrons in the sample. We show that the hydrodynamic tail of the Gurzhi effect is also realized in strongly coupled and fully relativistic fluids, but with modified quantitative features. Namely, strongly-coupled fluids always exhibit a smaller resistance than weakly coupled ones and are, thus, far more efficient conductors. We also suggest that the coupling dependence of the resistance can be used to measure the coupling strength of the fluid. In view of these measurements, we provide analytical results for the resistance as a function of the shear viscosity over entropy density \(\eta/s\) of the fluid. \(\eta/s\) is itself a known function of the coupling strength in the weak and infinite coupling limits.
In further analysis for strongly-coupled fluids, we propose a novel strongly coupled Dirac material based on a kagome lattice, Scandium-substituted Herbertsmithite (ScHb). The large coupling strength of this material, as well as its Dirac nature, provides us with theoretical and experimental access to non-perturbative relativistic and quantum critical physics. A highly suitable method for analyzing such a material's transport properties is the AdS/CFT correspondence. Concretely, using AdS/CFT we derive an estimate for ScHb's \(\eta/s\) and show that it takes a value much smaller than that observed in weakly coupled materials. In turn, the smallness of \(\eta/s\) implies that ScHb's Reynolds number, \(Re\), is large. In fact, \(Re\) is large enough for turbulence, the most prevalent feature of fluids in nature, to make its appearance for the first time in electronic fluids.
Switching gears, we proceed to the second research topic considered in this thesis: Weakly coupled parity-breaking electron fluids. More precisely, we analyze the quantitative and qualitative changes to the classical Hall effect, for electrons propagating hydrodynamically in a lead. Apart from the Lorentz force, a parity-breaking fluid's motion is also impacted by the Hall-viscous force; the shear-stress force induced by the Hall-viscosity. We show that the interplay of these two forces leads to a hydrodynamic Hall voltage with non-linear dependence on the magnetic field. More importantly, the Lorentz and Hall-viscous forces become equal at a non-vanishing magnetic field, leading to a trivial hydrodynamic Hall voltage. Moreover, for small magnetic fields we provide analytic results for the dependence of the hydrodynamic Hall voltage on all experimentally-tuned parameters of our simulations, such as temperature and density. These dependences, along with the zero of the hydrodynamic Hall voltage, are distinct features of hydrodynamic transport and can be used to verify our predictions in experiments.
Last but not least, we consider how a distinctly electronic property, spin, can be included into the hydrodynamic framework. In particular, we construct an effective action for non-dissipative spin hydrodynamics up to first order in a suitably defined derivative expansion. We also show that interesting spin-transport effects appear at second order in the derivative expansion. Namely, we show that the fluid's rotation polarizes its spin. This is the hydrodynamic manifestation of the Barnett effect and provides us with an example of hydrodynamic spintronics.
To conclude this thesis, we discuss several possible extensions of our research, as well as proposals for research in related directions.
We review the physical aggregation of value added and capital in terms of work performance and information processing and its relation to the deflated monetary time series of output and capital. In growth accounting it complements the time series of labor and energy, measured in hours worked per year and kilowatt-hours consumed per year, respectively. This aggregation is the conceptual basis on which those energy-dependent production functions have been constructed that reproduce economic growth of major industrial countries in the 20th century with small residuals and output elasticities that are for energy much larger and for labor much smaller than the cost shares of these factors. Accounting for growth in such a way, which deviates from that of mainstream economics, may serve as a first step towards integrating the First and the Second Law of Thermodynamics into economics.
The main goal of this thesis is to elucidate the sense in which recent experimental progress in condensed matter physics, namely the verification of two-dimensional Dirac-like materials and their control in ballistic- as well as hydrodynamic transport experiments enables the observation of a well-known 'high-energy' phenomenon: The parity anomaly of planar quantum electrodynamics (QED\(_{2+1}\)). In a nutshell, the low-energy physics of two-dimensional Quantum Anomalous Hall (QAH) insulators like (Hg,Mn)Te quantum wells or magnetically doped (Bi,Sb)Te thin films can be described by the combined response of two 2+1 space-time dimensional Chern insulators with a linear dispersion in momentum. Due to their Dirac-like spectra, each of those Chern insulators is directly related to the parity anomaly of planar quantum electrodynamics. However, in contrast to a pure QED\(_{2+1}\) system, the Lagrangian of each Chern insulator is described by two different mass terms: A conventional momentum-independent Dirac mass \(m\), as well as a momentum-dependent so-called Newtonian mass term \(B \vert \mathbf{k} \vert^2\). According to the parity anomaly it is not possible to well-define a parity- and U(1) gauge invariant quantum system in 2+1 space-time dimensions. More precisely, starting with a parity symmetric theory at the classical level, insisting on gauge-invariance at the quantum level necessarily induces parity-odd terms in the calculation of the quantum effective action. The role of the Dirac mass term in the calculation of the effective QED\(_{2+1}\) action has been initially studied in Phys. Rev. Lett. 51, 2077 (1983). Even in the presence of a Dirac mass, the associated fermion determinant diverges and lacks gauge invariance. This requires a proper regularization/renormalizaiton scheme and, as such, transfers the peculiarities of the parity anomaly to the massive case.
In the scope of this thesis, we connect the momentum-dependent Newtonian mass term of a Chern insulator to the parity anomaly. In particular, we reveal, that in the calculation of the effective action, before renormalization, the Newtonian mass term acts similarly to a parity-breaking element of a high-energy regularization scheme. This calculation allows us to derive the finite frequency correction to the DC Hall conductivity of a QAH insulator. We derive that the leading order AC correction contains a term proportional to the Chern number. This term originates from the Newtonian mass and can be measured via electrical or via magneto-optical experiments. The Newtonian mass, in particular, significantly changes the resonance structure of the AC Hall conductivity in comparison to pure Dirac systems like graphene.
In addition, we study the effective action of the aforementioned Chern insulators in external out-of-plane magnetic fields. We show that as a consequence of the parity anomaly the QAH phase in (Hg,Mn)Te quantum wells or in magnetically doped (Bi,Sb)Te thin films survives in out-of-plane magnetic fields, violates the Onsager relation, and can therefore be distinguished from a conventional quantum Hall (QH) response. As a smoking-gun of the QAH phase in increasing magnetic fields, we predict a transition from a quantized Hall plateau with \(\sigma_\mathrm{xy}= -\mathrm{e}^2/\mathrm{h}\) to a not perfectly quantized plateau which is caused by scattering processes between counter-propagating QH and QAH edge states. This transition is expected to be of significant relevance in paramagnetic QAH insulators like (Hg,Mn)Te/CdTe quantum wells, in which the exchange interaction competes against the out-of-plane magnetic field.
All of the aforementioned results do not incorporate finite temperature effects. In order to shed light on such phenomena, we further analyze the finite temperature Hall response of 2+1 dimensional Chern insulators under the combined influence of a chemical potential and an out-of-plane magnetic field. As we have mentioned above, this non-dissipative transport coefficient is directly related to the parity anomaly of planar quantum electrodynamics. Within the scope of our analysis we show that the parity anomaly itself is not renormalized by finite temperature effects. However, the parity anomaly induces two terms of different physical origin in the effective Chern-Simons action of a QAH insulator, which are directly proportional to its Hall conductivity. The first term is temperature and chemical potential independent and solely encodes the intrinsic topological response. The second term specifies the non-topological thermal response of conduction- and valence band modes, respectively. We show that the relativistic mass \(m\) of a Chern insulator counteracts finite temperature effects, whereas its non-relativistic Newtonian mass \(B \vert \mathbf{k} \vert^2 \) enhances these corrections. In addition, we are extending our associated analysis to finite out-of-plane magnetic fields, and relate the thermal response of a Chern insulator therein to the spectral asymmetry, which is a measure of the parity anomaly in out-of-plane magnetic fields.
In the second part of this thesis, we study the hydrodynamic properties of two-dimensional electron systems with a broken time-reversal and parity symmetry. Within this analysis we are mainly focusing on the non-dissipative transport features originating from a peculiar hydrodynamic transport coefficient: The Hall viscosity \(\eta_\mathrm{H}\). In out-of-plane magnetic fields, the Hall viscous force directly competes with the Lorentz force, as both mechanisms contribute to the overall Hall voltage. In our theoretical considerations, we present a way of uniquely distinguishing these two contributions in a two-dimensional channel geometry by calculating their functional dependencies on all external parameters. We are in particular deriving that the ratio of the Hall viscous contribution to the Lorentz force contribution is negative and that its absolute value decreases with an increasing width, slip-length and carrier density. Instead, it increases with the electron-electron mean free path in the channel geometry considered. We show that in typical materials such as GaAs the Hall viscous contribution can dominate the Lorentz signal up to a few tens of millitesla until the total Hall voltage vanishes and eventually is exceeded by the Lorentz contribution. Last but not least, we derive that the total Hall electric field has a parabolic form originating from Lorentz effects. Most remarkably, the offset of this parabola is directly characterized by the Hall viscosity. Therefore, in summary, our results pave the way to measure and to identify the Hall viscosity via both global and local measurements of the entire Hall voltage.
In this thesis, we investigate several topics pertaining to emergent collective quantum phenomena in the domain of correlated fermions, using the quantum Monte Carlo method. They display exotic low temperature phases as well as phase transitions which are beyond the Landau–Ginzburg theory. The interplay between three key points is crucial for us: fermion statistics, many body effects and topology. We highlight the following several achievements: 1. Successful modeling of continuum field theories with lattice Hamiltonians, 2. their sign-problem-free Monte Carlo simulations of these models, 3. and numerical results beyond mean field descriptions. First, we consider a model of Dirac fermions with a spin rotational invariant inter- action term that dynamically generates a quantum spin Hall insulator. Surprisingly, an s-wave superconducting phase emerges due to the condensation of topological de- fects of the spin Hall order parameter. When particle-hole symmetry is present, the phase transition between the topological insulator and the superconducting phase is an example of a deconfined quantum critical point(DQCP). Although its low energy effec- tive field theory is purely bosonic, the exact conservation law of the skyrmion number operator rules out the possibility of realizing this critical point in lattice boson models. This work is published in Ref. [1]. Second, we dope the dynamically generated quantum spin Hall insulator mentioned above. Hence it is described by a field theory without Lorentz invariance due to the lack of particle-hole symmetry. This sheds light on the extremely hot topic of twisted bilayergraphene: Why is superconductivity generated when the repulsive Coulomb interaction is much stronger than the electron-phonon coupling energy scale? In our case, Cooper pairs come from the topological skyrmion defects of the spin current order parameter, which are charged. Remarkably, the nature of the phase transition is highly non-mean-field-like: one is not allowed to simply view pairs of electrons as single bosons in a superfluid-Mott insulator transition, since the spin-current order parameter can not be ignored. Again, due to the aforementioned skyrmions, the two order parameters are intertwined: One phase transition occurs between the two symmetry breaking states. This work is summarized in Ref. [2]. Third, we investigate the 2 + 1 dimensional O(5) nonlinear sigma model with a topological Wess-Zumino-Witten term. Remarkably, we are able to perform Monte Carlo calculations with a UV cutoff given by the Dirac Landau level quantization. It is a successful example of simulating a continuous field theory without lattice regularization which leads to an additional symmetry breaking. The Dirac background and the five anti-commuting Dirac mass terms naturally introduce the picture of a non-trivial Berry phase contribution in the parameter space of the five component order parameter. Using the finite size scaling method given by the flux quantization, we find a stable critical phase in the low stiffness region of the sigma model. This is a candidate ground state of DQCP when the O(5) symmetry breaking terms are irrelevant at the critical point. Again, it has a bosonic low energy field theory which is seemingly unable to be realized in pure boson Hamiltonians. This work is summarized in Ref. [3].
Just as photons are the quanta of light, plasmons are the quanta of orchestrated charge-density oscillations in conducting media. Plasmon phenomena in normal metals, superconductors, and doped semiconductors are often driven by long-wavelength Coulomb interactions. However, in crystals whose Fermi surface is comprised of disconnected pockets in the Brillouin zone, collective electron excitations can also attain a shortwave component when electrons transition between these pockets. In this work, we show that the band structure of monolayer transition-metal dichalcogenides gives rise to an intriguing mechanism through which shortwave plasmons are paired up with excitons. The coupling elucidates the origin for the optical sideband that is observed repeatedly in monolayers of WSe\(_2\) and WS\(_2\) but not understood. The theory makes it clear why exciton-plasmon coupling has the right conditions to manifest itself distinctly only in the optical spectra of electron-doped tungsten-based monolayers.
Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. Here we employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet \({ZnCr_2Se_4}\) with a cubic spinel structure, in which spin\(-3/2\) magnetic \({Cr^{3+}}\) ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional Goldstone mode emanating from the \((0~ 0~ {q_h})\) ordering vector, low-energy magnetic excitations in the single-domain proper-screw spiral phase show soft helimagnon modes with a small energy gap of \({∼0.17~ meV}\), emerging from two orthogonal wave vectors \(({q_h}~ 0~ 0)\) and \({(0~ {q_h}~ 0)}\) where no magnetic Bragg peaks are present. We term them pseudo-Goldstone magnons, as they appear gapless within linear spinwave theory and only acquire a finite gap due to higher-order quantum-fluctuation corrections. Our results are likely universal for a broad class of symmetric helimagnets, opening up a new way of studying weak magnon-magnon interactions with accessible spectroscopic methods.
We present a non-Hermitian Floquet model with topological edge states in real and imaginaryband gaps. The model utilizes two stacked honeycomb lattices which can be related via four different typesof non-Hermitian time-reversal symmetry. Implementing the correct time-reversal symmetry provides uswith either two counterpropagating edge states in a real gap, or a single edge state in an imaginary gap.The counterpropagating edge states allow for either helical or chiral transport along the lattice perimeter.In stark contrast, we find that the edge state in the imaginary gap does not propagate. Instead, it remainsspatially localized while its amplitude continuously increases. Our model is well-suited for realizing theseedge states in photonic waveguide lattices
A search for high-energy neutrino emission correlated with gamma-ray bursts outside the electromagnetic prompt-emission time window is presented. Using a stacking approach of the time delays between reported gamma-ray burst alerts and spatially coincident muon-neutrino signatures, data from the Antares neutrino telescope recorded between 2007 and 2012 are analysed. One year of public data from the IceCube detector between 2008 and 2009 have been also investigated. The respective timing profiles are scanned for statistically significant accumulations within 40 days of the Gamma Ray Burst, as expected from Lorentz Invariance Violation effects and some astrophysical models. No significant excess over the expected accidental coincidence rate could be found in either of the two data sets. The average strength of the neutrino signal is found to be fainter than one detectable neutrino signal per hundred gamma-ray bursts in the Antares data at 90% confidence level.
Clearly, in nature, but also in technological applications, complex systems built in an entirely ordered and regular fashion are the exception rather than the rule. In this thesis we explore how critical phenomena are influenced by quenched spatial randomness. Specifically, we consider physical systems undergoing a continuous phase transition in the presence of topological disorder, where the underlying structure, on which the system evolves, is given by a non-regular, discrete lattice. We therefore endeavour to achieve a thorough understanding of the interplay between collective dynamics and quenched randomness.
According to the intriguing concept of universality, certain laws emerge from collectively behaving many-body systems at criticality, almost regardless of the precise microscopic realization of interactions in those systems. As a consequence, vastly different phenomena show striking similarities at their respective phase transitions. In this dissertation we pursue the question of whether the universal properties of critical phenomena are preserved when the system is subjected to topological perturbations. For this purpose, we perform numerical simulations of several prototypical systems of statistical physics which show a continuous phase transition. In particular, the equilibrium spin-1/2 Ising model and its generalizations represent -- among other applications -- fairly natural approaches to model magnetism in solids, whereas the non-equilibrium contact process serves as a toy model for percolation in porous media and epidemic spreading. Finally, the Manna sandpile model is strongly related to the concept of self-organized criticality, where a complex dynamic system reaches a critical state without fine-tuning of external variables.
Our results reveal that the prevailing understanding of the influence of topological randomness on critical phenomena is insufficient. In particular, by considering very specific and newly developed lattice structures, we are able to show that -- contrary to the popular opinion -- spatial correlations in the number of interacting neighbours are not a key measure for predicting whether disorder ultimately alters the behaviour of a given critical system.
Topological superconductors represent a fruitful playing ground for fundamental research as well as for potential applications in fault-tolerant quantum computing. Especially Josephson junctions based on topological superconductors remain intensely studied, both theoretically and experimentally. The characteristic property of these junctions is their 4-periodic ground-state fermion parity in the superconducting phase difference. Using such topological Josephson junctions, we introduce the concept of a topological Josephson heat engine. We discuss how this engine can be implemented as a Josephson-Stirling cycle in topological superconductors, thereby illustrating the potential of the intriguing and fruitful marriage between topology and coherent thermodynamics. It is shown that the Josephson-Stirling cycle constitutes a highly versatile thermodynamic machine with different modes of operation controlled by the cycle temperatures. Finally, the thermodynamic cycle reflects the hallmark 4 pi -periodicity of topological Josephson junctions and could therefore be envisioned as a complementary approach to test topological superconductivity. Topological superconductors are expected to be a key component of quantum computing systems but reliably detecting their exotic properties is a challenge. Here, the authors propose a topological Josephson heat engine which uses thermodynamic effects to probe the 4 pi -periodic ground state of a topological superconductor.
Knots are intricate structures that cannot be unambiguously distinguished with any single topological invariant. Momentum space knots, in particular, have been elusive due to their requisite finely tuned long-ranged hoppings. Even if constructed, probing their intricate linkages and topological "drumhead" surface states will be challenging due to the high precision needed. In this work, we overcome these practical and technical challenges with RLC circuits, transcending existing theoretical constructions which necessarily break reciprocity, by pairing nodal knots with their mirror image partners in a fully reciprocal setting. Our nodal knot circuits can be characterized with impedance measurements that resolve their drumhead states and image their 3D nodal structure. Doing so allows for reconstruction of the Seifert surface and hence knot topological invariants like the Alexander polynomial. We illustrate our approach with large-scale simulations of various nodal knots and an experiment which maps out the topological drumhead region of a Hopf-link. Topological phases with knotted configurations in momentum space have been challenging to realize. Here, Lee et al. provide a systematic design and measurement of a three-dimensional knotted nodal structure, and resolve its momentum space drumhead states via a topolectrical RLC-type circuit.
Background and Objectives
To analyze the impact of humidity and temperature on excimer laser ablation of polyethylene terephthalate (PET), polymethylmethacrylate (PMMA) and porcine corneal tissue, and an ablation model to compensate for the temperature and humidity changes on ablation efficiency.
Study Design/Materials and Methods
The study was conducted using an AMARIS 1050RS (Schwind eye‐tech‐solutions) placed inside a climate chamber at ACTS. Ablations were performed on PET, PMMA, and porcine cornea. The impact of a wide range of temperature (~18°C to ~30°C) and relative humidity (~25% to ~80%) on laser ablation outcomes was tested using nine climate test settings. For porcine eyes, change in defocus was calculated from the difference of post‐ablation to pre‐ablation average keratometry readings. Laser scanning deflectometry was performed to measure refractive change achieved in PMMA. Multiple linear regression was performed using the least square method with predictive factors: temperature, relative humidity, time stamp. Influence of climate settings was modeled for pulse energy, pulse fluence, ablation efficiency on PMMA and porcine cornea tissue.
Results
Temperature changes did not affect laser pulse energy, pulse fluence (PET), and ablation efficiency (on PMMA or porcine corneal tissue) significantly. Changes in relative humidity were critical and significantly affected laser pulse energy, high fluence and low fluence. The opposite trend was observed between the ablation performance on PMMA and porcine cornea.
Conclusions
The proposed well‐fitting multi‐linear model can be utilized for compensation of temperature and humidity changes on ablation efficiency. Based on this model, a working window for optimum operation has been found (temperature 18°C to 28°C and relative humidity 25% to 65%) for a maximum deviation of ±2.5% in ablation efficiency in PMMA and porcine corneal tissue.
High-energy jets recoiling against missing transverse energy (MET) are powerful probes of dark matter at the LHC. Searches based on large MET signatures require a precise control of the \({Z(ν\overline{ν})}+\) jet background in the signal region. This can be achieved by taking accurate data in control regions dominated by \(Z(ℓ^+ℓ^−)+\) jet, \(W(ℓν)+\) jet and \(γ+\) jet production, and extrapolating to the \({Z(ν\overline{ν})}+\) jet background by means of precise theoretical predictions. In this context, recent advances in perturbative calculations open the door to significant sensitivity improvements in dark matter searches. In this spirit, we present a combination of state-of-the-art calculations for all relevant \(V+\) jets processes, including throughout NNLO QCD corrections and NLO electroweak corrections supplemented by Sudakov logarithms at two loops. Predictions at parton level are provided together with detailed recommendations for their usage in experimental analyses based on the reweighting of Monte Carlo samples. Particular attention is devoted to the estimate of theoretical uncertainties in the framework of dark matter searches, where subtle aspects such as correlations across different \(V+\) jet processes play a key role. The anticipated theoretical uncertainty in the \({Z(ν\overline{ν})}+\) jet background is at the few percent level up to the TeV range.
Advanced LIGO detected a significant gravitational wave signal (GW170104) originating from the coalescence of two black holes during the second observation run on January 4th, 2017. An all-sky high-energy neutrino follow-up search has been made using data from the Antares neutrino telescope, including both upgoing and downgoing events in two separate analyses. No neutrino candidates were found within ±500 s around the GW event time nor any time clustering of events over an extended time window of ±3 months. The non-detection is used to constrain isotropic-equivalent high-energy neutrino emission from GW170104 to less than ∼ 1.2 × \(10^{55}\) erg for a \(E^{−2}\) spectrum. This constraint is valid in the energy range corresponding to the 5–95% quantiles of the neutrino flux [3.2 TeV; 3.6 PeV], if the GW emitter was below the Antares horizon at the alert time.
Next-to-leading-order electroweak corrections to the production of four charged leptons at the LHC
(2017)
We present a state-of-the-art calculation of the next-to leading-order electroweak corrections to ZZ production, including the leptonic decays of the Z bosons into μ\(^+\)μ\(^ −\)e\(^+\)e\(^−\) or μ\(^+\)μ\(^−\)μ\(^+\)μ\(^−\) final states. We use complete leading-order and next-to-leading-order matrix elements for four-lepton production, including contributions of virtual photons and all off-shell effects of Z bosons, where the finite Z-boson width is taken into account using the complex-mass scheme. The matrix elements are implemented into Monte Carlo programs allowing for the evaluation of arbitrary differential distributions. We present integrated and differential cross sections for the LHC at 13 TeV both for an inclusive setup where only lepton identification cuts are applied, and for a setup motivated by Higgs-boson analyses in the four-lepton decay channel. The electroweak corrections are divided into photonic and purely weak contributions. The former show the well-known pronounced tails near kinematical thresholds and resonances; the latter are generically at the level of ∼ −5% and reach several −10% in the high-energy tails of distributions. Comparing the results for μ\(^+\)μ\(^−\)e\(^+\)e\(^−\) and μ\(^+\)μ\(^−\)μ\(^+\)μ\(^−\) final states, we find significant differences mainly in distributions that are sensitive to the μ\(^+\)μ\(^−\) pairing in the μ\(^+\)μ\(^−\)μ\(^+\)μ\(^−\) final state. Differences between μ\(^+\)μ\(^−\)e\(^+\)e\(^−\) and μ\(^+\)μ\(^−\)μ\(^+\)μ\(^−\) channels due to interferences of equal-flavour leptons in the final state can reach up to 10% in off-shell-sensitive regions. Contributions induced by incoming photons, i.e. photon-photon and quark-photon channels, are included, but turn out to be phenomenologically unimportant.
Higgs production in association with off-shell top-antitop pairs at NLO EW and QCD at the LHC
(2017)
We present NLO electroweak corrections to Higgs production in association with off-shell top-antitop quark pairs. The full process pp → e +νeµ −ν¯µbb¯H is considered, and hence all interference, off-shell, and non-resonant contributions are taken into account.
The electroweak corrections turn out to be below one per cent for the integrated cross section but can exceed 10% in certain phase-space regions. In addition to its phenomenological relevance, the computation constitutes a major technical achievement as the full NLO virtual corrections involving up to 9-point functions have been computed exactly. The results of the full computation are supported by two calculations in the double-pole approximation. These also allow to infer the effect of off-shell contributions and emphasise their importance especially for the run II of the LHC. Finally, we present combined predictions featuring both NLO electroweak and QCD corrections in a common set-up that will help the experimental collaborations in their quest of precisely measuring the aforementioned process.
The quantum Hall (QH) effect, which can be induced in a two-dimensional (2D) electron gas by an external magnetic field, paved the way for topological concepts in condensed matter physics. While the QH effect can for that reason not exist without Landau levels, there is a plethora of topological phases of matter that can exist even in the absence of a magnetic field. For instance, the quantum spin Hall (QSH), the quantum anomalous Hall (QAH), and the three-dimensional (3D) topological insulator (TI) phase are insulating phases of matter that owe their nontrivial topology to an inverted band structure. The latter results from a strong spin-orbit interaction or, generally, from strong relativistic corrections. The main objective of this thesis is to explore the fate of these preexisting topological states of matter, when they are subjected to an external magnetic field, and analyze their connection to quantum anomalies. In particular, the realization of the parity anomaly in solid state systems is discussed. Furthermore, band structure engineering, i.e., changing the quantum well thickness, the strain, and the material composition, is employed to manipulate and investigate various topological properties of the prototype TI HgTe.
Like the QH phase, the QAH phase exhibits unidirectionally propagating metallic edge channels. But in contrast to the QH phase, it can exist without Landau levels. As such, the QAH phase is a condensed matter analog of the parity anomaly. We demonstrate that this connection facilitates a distinction between QH and QAH states in the presence of a magnetic field. We debunk therefore the widespread belief that these two topological phases of matter cannot be distinguished, since they are both described by a $\mathbb{Z}$ topological invariant. To be more precise, we demonstrate that the QAH topology remains encoded in a peculiar topological quantity, the spectral asymmetry, which quantifies the differences in the number of states between the conduction and valence band. Deriving the effective action of QAH insulators in magnetic fields, we show that the spectral asymmetry is thereby linked to a unique Chern-Simons term which contains the information about the QAH edge states. As a consequence, we reveal that counterpropagating QH and QAH edge states can emerge when a QAH insulator is subjected to an external magnetic field. These helical-like states exhibit exotic properties which make it possible to disentangle QH and QAH phases. Our findings are of particular importance for paramagnetic TIs in which an external magnetic field is required to induce the QAH phase.
A byproduct of the band inversion is the formation of additional extrema in the valence band dispersion at large momenta (the `camelback'). We develop a numerical implementation of the $8 \times 8$ Kane model to investigate signatures of the camelback in (Hg,Mn)Te quantum wells. Varying the quantum well thickness, as well as the Mn-concentration, we show that the class of topologically nontrivial quantum wells can be subdivided into direct gap and indirect gap TIs. In direct gap TIs, we show that, in the bulk $p$-regime, pinning of the chemical potential to the camelback can cause an onset to QH plateaus at exceptionally low magnetic fields (tens of mT). In contrast, in indirect gap TIs, the camelback prevents the observation of QH plateaus in the bulk $p$-regime up to large magnetic fields (a few tesla). These findings allowed us to attribute recent experimental observations in (Hg,Mn)Te quantum wells to the camelback. Although our discussion focuses on (Hg,Mn)Te, our model should likewise apply to other topological materials which exhibit a camelback feature in their valence band dispersion.
Furthermore, we employ the numerical implementation of the $8\times 8$ Kane model to explore the crossover from a 2D QSH to a 3D TI phase in strained HgTe quantum wells. The latter exhibit 2D topological surface states at their interfaces which, as we demonstrate, are very sensitive to the local symmetry of the crystal lattice and electrostatic gating. We determine the classical cyclotron frequency of surface electrons and compare our findings with experiments on strained HgTe.
Active Galactic Nuclei emit radiation over the whole electromagnetic spectrum up to TeV energies. Blazars are one subtype with their jets pointing towards the observer. One of their typical features is extreme variability on timescales, from minutes to years. The fractional variability is an often used parameter for investigating the degree of variability of a light curve. Different detection methods and sensitivities of the instruments result in differently binned data and light curves with gaps. As they can influence the physics interpretation of the broadband variability, the effects of these differences on the fractional variability need to be studied. In this paper, we study the systematic effects of completeness in time coverage and the sampling rate. Using public data from instruments monitoring blazars in various energy ranges, we study the variability of the bright TeV blazars Mrk 421 and Mrk 501 over the electromagnetic spectrum, taking into account the systematic effects, and compare our findings with previous results. Especially in the TeV range, the fractional variability is higher than in previous studies, which can be explained by the much longer (seven years compared to few weeks) and more complete data sample.
Phase coexistence phenomena have been intensively studied in strongly correlated materials where several ordered states simultaneously occur or compete. Material properties critically depend on external parameters and boundary conditions, where tiny changes result in qualitatively different ground states. However, up to date, phase coexistence phenomena have exclusively been reported for complex compounds composed of multiple elements. Here we show that charge- and magnetically ordered states coexist in double-layer Fe/Rh(001). Scanning tunnelling microscopy and spectroscopy measurements reveal periodic charge-order stripes below a temperature of 130 K. Close to liquid helium temperature, they are superimposed by ferromagnetic domains as observed by spin-polarized scanning tunnelling microscopy. Temperature-dependent measurements reveal a pronounced cross-talk between charge and spin order at the ferromagnetic ordering temperature about 70 K, which is successfully modelled within an effective Ginzburg–Landau ansatz including sixth-order terms. Our results show that subtle balance between structural modifications can lead to competing ordering phenomena.
The next-to-leading-order electroweak corrections to pp→l\(^{+}\)l\(^{-}\)/ν¯¯¯ν+γ+X production, including all off-shell effects of intermediate Z bosons in the complex-mass scheme, are calculated for LHC energies, revealing the typically expected large corrections of tens of percent in the TeV range. Contributions from quark-photon and photon-photon initial states are taken into account as well, but their impact is found to be moderate or small. Moreover, the known next-to-leading-order QCD corrections are reproduced. In order to separate hard photons from jets, both a quark-to-photon fragmentation function á la Glover/Morgan and Frixione’s cone isolation are employed. The calculation is available in the form of Monte Carlo programs allowing for the evaluation of arbitrary differential cross sections. Predictions for integrated cross sections are presented for the LHC at 7 TeV, 8 TeV, and 14 TeV, and differential distributions are discussed at 14 TeV for bare muons and dressed leptons. Finally, we consider the impact of anomalous ZZγ and Zγγ couplings.
We present a supersymmetric left-right model which predicts gauge coupling unification close to the string scale and extra vector bosons at the TeV scale. The subtleties in constructing a model which is in agreement with the measured quark masses and mixing for such a low left-right breaking scale are discussed. It is shown that in the constrained version of this model radiative breaking of the gauge symmetries is possible and a SM-like Higgs is obtained. Additional CP-even scalars of a similar mass or even much lighter are possible. The expected mass hierarchies for the supersymmetric states differ clearly from those of the constrained MSSM. In particular, the lightest down-type squark, which is a mixture of the sbottom and extra vector-like states, is always lighter than the stop. We also comment on the model’s capability to explain current anomalies observed at the LHC.
Next-to-leading-order electroweak corrections to pp -> W\(^{+}\)W\(^{-}\) -> 4 leptons at the LHC
(2016)
We present results of the first calculation of next-to-leading-order electroweak corrections to W-boson pair production at the LHC that fully takes into account leptonic W-boson decays and off-shell effects. Employing realistic event selections, we discuss the corrections in situations that are typical for the study of W-boson pairs as a signal process or of Higgs-boson decays H → WW∗, to which W-boson pair production represents an irreducible background. In particular, we compare the full off-shell results, obtained treating the W-boson resonances in the complex-mass scheme, to previous results in the so-called double-pole approximation, which is based on an expansion of the loop amplitudes about the W resonance poles. At small and intermediate scales, i.e. in particular in angular and rapidity distributions, the two approaches show the expected agreement at the level of fractions of a percent, but larger differences appear in the TeV range. For transverse-momentum distributions, the differences can even exceed the 10% level in the TeV range where “background diagrams” with one instead of two resonant W bosons gain in importance because of recoil effects.
The nature of dark matter and the origin of the baryon asymmetry are two of the deepest mysteries of modern particle physics. In the absence of hints regarding a possible solution to these mysteries, many approaches have been developed to tackle them simultaneously leading to very diverse and rich models. We give a short review where we describe the general features of some of these models and an overview on the general problem. We also propose a diagrammatic notation to label the different models.
A search for Secluded Dark Matter annihilation in the Sun using 2007-2012 data of the ANTARES neutrino telescope is presented. Three different cases are considered: a) detection of dimuons that result from the decay of the mediator, or neutrino detection from: b) mediator that decays into a dimuon and, in turn, into neutrinos, and c) mediator that decays directly into neutrinos. As no significant excess over background is observed, constraints are derived on the dark matter mass and the lifetime of the mediator.
This Thesis explores hybrid structures on the basis of quantum spin Hall insulators, and in particular the interplay of their edge states and superconducting and magnetic order. Quantum spin Hall insulators are one example of topological condensed matter systems, where the topology of the bulk bands is the key for the understanding of their physical properties. A remarkable consequence is the appearance of states at the boundary of the system, a phenomenon coined bulk-boundary correspondence. In the case of the two-dimensional quantum spin Hall insulator, this is manifested by so-called helical edge states of counter-propagating electrons with opposite spins. They hold great promise, \emph{e.g.}, for applications in spintronics -- a paradigm for the transmission and manipulation of information based on spin instead of charge -- and as a basis for quantum computers. The beginning of the Thesis consists of an introduction to one-dimensional topological superconductors, which illustrates basic concepts and ideas. In particular, this includes the topological distinction of phases and the accompanying appearance of Majorana modes at their ends. Owing to their topological origin, Majorana modes potentially are essential building-blocks for topological quantum computation, since they can be exploited for protected operations on quantum bits. The helical edge states of quantum spin Hall insulators in conjunction with $s$-wave superconductivity and magnetism are a suitable candidate for the realization of a one-dimensional topological superconductor. Consequently, this Thesis investigates the conditions in which Majorana modes can appear. Typically, this happens between regions subjected to either only superconductivity, or to both superconductivity and magnetism. If more than one superconductor is present, the phase difference is of paramount importance, and can even be used to manipulate and move Majorana modes. Furthermore, the Thesis addresses the effects of the helical edge states on the anomalous correlation functions characterizing proximity-induced superconductivity. It is found that helicity and magnetism profoundly enrich their physical structure and lead to unconventional, exotic pairing amplitudes. Strikingly, the nonlocal correlation functions can be connected to the Majorana bound states within the system. Finally, a possible thermoelectric device on the basis of hybrid systems at the quantum spin Hall edge is discussed. It utilizes the peculiar properties of the proximity-induced superconductivity in order to create spin-polarized Cooper pairs from a temperature bias. Cooper pairs with finite net spin are the cornerstone of superconducting spintronics and offer tremendous potential for efficient information technologies.
Although the contribution to the Isotropic Gamma-Ray Background (IGRB) from unresolved extragalactic objects has been studied for many years, its exact composition and origin are as of yet unknown. It is suspected that diffuse processes such as dark matter annihilation contribute to the total IGRB, as well as unresolved gamma-ray emission from Active Galactic Nuclei (AGN), including radio galaxies. Radio galaxies are a source class that emit strongly at radio wavelengths, some of which have also been detected at gamma-ray wavelengths by the Fermi Large Area Telescope (Fermi-LAT), and by very high energy gamma-ray Cherenkov telescopes. It is thought that due to the orientation of their jets, radio galaxies are detected less numerously at gamma-ray energies than blazars. Furthermore, only a small number of radio galaxies have been detected at gamma-ray energies though it is considered that others do as well. It is for these reasons that gamma-ray emitting radio galaxies, an interesting and elusive class of objects, are selected for investigation in this work.
In order to reach the goal of better understanding diffuse processes, it is necessary to model the radio galaxy spectral energy distributions (SEDs). As AGN emission is variable with respect to time, it is critical to use simultaneously collected observations. Calculation of the SED based on simultaneous, multiwavelength data across the electromagnetic spectrum produces a reasonably accurate representation of the state of an object in a given time range. The gamma-ray emitting radio galaxies M 87, NGC 1275, Pictor A, and Centaurus A are selected here based on having been detected in very high energy gamma-rays by Cherenkov telescopes, as well as in other wavelengths. A uniquely consistent analysis approach is applied, in which each radio galaxy is analyzed the same way using simultaneously collected data. This approach sets it apart from other studies.
Fermi-LAT raw data for each source in the sample is analyzed in time ranges which directly overlap the very high energy gamma-ray Cherenkov observations, as well as several other wavelength ranges. A synchrotron self-Compton (SSC) model is applied, which provides accurate treatment of synchrotron and inverse-Compton processes occurring in the jets of AGN, while estimating physical characteristics of the source. It is found that the spectra of M 87, NGC 1275, Pictor A, and Centaurus A can be well described by the same SSC model, producing values for the physical characteristics such as the doppler factor and magnetic field, which are relatively consistent with each other.
In order to characterize the diffuse emission from dark matter self-annihilation, the radio galaxy SEDs are also fit with a dark matter model, resulting in an estimated dark matter particle mass of around 4.7 TeV which lies within predicted ranges.
The highly dense regions near the black holes of AGN provide the optimal conditions for detecting these signatures. It is also found here that discrepancies between the expected emission and the observed emission in the spectra of some radio galaxies can be explained using the combined SSC and dark matter model. As emission from dark matter annihilation is expected to remain steady with respect to time, a key feature of this work is the novelty of the combined SSC and dark matter model, and the finding that dark matter characteristics may be revealed through similar multiwavelength analyses during future low emission states of the AGN.
The radio galaxy sample is then extended to include all gamma-ray emitting radio galaxies detected by the Fermi-LAT, and a calculation of the core radio, total radio, and gamma-ray luminosities is followed through. A future step in extending this work would be to estimate the gamma-ray luminosity function of radio galaxies and their percent contribution to the total IGRB, based on the widely agreed upon assumption that a reasonable estimate of the gamma-ray luminosity function of a population can be attained by appropriately scaling its radio luminosity function, as gamma-ray luminosities and radio luminosities are strongly linearly correlated. This work has also provided the basis for such a calculation by outlining the theory and initial steps.
It is the hope that the vast scope of the gathered data, its simultaneity, and the use of consistent analysis methods across the sample, will provide an improved foundation for a future calculation of the contribution of this population to the IGRB, as well as encourage stricter requirements for multiwavelength studies.
In this thesis we discuss the potential of nanodevices based on topological insulators. This novel class of matter is characterized by an insulating bulk with simultaneously conducting boundaries. To lowest order, the states that are evoking the conducting behavior in TIs are typically described by a Dirac theory. In the two-dimensional case, together with time- reversal symmetry, this implies a helical nature of respective states. Then, interesting physics appears when two such helical edge state pairs are brought close together in a two-dimensional topological insulator quantum constriction. This has several advantages. Inside the constriction, the system obeys essentially the same number of fermionic fields as a conventional quantum wire, however, it possesses more symmetries. Moreover, such a constriction can be naturally contacted by helical probes, which eventually allows spin- resolved transport measurements.
We use these intriguing properties of such devices to predict the formation and detection of several profound physical effects. We demonstrate that narrow trenches in quantum spin Hall materials – a structure we coin anti-wire – are able to show a topological super- conducting phase, hosting isolated non-Abelian Majorana modes. They can be detected by means of a simple conductance experiment using a weak coupling to passing by helical edge states. The presence of Majorana modes implies the formation of unconventional odd-frequency superconductivity. Interestingly, however, we find that regardless of the presence or absence of Majoranas, related (superconducting) devices possess an uncon- ventional odd-frequency superconducting pairing component, which can be associated to a particular transport channel. Eventually, this enables us to prove the existence of odd- frequency pairing in superconducting quantum spin Hall quantum constrictions. The symmetries that are present in quantum spin Hall quantum constrictions play an essen- tial role for many physical effects. As distinguished from quantum wires, quantum spin Hall quantum constrictions additionally possess an inbuilt charge-conjugation symmetry. This can be used to form a non-equilibrium Floquet topological phase in the presence of a time-periodic electro-magnetic field. This non-equilibrium phase is accompanied by topological bound states that are detectable in transport characteristics of the system. Despite single-particle effects, symmetries are particularly important when electronic in- teractions are considered. As such, charge-conjugation symmetry implies the presence of a Dirac point, which in turn enables the formation of interaction induced gaps. Unlike single-particle gaps, interaction induced gaps can lead to large ground state manifolds. In combination with ordinary superconductivity, this eventually evokes exotic non-Abelian anyons beyond the Majorana. In the present case, these interactions gaps can even form in the weakly interacting regime (which is rather untypical), so that the coexistence with superconductivity is no longer contradictory. Eventually this leads to the simultaneous presence of a Z4 parafermion and a Majorana mode bound at interfaces between quantum constrictions and superconducting regions.
The AdS/CFT correspondence is an explicit realization of the holographic principle. It describes a field theory living on the boundary of a volume by a gravitational theory living in the interior and vice-versa. With its origins in string theory, the correspondence incorporates an explicit relationship between the degrees of freedom of both theories: the AdS/CFT dictionary. One astonishing aspect of the AdS/CFT correspondence is the emergence of geometry from field theory.
On the gravity side, a natural way to probe the geometry is to study boundary-anchored extremal surfaces of different dimensionality. While there is no unified way to determine the field theory dual for such non-local quantities, the AdS/CFT dictionary contains entries for surfaces of certain dimensionality: it relates two-point functions to geodesics, the Wilson loop expectation value to two-dimensional surfaces and the entanglement entropy, i.e. a measure for entanglement between states in a region and in its complement, to co-dimension two surfaces in the bulk.
In this dissertation, we calculate these observables for gravity setups dual to thermal states in the field theory. The geometric dual is given by AdS Schwarzschild black holes in general dimensions. We find analytic results for minimal areas in this setup. One focus of our analysis is the high-temperature limit. The leading and subleading term in this limit have diverse interpretation for the different observables. For example, the subleading term of the entanglement entropy satisfies a c-theorem for renormalization flows and gives insights into the number of effective degrees of freedom.
The entanglement entropy emerged as the favorable way to probe the geometric dual. In addition to the extremal bulk surface, the holographic entanglement entropy associates a bulk region to the considered boundary region. The volume of this region is conjectured to be a measure of complexity, i.e. a measure of how difficult it is to obtain the corresponding field-theory state. Building on our aforementioned results for the entanglement entropy, we study this complexity for AdS Schwarzschild black holes in general dimensions.
In particular, we draw conclusions on how efficient holography encodes the field theory and compare these results to MERA tensor networks, a numerical tool to study quantum many-body systems.
Moreover, we holographically study the complexity of pure states. This sheds light on the notion of complexity in field theories. We calculate the complexity for a simple, calculable example: states obtained by conformal transformations of the vacuum state in AdS3/CFT2. In this lower-dimensional realization of AdS/CFT, the conformal group is infinite dimensional. We construct a continuous space of states with the same complexity as the vacuum state. Furthermore, we determine the change of complexity caused by small conformal transformation. The field-theory operator implementing this transformation is known and allows to compare the holographic results to field theory expectations.
Flux distribution is an important tool to understand the variability processes in activegalactic nuclei. We now have available a great deal of observational evidences pointing towards thepresence of log-normal components in the high energy light curves, and different models have beenproposed to explain these data. Here, we collect some of the recent developments on this topic usingthe well-known blazar Mrk 501 as example of complex and interesting aspects coming from its fluxdistribution in different energy ranges and at different timescales. The observational data we refer toare those collected in a complementary manner by Fermi-LAT over multiple years, and by the FirstG-APD Cherenkov Telescope (FACT) telescope and the H.E.S.S. array in correspondence of the brightflare of June 2014
The main objectives of the KM3NeT Collaboration are (i) the discovery and subsequent observation of high-energy neutrino sources in the Universe and (ii) the determination of the mass hierarchy of neutrinos. These objectives are strongly motivated by two recent important discoveries, namely: (1) the high-energy astrophysical neutrino signal reported by IceCube and (2) the sizable contribution of electron neutrinos to the third neutrino mass eigenstate as reported by Daya Bay, Reno and others. To meet these objectives, the KM3NeT Collaboration plans to build a new Research Infrastructure consisting of a network of deep-sea neutrino telescopes in the Mediterranean Sea. A phased and distributed implementation is pursued which maximises the access to regional funds, the availability of human resources and the synergistic opportunities for the Earth and sea sciences community. Three suitable deep-sea sites are selected, namely off-shore Toulon (France), Capo Passero (Sicily, Italy) and Pylos (Peloponnese, Greece). The infrastructure will consist of three so-called building blocks. A building block comprises 115 strings, each string comprises 18 optical modules and each optical module comprises 31 photo-multiplier tubes. Each building block thus constitutes a three-dimensional array of photo sensors that can be used to detect the Cherenkov light produced by relativistic particles emerging from neutrino interactions. Two building blocks will be sparsely configured to fully explore the IceCube signal with similar instrumented volume, different methodology, improved resolution and
It has been proposed that the observed diphoton excess at 750 GeV could be explained within the constrained minimal supersymmetric standard model via resonantly produced stop bound states. We reanalyze this scenario critically and extend previous work to include the constraints from the stability of the electroweak vacuum and from the decays of the stoponium into a pair of Higgs bosons. It is shown that the interesting regions of parameter space with a light stop and Higgs of the desired mass are ruled out by these constraints. This conclusion is not affected by the presence of the bound states because the binding energy is usually very small in the regions of parameter space which can explain the Higgs mass. Thus, this also leads to strong constraints on the diphoton production cross section which is in general too small.
Adding interactions to topological (non-)trivial free fermion systems can in general have four different effects: (i) In symmetry protected topological band insulators, the correlations may lead to the spontaneous breaking of some protecting symmetries by long-range order that gaps the topological boundary modes. (ii) In free fermion (semi-)metal, the interaction could vice versa also generate long-range order that in turn induces a topological mass term and thus generates non-trivial phases dynamically. (iii) Correlation might reduce the topological classification of free fermion systems by allowing adiabatic deformations between states of formerly distinct phases. (iv) Interaction can generate long-range entangled topological order in states such as quantum spin liquids or fractional quantum Hall states that cannot be represented by non-interacting systems. During the course of this thesis, we use numerically exact quantum Monte Carlo algorithms to study various model systems that (potentially) represent one of the four scenarios, respectively.
First, we investigate a two-dimensional $d_{xy}$-wave, spin-singlet superconductor, which is relevant for high-$T_c$ materials such as the cuprates. This model represents nodal topological superconductors and exhibits chiral flat-band edge states that are protected by time-reversal and translational invariance. We introduce the conventional Hubbard interaction along the edge in order to study their stability with respect to correlations and find ferromagnetic order in case of repulsive interaction as well as charge-density-wave order and/or additional $i$s-wave pairing for attractive couplings. A mean-field analysis that, for the first time, is formulated in terms of the Majorana edge modes suggests that any order has normal and superconducting contributions. For example, the ferromagnetic order appears in linear superposition with triplet pairing. This finding is well confirmed by the numerically exact quantum Monte Carlo investigation.
Second, we consider spinless electrons on a two-dimensional Lieb lattice that are subject to nearest-neighbor Coulomb repulsion. The low energy modes of the free fermion part constitute a spin-$1$ Dirac cone that might be gapped by several mass terms. One option breaks time-reversal symmetry and generates a topological Chern insulator, which mainly motivated this study. We employ two flavors of quantum Monte Carlo methods and find instead the formation of charge-density-wave order that breaks particle-hole symmetry. Additionally, due to sublattices of unequal size in Lieb lattices, this induces a finite chemical potential that drives the system away from half-filling. We argue that this mechanism potentially extends the range of solvable models with finite doping by coupling the Lieb lattice to the target system of interest.
Third, we construct a system with four layers of a topological insulators and interlayer correlation that respects one independent time-reversal and a unitary $\mathbb{Z}_2$ symmetry. Previous studies claim a reduced topological classification from $\mathbb{Z}$ to $\mathbb{Z}_4$, for example by gapping out degenerate zero modes in topological defects once the correlation term is designed properly. Our interaction is chosen according to this analysis such that there should exist an adiabatic deformation between states whose topological invariant differs by $\Delta w=\pm4$ in the free fermion classification. We use a projective quantum Monte Carlo algorithm to determine the ground-state phase diagram and find a symmetry breaking regime, in addition to the non-interacting semi-metal, that separates the free fermion insulators. Frustration reduces the size of the long-range ordered region until it is replaced by a first order phase transition. Within the investigated range of parameters, there is no adiabatic path deforming the formerly distinct free fermion states into each other. We conclude that the prescribed reduction rules, which often use the bulk-boundary correspondence, are necessary but not sufficient and require a more careful investigation.
Fourth, we study conduction electron on a honeycomb lattice that form a Dirac semi-metal Kondo coupled to spin-1/2 degrees of freedom on a Kagome lattice. The local moments are described by a variant of the Balents-Fisher-Girvin model that has been shown to host a ferromagnetic phase and a $\mathbb{Z}_2$ spin liquid at strong frustration. Here, we report the first numerical exact quantum Monte Carlo simulation of the Kondo-coupled system that does not exhibit the negative-sign problem. When the local moments form a ferromagnet, the Kondo coupling induces an anti-ferromagnetic mass term in the conduction-electron system. At large frustration, the Dirac cone remains massless and the spin system forms a $\mathbb{Z}_2$ spin liquid. Owing to the odd number of spins per unit cell, this constitutes a non-Fermi liquid that violates Luttinger's theorem which relates the Fermi volume to the particle density in a Fermi liquid. This phase is a specific realization of the so called 'fractional Fermi liquid` as it has been first introduced in the context of heavy fermion models.
In this thesis we consider the hybrid quantum Monte Carlo method for simulations of the Hubbard and Su-Schrieffer-Heeger model. In the first instance, we discuss the hybrid quantum Monte Carlo method for the Hubbard model on a square lattice. We point out potential ergodicity issues and provide a way to circumvent them by a complexification of the method. Furthermore, we compare the efficiency of the hybrid quantum Monte Carlo method with a well established determinantal quantum Monte Carlo method for simulations of the half-filled Hubbard model on square lattices. One reason why the hybrid quantum Monte Carlo method loses the comparison is that we do not observe the desired sub-quadratic scaling of the numerical effort. Afterwards we present a formulation of the hybrid quantum Monte Carlo method for the Su-Schrieffer-Heeger model in two dimensions. Electron-phonon models like this are in general very hard to simulate using other Monte Carlo methods in more than one dimensions. It turns out that the hybrid quantum Monte Carlo method is much better suited for this model . We achieve favorable scaling properties and provide a proof of concept. Subsequently, we use the hybrid quantum Monte Carlo method to investigate the Su-Schrieffer-Heeger model in detail at half-filling in two dimensions. We present numerical data for staggered valence bond order at small phonon frequencies and an antiferromagnetic order at high frequencies. Due to an O(4) symmetry the antiferromagnetic order is connected to a superconducting charge density wave. Considering the Su-Schrieffer-Heeger model without tight-binding hopping reveals an additional unconstrained Z_2 gauge theory. In this case, we find indications for π-fluxes and a possible Z_2 Dirac deconfined phase as well as for a columnar valence bond ordered state at low phonon energies. In our investigations of the several phase transitions we discuss the different possibilities for the underlying mechanisms and reveal first insights into a rich phase diagram.
Blazars like Markarian 421 or Markarian 501 are active galactic nuclei (AGN), with their jets orientated towards the observer. They are among the brightest objects in the very high energy (VHE) gamma ray regime (>100 GeV). Their emitted gamma-ray fluxes are extremely variable, with changing activity levels on timescales between minutes, months, and even years. Several questions are part of the current research, such as the question of the emission regions or the engine of the AGN and the particle acceleration. A dedicated longterm monitoring program is necessary to investigate the properties of blazars in detail. A densely sampled and unbiased light curve allows for observation of both high and low states of the sources, and the combination with multi-wavelength observation could contribute to the answer of several questions mentioned above. FACT (First G-APD Cherenkov Telescope) is the first operational telescope using silicon photomultiplier (SiPM, also known as Geigermode—Avalanche Photo Diode, G-APD) as photon detectors. SiPM have a very homogenous and stable longterm performance, and allow operation even during full moon without any filter, leading to a maximal duty cycle for an Imaging Air Cherenkov Telescope (IACT). Hence, FACT is an ideal device for such a longterm monitoring of bright blazars. A small set of sources (e.g., Markarian 421, Markarian 501, 1ES 1959+650, and 1ES 2344+51.4) is currently being monitored. In this contribution, the FACT telescope and the concept of longterm monitoring of bright blazars will be introduced. The results of the monitoring program will be shown, and the advantages of densely sampled and unbiased light curves will be discussed.
A prototype detection unit of the KM3NeT deep-sea neutrino telescope has been installed at 3500m depth 80 km offshore the Italian coast. KM3NeT in its final configuration will contain several hundreds of detection units. Each detection unit is a mechanical structure anchored to the sea floor, held vertical by a submerged buoy and supporting optical modules for the detection of Cherenkov light emitted by charged secondary particles emerging from neutrino interactions. This prototype string implements three optical modules with 31 photomultiplier tubes each. These optical modules were developed by the KM3NeT Collaboration to enhance the detection capability of neutrino interactions. The prototype detection unit was operated since its deployment in May 2014 until its decommissioning in July 2015. Reconstruction of the particle trajectories from the data requires a nanosecond accuracy in the time calibration. A procedure for relative time calibration of the photomultiplier tubes contained in each optical module is described. This procedure is based on the measured coincidences produced in the sea by the 40K background light and can easily be expanded to a detector with several thousands of optical modules. The time offsets between the different optical modules are obtained using LED nanobeacons mounted inside them. A set of data corresponding to 600 h of livetime was analysed. The results show good agreement with Monte Carlo simulations of the expected optical background and the signal from atmospheric muons. An almost background-free sample of muons was selected by filtering the time correlated signals on all the three optical modules. The zenith angle of the selected muons was reconstructed with a precision of about 3∘.
Killing the cMSSM softly
(2016)
We investigate the constrained Minimal Supersymmetric Standard Model (cMSSM) in the light of constraining experimental and observational data from precision measurements, astrophysics, direct supersymmetry searches at the LHC and measurements of the properties of the Higgs boson, by means of a global fit using the program Fittino. As in previous studies, we find rather poor agreement of the best fit point with the global data. We also investigate the stability of the electro-weak vacuum in the preferred region of parameter space around the best fit point. We find that the vacuum is metastable, with a lifetime significantly longer than the age of the Universe. For the first time in a global fit of supersymmetry, we employ a consistent methodology to evaluate the goodness-of-fit of the cMSSM in a frequentist approach by deriving p values from large sets of toy experiments. We analyse analytically and quantitatively the impact of the choice of the observable set on the p value, and in particular its dilution when confronting the model with a large number of barely constraining measurements. Finally, for the preferred sets of observables, we obtain p values for the cMSSM below 10 %, i.e. we exclude the cMSSM as a model at the 90 % confidence level.
Active galactic nuclei (AGN) are among the brightest and most frequent sources on the extragalactic X-ray and gamma-ray sky. Their central supermassive blackhole generates an enormous luminostiy through accretion of the surrounding gas. A few AGN harbor highly collimated, powerful jets in which are observed across the entire electromagnetic spectrum. If their jet axis is seen in a small angle to our line-of-sight (these objects are then called blazars) jet emission can outshine any other emission component from the system. Synchrotron emission from electrons and positrons clearly prove the existence of a relativistic leptonic component in the jet plasma. But until today, it is still an open question whether heavier particles, especially protons, are accelerated as well. If this is the case, AGN would be prime candidates for extragalactic PeV neutrino sources that are observed on Earth. Characteristic signatures for protons can be hidden in the variable high-energy emission of these objects. In this thesis I investigated the broadband emission, particularly the high-energy X-ray and gamma-ray emission of jetted AGN to address open questions regarding the particle acceleration and particle content of AGN jets, or the evolutionary state of the AGN itself. For this purpose I analyzed various multiwavelength observations from optical to gamma-rays over a period of time using a combination of state-of-the-art spectroscopy and timing analysis. By nature, AGN are highly variable. Time-resolved spectral analysis provided a new dynamic view of these sources which helped to determine distinct emission processes that are difficult to disentangle from spectral or timing methods alone.
Firstly, this thesis tackles the problem of source classification in order to facilitate the search for interesting sources in large data archives and characterize new transient sources. I use spectral and timing analysis methods and supervised machine learning algorithms to design an automated source classification pipeline. The test and training sample were based on the third XMM-Newton point source catalog (3XMM-DR6). The set of input features for the machine learning algorithm was derived from an automated spectral modeling of all sources in the 3XMM-DR6, summing up to 137200 individual detections. The spectral features were complemented by results of a basic timing analysis as well as multiwavelength information provided by catalog cross-matches. The training of the algorithm and application to a test sample showed that the definition of the training sample was crucial: Despite oversampling minority source types with synthetic data to balance out the training sample, the algorithm preferably predicted majority source types for unclassified objects. In general, the training process showed that the combination of spectral, timing and multiwavelength features performed best with the lowest misclassification rate of \\sim2.4\\%.
The methods of time-resolved spectroscopy was then used in two studies to investigate the properties of two individual AGN, Mrk 421 and PKS 2004-447, in detail. Both objects belong to the class of gamma-ray emitting AGN. A very elusive sub-class are gamma-ray emitting Narrow Line Seyfert 1 (gNLS1) galaxies. These sources have been discovered as gamma-ray sources only recently in 2010 and a connection to young radio galaxies especially compact steep spectrum (CSS) radio sources has been proposed. The only gNLS1 on the Southern Hemisphere so far is PKS2004-447 which lies at the lower end of the luminosity distribution of gNLS1. The source is part of the TANAMI VLBI program and is regularly monitored at radio frequencies. In this thesis, I presented and analyzed data from a dedicated multiwavelength campaign of PKS 2004-447 which I and my collaborators performed during 2012 and which was complemented by individual observations between 2013 and 2016. I focussed on the detailed analysis of the X-ray emission and a first analysis of its broadband spectrum from radio to gamma-rays. Thanks to the dynamic SED I could show that earlier studies misinterpreted the optical spectrum of the source which had led to an underestimation of the high-energy emission and had ignited a discussion on the source class. I show that the overall spectral properties are consistent with dominating jet emission comprised of synchrotron radiation and inverse Compton scattering from accelerated leptons. The broadband emission is very similar to typical examples of a certain type of blazars (flat-spectrum radio quasars) and does not present any unusual properties in comparison. Interestingly, the VLBI data showed a compact jet structure and a steep radio spectrum consistent with a compact steep spectrum source. This classified PKS 2004-447 as a young radio galaxy, in which the jet is still developing.
The investigation of Mrk 421 introduced the blazar monitoring program which I and collaborator have started in 2014. By observing a blazar simultaneously from optical, X-ray and gamma-ray bands during a VHE outbursts, the program aims at providing extraordinary data sets to allow for the generation of a series of dynamical SEDs of high spectral and temporal resolution. The program makes use of the dense VHE monitoring by the FACT telescope. So far, there are three sources in our sample that we have been monitoring since 2014. I presented the data and the first analysis of one of the brightest and most variable blazar, Mrk 421, which had a moderate outbreak in 2015 and triggered our program for the first time. With spectral timing analysis, I confirmed a tight correlation between the X-ray and TeV energy bands, which indicated that these jet emission components are causally connected. I discovered that the variations of the optical band were both correlated and anti-correlated with the high-energy emission, which suggested an independent emission component. Furthermore, the dynamic SEDs showed two different flaring behaviors, which differed in the presence or lack of a peak shift of the low-energy emission hump. These results further supported the hypothesis that more than one emission region contributed to the broadband emission of Mrk 421 during the observations.
Overall,the studies presented in this thesis demonstrated that time-resolved spectroscopy is a powerful tool to classify both source types and emission processes of astronomical objects, especially relativistic jets in AGN, and thus provide a deeper understanding and new insights of their physics and properties.
Interplanetary shocks are believed to play an important role in the acceleration of charged particles in the heliosphere. While the acceleration to high energies proceeds via the diffusive mechanism at the scales exceeding by far the shock width, the initial stage (injection) should occur at the shock itself. Numerical tracing of ions is done in a model quasi-perpendicular shock front with a typical interplanetary shock parameters (Mach number, upstream ion temperature). The analysis of the distribution of the transmitted solar wind is used to adjust the cross-shock potential which is not directly measured. It is found that, for typical upstream ion temperatures, acceleration of the ions from the tail of the solar wind distribution is unlikely. Pickup ions with a shell distribution are found to be effectively energized and may be injected into further diffusive acceleration regime. Pre-accelerated ions are efficiently upscaled in energies. A part of these ions is returned to the upstream region where they can further be diffusively accelerated.
This dissertation employs gauge/gravity duality to investigate features
of ( 2 + 1 ) -dimensional quantum gravity in Anti-de Sitter space (AdS)
and its relation to conformal field theory (CFT) in 1 + 1 dimensions.
Concretely, we contribute to research on the frontier of gauge/gravity
with condensed matter as well as the frontier with quantum informa-
tion.
The first research topic of this thesis is motivated by the Kondo
model, which describes the screening of magnetic impurities in metals
by conduction electrons at low temperatures. This process has a de-
scription in the language of string theory via fluctuating surfaces in
spacetime, called branes. At high temperatures the unscreened Kondo
impurity is modelled by a stack of pointlike branes. At low tempera-
tures this stack condenses into a single spherical, two-dimensional brane
which embodies the screened impurity.
This thesis demonstrates how this condensation process is naturally
reinvoked in the holographic D1/D5 system. We find brane configu-
rations mimicking the Kondo impurities at high and low energies and
establish the corresponding brane condensation, where the brane grows
two additional dimensions. We construct supergravity solutions, which
fully take into account the effect of the brane on its surrounding space-
time before and after the condensation takes place. This enables us
to compute the full impurity entropies through which we confirm the
validity of the g-theorem.
The second research topic is rooted in the connection of geometry
with quantum information. The motivation stems from the “complexity
equals volume” proposal, which relates the volume of wormholes to
the cicruit complexity of a thermal quantum state. We approach this
proposal from a pragmatic point of view by studying the properties of
certain volumes in gravity and their description in the CFT.
We study subregion complexities, which are the volumes of the re-
gions subtended by Ryu-Takayanagi (RT) geodesics. On the gravity
side we reveal their topological properties in the vacuum and in ther-
mal states, where they turn out to be temperature independent. On the
field theory side we develop and proof a formula using kinematic space
which computes subregion complexities without referencing the bulk.
We apply our formula to global AdS 3 , the conical defect and a black
hole. While entanglement, i.e. minimal boundary anchored geodesics,
suffices to produce vacuum geometries, for the conical defect we also
need geodesics windings non-trivially around the singularity. The black
hole geometry requires additional thermal contributions.
We develop the formalism of holographic renormalization to compute two-point functions in a holographic Kondo model. The model describes a (0 + 1)-dimensional impurity spin of a gauged SU(N ) interacting with a (1 + 1)-dimensional, large-N , strongly-coupled Conformal Field Theory (CFT). We describe the impurity using Abrikosov pseudo-fermions, and define an SU(N )-invariant scalar operator O built from a pseudo-fermion and a CFT fermion. At large N the Kondo interaction is of the form O\(^{†}\)O, which is marginally relevant, and generates a Renormalization Group (RG) flow at the impurity. A second-order mean-field phase transition occurs in which O condenses below a critical temperature, leading to the Kondo effect, including screening of the impurity. Via holography, the phase transition is dual to holographic superconductivity in (1 + 1)-dimensional Anti-de Sitter space. At all temperatures, spectral functions of O exhibit a Fano resonance, characteristic of a continuum of states interacting with an isolated resonance. In contrast to Fano resonances observed for example in quantum dots, our continuum and resonance arise from a (0 + 1)-dimensional UV fixed point and RG flow, respectively. In the low-temperature phase, the resonance comes from a pole in the Green’s function of the form −i〈O〉\(^{2}\), which is characteristic of a Kondo resonance.
Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enable the detection of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency f\(_{J}\) rather than conventional emission at f\(_{J}\). Here, we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the Josephson frequency f\(_{J}\)/2. The linewidths of emission lines indicate a coherence time of 0.3–4 ns for the f\(_{J}\)/2 line, much shorter than for the f\(_{J}\) line (3–4 ns). These observations strongly point towards the presence of topological gapless Andreev bound states and pave the way for a future HgTe-based platform for topological quantum computation.
We analyze the concomitant spontaneous breaking of translation and conformal symmetries by introducing in a CFT a complex scalar operator that acquires a spatially dependent expectation value. The model, inspired by the holographic Q-lattice, provides a privileged setup to study the emergence of phonons from a spontaneous translational symmetry breaking in a conformal field theory and offers valuable hints for the treatment of phonons in QFT at large. We first analyze the Ward identity structure by means of standard QFT techniques, considering both spontaneous and explicit symmetry breaking. Next, by implementing holographic renormalization, we show that the same set of Ward identities holds in the holographic Q-lattice. Eventually, relying on the holographic and QFT results, we study the correlators realizing the symmetry breaking pattern and how they encode information about the low-energy spectrum.
The electrodynamics of topological insulators (TIs) is described by modified Maxwell’s equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e\(^{2}\)/2E\(_{0}\)hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.
Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to the band-structure properties. Another known source of electronic localization in solids is the Coulomb repulsion in partially filled d or f orbitals, which leads to the formation of local magnetic moments. The combination of these two effects is usually considered of little relevance to strongly correlated materials. Here we show that it represents, instead, the underlying physical mechanism in two of the most important ferromagnets: nickel and iron. In nickel, the van Hove singularity has an unexpected impact on the magnetism. As a result, the electron–electron scattering rate is linear in temperature, in violation of the conventional Landau theory of metals. This is true even at Earth’s core pressures, at which iron is instead a good Fermi liquid. The importance of nickel in models of geomagnetism may have therefore to be reconsidered.
We present the computer code RECOLA2 along with the first NLO electroweak corrections to Higgs production in vector-boson fusion and updated results for Higgs strahlung in the Two-Higgs-Doublet Model and Higgs-Singlet extension of the Standard Model. A fully automated procedure for the generation of tree-level and one-loop matrix elements in general models, including renormalization, is presented. We discuss the application of the Background-Field Method to the extended models. Numerical results for NLO electroweak cross sections are presented for different renormalization schemes in the Two-Higgs-Doublet Model and the Higgs-Singlet extension of the Standard Model. Finally, we present distributions for the production of a heavy Higgs boson.
In recent years many discoveries have been made that reveal a close relation between quantum information and geometry in the context of the AdS/CFT correspondence. In this duality between a conformal quantum field theory (CFT) and a theory of gravity on Anti-de Sitter spaces (AdS) quantum information quantities in CFT are associated with geometric objects in AdS. Subject of this thesis is the examination of this intriguing property of AdS/CFT. We study two central elements of quantum information: subregion complexity -- which is a measure for the effort required to construct a given reduced state -- and the modular Hamiltonian -- which is given by the logarithm of a considered reduced state.
While a clear definition for subregion complexity in terms of unitary gates exists for discrete systems, a rigorous formulation for quantum field theories is not known.
In AdS/CFT, subregion complexity is proposed to be related to certain codimension one regions on the AdS side.
The main focus of this thesis lies on the examination of such candidates for gravitational duals of subregion complexity.
We introduce the concept of \textit{topological complexity}, which considers subregion complexity to be given by the integral over the Ricci scalar of codimension one regions in AdS. The Gauss-Bonnet theorem provides very general expressions for the topological complexity of CFT\(_2\) states dual to global AdS\(_3\), BTZ black holes and conical defects. In particular, our calculations show that the topology of the considered codimension one bulk region plays an essential role for topological complexity.
Moreover, we study holographic subregion complexity (HSRC), which associates the volume of a particular codimension one bulk region with subregion complexity. We derive an explicit field theory expression for the HSRC of vacuum states. The formulation of HSRC in terms of field theory quantities may allow to investigate whether this bulk object indeed provides a concept of subregion complexity on the CFT side. In particular, if this turns out to be the case, our expression for HSRC may be seen as a field theory definition of subregion complexity. We extend our expression to states dual to BTZ black holes and conical defects.
A further focus of this thesis is the modular Hamiltonian of a family of states \(\rho_\lambda\) depending on a continuous parameter \(\lambda\). Here \(\lambda\) may be associated with the energy density or the temperature, for instance.
The importance of the modular Hamiltonian for quantum information is due to its contribution to relative entropy -- one of the very few objects in quantum information with a rigorous definition for quantum field theories.
The first order contribution in \(\tilde{\lambda}=\lambda-\lambda_0\) of the modular Hamiltonian to the relative entropy between \(\rho_\lambda\) and a reference state \(\rho_{\lambda_0}\) is provided by the first law of entanglement. We study under which circumstances higher order contributions in \(\tilde{\lambda}\) are to be expected.
We show that for states reduced to two entangling regions \(A\), \(B\) the modular Hamiltonian of at least one of these regions is expected to provide higher order contributions in \(\tilde{\lambda}\) to the relative entropy if \(A\) and \(B\) saturate the Araki-Lieb inequality. The statement of the Araki-Lieb inequality is that the difference between the entanglement entropies of \(A\) and \(B\) is always smaller or equal to the entanglement entropy of the union of \(A\) and \(B\).
Regions for which this inequality is saturated are referred to as entanglement plateaux. In AdS/CFT the relation between geometry and quantum information provides many examples for entanglement plateaux. We apply our result to several of them, including large intervals for states dual to BTZ black holes and annuli for states dual to black brane geometries.
The topic of this thesis is generalizations of the Anti de Sitter/Conformal Field Theory (AdS/CFT) correspondence, often referred to as holography, and their application to models relevant for condensed matter physics. A particular virtue of AdS/CFT is to map strongly coupled quantum field theories, for which calculations are inherently difficult, to more tractable classical gravity theories. I use this approach to study the crossover between Bose-Einstein condensation (BEC) and the Bardeen-Cooper-Schrieffer (BCS) superconductivity mechanism. I also study the phase transitions between the AdS black hole and AdS soliton spacetime in the presence of disorder. Moreover, I consider a holographic model of a spin impurity interacting with a strongly correlated electron gas, similar to the Kondo model.
In AdS/CFT, the BEC/BCS crossover is modeled by a soliton configuration in the dual geometry and we study the BEC and BCS limits. The backreaction of the matter field on the background geometry is considered, which provides a new approach to study the BEC/BCS crossover. The behaviors of some physical quantities such as depletion of charge density under different strength of backreaction are presented and discussed. Moreover, the backreaction enables us to obtain the effective energy density of the soliton configurations, which together with the surface tension of the solitons leads to an argument for the occurrence of so called snake instability for dark solitons, i.e. for the solitons to form a vortex-like structures.
Disordering strongly coupled and correlated quantum states of matter may lead to new insights into the physics of many body localized (MBL) strongly correlated states, which may occur in the presence of strong disorder. We are interested in potential insulator-metal transitions induced by disorder, and how disorder affects the Hawking-Page phase transition in AdS gravity in general. We introduce a metric ansatz and numerically construct the corresponding disordered AdS soliton and AdS black hole solutions, and discuss the calculation of the free energy in these states.
In the Kondo effect, the rise in resistivity in metals with scarce magnetic impurities at low temperatures can be explained by the RG flow of the antiferromagnetic coupling between the impurity and conduction electrons in CFT. The generalizations to SU(N) in the large N limit make the treatment amenable to the holographic approach. We add a Maxwell term to a previously existing holographic model to study the conductivity of the itinerant electrons. Our goal is to find the log(T) behavior in the DC resistivity. In the probe limit, we introduce junction conditions to connect fields crossing the defect. We then consider backreactions, which give us a new metric ansatz and new junction conditions for the gauge fields.
Paramagnetic heavy fermion insulators consist of fully occupied quasiparticle bands inherent to Fermi liquid theory. The gap emergence below a characteristic temperature is the ultimate sign of coherence for a many-body system, which in addition can induce a non-trivial band topology. Here, we demonstrate a simple and efficient method to compare a model study and an experimental result for heavy fermion insulators. The temperature dependence of the gap formation in both local moment and mixed valence regimes is captured within the dynamical mean field (DMFT) approximation to the periodic Anderson model (PAM). Using the topological coherence temperature as the scaling factor and choosing the input parameter set within the mixed valence regime, we can unambiguously link the theoretical energy scales to the experimental ones. As a particularly important result, we find improved consistency between the scaled DMFT density of states and the photoemission near-gap spectra of samarium hexaboride (SmB\(_{6}\)).
The production of a neutral and a charged vector boson with subsequent decays into three charged leptons and a neutrino is a very important process for precision tests of the Standard Model of elementary particles and in searches for anomalous triple-gauge-boson couplings. In this article, the first computation of next-to-leading-order electroweak corrections to the production of the four-lepton final states μ\(^{+}\)μ\(^{−}\)e\(^{+}\)ν\(_{e}\), μ\(^{+}\)μ\(^{−}\)e\(^{−}\)ν\(_{e}\), μ\(^{+}\)μ\(^{−}\)μ\(^{+}\)ν\(_{μ}\), and μ\(^{+}\)μ\(^{−}\)μ\(^{−}\)ν\(_{μ}\) at the Large Hadron Collider is presented. We use the complete matrix elements at leading and next-to-leading order, including all off-shell effects of intermediate massive vector bosons and virtual photons. The relative electroweak corrections to the fiducial cross sections from quark-induced partonic processes vary between −3% and −6%, depending significantly on the event selection. At the level of differential distributions, we observe large negative corrections of up to −30% in the high-energy tails of distributions originating from electroweak Sudakov logarithms. Photon-induced contributions at next-to-leading order raise the leading-order fiducial cross section by +2%. Interference effects in final states with equal-flavour leptons are at the permille level for the fiducial cross section, but can lead to sizeable effects in off-shell sensitive phase-space regions.
Complete NLO corrections to W\(^{+}\)W\(^{+}\) scattering and its irreducible background at the LHC
(2017)
The process pp → μ\(^{+}\)ν\(_{μ}\)e\(^{+}\)ν\(_{e}\)jj receives several contributions of different orders in the strong and electroweak coupling constants. Using appropriate event selections, this process is dominated by vector-boson scattering (VBS) and has recently been measured at the LHC. It is thus of prime importance to estimate precisely each contribution. In this article we compute for the first time the full NLO QCD and electroweak corrections to VBS and its irreducible background processes with realistic experimental cuts. We do not rely on approximations but use complete amplitudes involving two different orders at tree level and three different orders at one-loop level. Since we take into account all interferences, at NLO level the corrections to the VBS process and to the QCD-induced irreducible background process contribute at the same orders. Hence the two processes cannot be unambiguously distinguished, and all contributions to the μ\(^{+}\)ν\(_{μ}\)e\(^{+}\)ν\(_{e}\)jj final state should be preferably measured together.