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Institute
Sonstige beteiligte Institutionen
- Arizona State University, Tempe, Arizona, USA (1)
- Fraunhofer-Institute for Applied Optics and Precision Engineering IOF Jena, Germany (1)
- Friedrich Schiller University Jena, Germany (1)
- LMU München (1)
- Max Planck School of Photonics Jena, Germany (1)
- National Institute for Materials Science, Tsukuba, Japan (1)
- University of Oldenburg, Germany (1)
- University of Science and Technology of China, Hefei, China (1)
- Universität Bielefeld (1)
- Wilhelm Conrad Röntgen-Center for Complex Material Systems, Würzburg (1)
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.
This doctoral thesis investigates magneto-optical properties of mercury telluride layers grown tensile strained on cadmium telluride substrates. Here, layer thicknesses start above the usual quantum well thickness of about 20 nm and have a upper boundary around 100 nm due to lattice relaxation effects. This kind of layer system has been attributed to the material class of three-dimensional topological insulators in numerous publications. This class stands out due to intrinsic boundary states which cross the energetic band gap of the layer's bulk.
In order to investigate the band structure properties in a narrow region around the Fermi edge, including possible boundary states, the method of highly precise time-domain Terahertz polarimetry is used. In the beginning, the state of the art of Teraherz technology at the start of this project is discussed, moving on to a detailed description and characterization of the self-built measurement setup. Typical standard deviation of a polarization rotation or ellipticity measurement are on the order of 10 to 100 millidegrees, according to the transmission strength through investigated samples. A range of polarization spectra, depending on external magnetic fields up to 10 Tesla, can be extracted from the time-domain signal via Fourier transformation.
The identification of the actual band structure is done by modeling possible band structures by means of the envelope function approximation within the framework of the k·p method. First the bands are calculated based on well-established model parameters and from them the possible optical transitions and expected ellipticity spectra, all depending on external magnetic fields and the layer's charge carrier concentration. By comparing expected with measured spectra, the validity of k·p models with varying depths of detail is analyzed throughout this thesis. The rich information encoded in the ellipitcity spectra delivers key information for the attribution of single optical transitions, which are not part of pure absorption spectroscopy. For example, the sign of the ellipticity signals is linked to the mix of Landau levels which contribute to an optical transition, which shows direct evidence for bulk inversion asymmetry effects in the measured spectra.
Throughout the thesis, the results are compared repeatedly with existing publications on the topic. It is shown that the models used there are often insufficient or, in worst case, plainly incorrect. Wherever meaningful and possible without greater detours, the differences to the conclusions that can be drawn from the k·p model are discussed.
The analysis ends with a detailed look on remaining differences between model and measurement. It contains the quality of model parameters as well as different approaches to integrate electrostatic potentials that exist in the structures into the model.
An outlook on possible future developments of the mercury cadmium telluride layer systems, as well as the application of the methods shown here onto further research questions concludes the thesis.
Excitons in atomically thin transition-metal dichalcogenides (TMDs) have been established as an attractive platform to explore polaritonic physics, owing to their enormous binding energies and giant oscillator strength. Basic spectral features of exciton polaritons in TMD microcavities, thus far, were conventionally explained via two-coupled-oscillator models. This ignores, however, the impact of phonons on the polariton energy structure. Here we establish and quantify the threefold coupling between excitons, cavity photons, and phonons. For this purpose, we employ energy-momentum-resolved photoluminescence and spatially resolved coherent two-dimensional spectroscopy to investigate the spectral properties of a high-quality-factor microcavity with an embedded WSe\(_2\) van-der-Waals heterostructure at room temperature. Our approach reveals a rich multi-branch structure which thus far has not been captured in previous experiments. Simulation of the data reveals hybridized exciton-photon-phonon states, providing new physical insight into the exciton polariton system based on layered TMDs.
Plasmonic nanostructures are considered promising candidates for essential components of integrated quantum technologies because of their ability to efficiently localize broad-band electromagnetic fields on the nanoscale. The resulting local near field can be understood as a spatial superposition of spectrally different plasmon-polariton modes due to the spectrally broad optical excitation, and thus can be described as a classical wave packet. Since plasmon polaritons, in turn, can transmit and receive non-classical light states, the exciting question arises to what extent they have to be described as quantum mechanical wave packets, i.e. as a superposition of different quantum states.
But how to probe, characterize and eventually manipulate the quantum state of such plasmon polaritons? Up to now, probing at room temperatures relied completely on analyzing quantum optical properties of the corresponding in-going and out-going far-field photon modes. However, these methods so far only allow a rather indirect investigation of the plasmon-polariton quantum state by means of transfer into photons. Moreover, these indirect methods lack spatial resolution and therefore do not provide on-site access to the plasmon-polariton quantum state. However, since the spectroscopic method of coherent two-dimensional (2D) nanoscopy offers the capability to follow the plasmon-
polariton quantum state both in Hilbert space and in space and time domain a complete characterization of the plasmon polariton is possible.
In this thesis a versatile coherent 2D nanoscopy setup is presented combining spectral tunability and femtosecond time resolution with spatial resolution on the nanometer scale due to the detection of optically excited nonlinear emitted electrons via photoemission electron microscopy (PEEM). Optical excitation by amplitude- and phase-shaped, systematically-modified and interferometric-stable multipulse sequences is realized, and characterized via Fourier-transform spectral interferometry (FTSI). This linear technique enables efficient data acquisition in parallel to a simultaneously performed experiment. The full electric-field reconstruction of every generated multipulse sequence is used to analyze the effect of non-ideal pulse sequences on the two-dimensional spectral data of population-based multidimensional spectroscopy methods like, e.g., the coherent 2D nanoscopy applied in this thesis. Investigation of the spatially-resolved nonlinear electron emission yield from plasmonic gold nanoresonators by coherent 2D nanoscopy requires a quasi-particle treatment of the addressed plasmon-polariton mode and development of a quantum model to adequately describe the plasmon-assisted multi-quantum electron emission from nanostructures. Good agreement between simulated and experimental data enables to connect certain spectral features to superpositions of non-adjacent plasmon-polariton quantum states, i.e, non-adjacent occupation-number states of the underlying quantized, harmonic oscillator, thus direct probing of the plasmon-polariton quantum wave packet at the location of the nanostructure.
This is a necessary step to locally control and manipulate the plasmon-polariton quantum state and thus of general interest for the realization of nanoscale quantum optical devices.
Magnetic systems underlie the physics of quantum mechanics when reaching the limit of few or even single atoms. This behavior limits the minimum size of magnetic bits in data storage devices as spontaneous switching of the magnetization leads to the loss of information. On the other hand, exactly these quantum mechanic properties allow to use such systems in quantum computers. Proposals to realize qubits involve the spin states of single atoms as well as topologically protected Majorana zero modes, that emerge in coupled systems of magnetic atoms in proximity to a superconductor. In order to implement and control the proposed applications, a detailed understanding of atomic spins and their interaction with the environment is required.
In this thesis, two different systems of magnetic adatoms coupled to metallic and superconducting surfaces are studied by means of scanning tunneling microscopy (STM) and spectroscopy: Co atoms on the clean Cu(111) were among the first systems exhibiting signatures of the Kondo effect in an individual atom. Yet, a recent theoretical work proposed an alternative interpretation of these early experimental results, involving a newly described many-body state. Spin-averaged and -polarized experiments in high magnetic fields presented in this thesis confirm effects beyond the Kondo effect that determine the physics in these Co atoms and suggest a potentially even richer phenomenology than proposed by theory.
The second studied system are single and coupled Fe atoms on the superconducting Nb(110) surface. Magnetic impurities on superconducting surfaces locally induce Yu-Shiba-Rusinov (YSR) states inside the superconducting gap due to their pair breaking potential. Coupled systems of such impurities exhibit YSR bands and, if the bands cross the Fermi level such that the band structure is inverted, host Majorana zero modes. Using the example of Fe atoms on Nb(110), the YSR states’ dependence on the adatom–substrate interaction as well as the interatomic YSR state coupling is investigated. In the presence of oxygen on the Nb surface, the adatom–substrate interaction is shown to be heavily modified and the YSR states are found to undergo a quantum phase transition, which can be directly linked to a modified Kondo screening.
STM tips functionalized with CO molecules allow to resolve self-assembled one-dimensional chains of Fe atoms on the clean Nb(110) surface to study the YSR states’ coupling. Mapping out the states’ wave functions reveals their symmetry, which is shown to alter as a function of the states’ energy and number of atoms in the chain. These experimental results are reproduced in a simple tight-binding model, demonstrating a straightforward possibility to describe also more complex YSR systems toward engineered, potentially topologically non-trivial states.
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.
A plethora of novel material concepts are currently being investigated in the condensed matter research community. Some of them hold promise to shape our everyday world in a way that silicon-based semiconductor materials and the related development of semiconductor devices have done in the past. In this regard, the last decades have witnessed an explosion of studies concerned with so called ‘’quantum materials’’ with emerging novel functionalities. These could eventually lead to new generations of electronic and/or spintronic devices. One particular material class, the so called topological materials, play a central role. As far as their technological applicability is concerned, however, they are still facing outstanding challenges to date.
Predicted for the first time in 2005 and experimentally verified in 2007, two-dimensional topological insulators (2D TIs) (a.k.a. quantum spin Hall insulators) exhibit the outstanding property of hosting spin-polarized metallic states along the boundaries of the insulating 2D bulk material, which are protected from elastic single-particle backscattering and give rise to the quantum spin Hall effect (QSHE). Owing to these peculiar properties the QSHE holds promise for dissipationless charge and/or spin transport. However, also in today’s best 2D TIs the observation of the QSHE is still limited to cryogenic temperatures of maximum 100 K. Here, the discovery of bismuthene on SiC(0001) has marked a milestone towards a possible realization of the QSHE at or beyond room-temperature owing to the massively increased electronic bulk energy gap on the order of 1 eV. This thesis is devoted to and motivated by the goal of advancing its synthesis and to build a deeper understanding of its one-particle and two-particle electronic properties that goes beyond prior work.
Regarding the aspect of material synthesis, an improved growth procedure for bismuthene is elaborated that increases the domain size of the material considerably (by a factor of ≈ 3.2 - 6.5 compared to prior work). The improved film quality is an important step towards any future device application of bismuthene, but also facilitates all further basic studies of this material.
Moreover, the deposition of magnetic transition metals (Mn and Co) on bismuthene is investigated. Thereby, the formation of ordered magnetic Bi-Mn/Co alloys is realized, their structure is resolved with scanning tunneling microscopy (STM), and their pristine electronic properties are resolved with scanning tunneling spectroscopy (STS) and photoemission spectroscopy (PES). It is proposed that these ordered magnetic Bi-Mn/Co-alloys offer the potential to study the interplay between magnetism and topology in bismuthene in the future.
In this thesis, a wide variety of spectroscopic techniques are employed that aim to build an understanding of the single-particle, as well as two-particle level of description of bismuthene's electronic structure. The techniques involve STS and angle-resolved PES (ARPES) on the one hand, but also optical spectroscopy and time-resolved ARPES (trARPES), on the other hand. Moreover, these experiments are accompanied by advanced numerical modelling in form of GW and Bethe-Salpeter equation calculations provided by our theoretical colleagues. Notably, by merging many experimental and theoretical techniques, this work sets a benchmark for electronic structure investigations of 2D materials in general.
Based on the STS studies, electronic quasi-particle interferences in quasi-1D line defects in bismuthene that are reminiscent of Fabry-Pérot states are discovered. It is shown that they point to a hybridization of two pairs of helical boundary modes across the line defect, which is accompanied by a (partial) lifting of their topological protection against elastic single-particle backscattering.
Optical spectroscopy is used to reveal bismuthene's two-particle elecronic structure. Despite its monolayer thickness, a strong optical (two-particle) response due to enhanced electron-hole Coulomb interactions is observed. The presented combined experimental and theoretical approach (including GW and Bethe-Salpeter equation calculations) allows to conclude that two prominent optical transitions can be associated with excitonic transitions derived from the Rashba-split valence bands of bismuthene. On a broader scope this discovery might promote further experiments to elucidate links of excitonic and topological physics.
Finally, the excited conduction band states of bismuthene are mapped in energy and momentum space employing trARPES on bismuthene for the first time. The direct and indirect band gaps are succesfully extracted and the effect of excited charge carrier induced gap-renormalization is observed. In addition, an exceptionally fast excited charge carrier relaxation is identified which is explained by the presence of a quasi-metallic density of states from coupled topological boundary states of domain boundaries.
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.
This paper reports a search for triboson \({W^\pm}{W^\pm}{W^\mp}\) production in two decay channels (\({W^\pm}{W^\pm}{W^\mp}\) → \({ℓ^\pm}{νℓ^\pm}{νℓ^\mp}{ν}\) and \({W^\pm}{W^\pm}{W^\mp}\) → \({ℓ^\pm}{νℓ^\pm}{νjj}\) with \(ℓ=e,μ\)) in proton-proton collision data corresponding to an integrated luminosity of 20.3 fb\(^{−1}\) at a centre-of-mass energy of 8 TeV with the ATLAS detector at the Large Hadron Collider. Events with exactly three charged leptons, or two leptons with the same electric charge in association with two jets, are selected. The total number of events observed in data is consistent with the Standard Model (SM) predictions. The observed 95% confidence level upper limit on the SM \({W^\pm}{W^\pm}{W^\mp}\) production cross section is found to be 730 fb with an expected limit of 560 fb in the absence of SM \({W^\pm}{W^\pm}{W^\mp}\) production. Limits are also set on \(WWWW\) anomalous quartic gauge couplings.
A measurement of the calorimeter response to isolated charged hadrons in the ATLAS detector at the LHC is presented. This measurement is performed with 3.2 nb\(^{−1}\) of proton–proton collision data at \(\sqrt{s}\) = 7 TeV from 2010 and 0.1 nb\(^{−1}\) of data at \(\sqrt{s}\) = 8 TeV from 2012. A number of aspects of the calorimeter response to isolated hadrons are explored. After accounting for energy deposited by neutral particles, there is a 5% discrepancy in the modelling, using various sets of GEANT4 hadronic physics models, of the calorimeter response to isolated charged hadrons in the central calorimeter region. The description of the response to anti-protons at low momenta is found to be improved with respect to previous analyses. The electromagnetic and hadronic calorimeters are also examined separately, and the detector simulation is found to describe the response in the hadronic calorimeter well. The jet energy scale uncertainty and correlations in scale between jets of different momenta and pseudorapidity are derived based on these studies. The uncertainty is 2–5% for jets with transverse momenta above 2 TeV, where this method provides the jet energy scale uncertainty for ATLAS.
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.
This thesis examines the electronic properties of two materials that promise the realization and observation of novel exotic quantum phenomena. For this purpose, angle-resolved photoemission forms the experimental basis for the investigation of the electronic properties. Furthermore, the magnetic order is investigated utilizing X-ray dichroism measurements.
First, the bulk and surface electronic structure of epitaxially grown HgTe in its three-dimensional topological insulator phase is investigated. In this study, synchrotron radiation is used to address the three-dimensional band structure and orbital composition of the bulk states by employing photon-energy-dependent and polarization-dependent measurements, respectively. In addition, the topological surface state is examined on in situ grown samples using a laboratory photon source. The resulting data provide a means to experimentally localize the bulk band inversion in momentum space and to evidence the momentum-dependent change in the orbital character of the inverted bulk states.
Furthermore, a rather new series of van der Waals compounds, (MnBi\(_2\)Te\(_4\))(Bi\(_2\)Te\(_3\))\(_n\), is investigated. First, the magnetic properties of the first two members of the series, MnBi\(_2\)Te\(_4\) and MnBi\(_4\)Te\(_7\), are studied via X-ray absorption-based techniques. The topological surface state on the two terminations of MnBi\(_4\)Te\(_7\) is analyzed using circular dichroic, photon-energy-dependent, and spin-resolved photoemission. The topological state on the (MnBi\(_2\)Te\(_4\))-layer termination shows a free-standing Dirac cone with its Dirac point located in the bulk band gap. In contrast, on the (Bi\(_2\)Te\(_3\))-layer termination the surface state hybridizes with the bulk valences states, forming a spectral weight gap, and exhibits a Dirac point that is buried within the bulk continuum. Lastly, the lack of unambiguous evidence in the literature showing a temperature-dependent mass gap opening in these magnetic topological insulators is discussed through MnBi\(_2\)Te\(_4\).
Two-dimensional (2D) topological insulators are a new class of materials with properties that are
promising for potential future applications in quantum computers. For example, stanene represents
a possible candidate for a topological insulator made of Sn atoms arranged in a hexagonal
lattice. However, it has a relatively fragile low-energy spectrum and sensitive topology. Therefore,
to experimentally realize stanene in the topologically non-trivial phase, a suitable substrate
that accommodates stanene without compromising these topological properties must be found.
A heterostructure consisting of a SiC substrate with a buffer layer of adsorbed group-III elements
constitutes a possible solution for this problem. In this work, 2D adatom systems of Al and In
were grown epitaxially on SiC(0001) and then investigated structurally and spectroscopically by
scanning tunneling microscopy (STM) and photoelectron spectroscopy.
Al films in the high coverage regime \( (\Theta_{ML}\approx2\) ML\( ) \) exhibit unusually large, triangular- and
rectangular-shaped surface unit cells. Here, the low-energy electron diffraction (LEED)
pattern is brought into accordance with the surface topography derived from STM. Another Al
reconstruction, the quasi-one-dimensional (1D) Al phase, exhibits a striped surface corrugation,
which could be the result of the strain imprinted by the overlayer-substrate lattice mismatch.
It is suggested that Al atoms in different surface areas can occupy hexagonal close-packed and
face-centered cubic lattice sites, respectively, which in turn lead to close-packed transition regions
forming the stripe-like corrugations. On the basis of the well-known herringbone reconstruction
from Au(111), a first structural model is proposed, which fits well to the structural data from
STM. Ultimately, however, thermal treatments of the sample could not generate lower coverage
phases, i.e. in particular, a buffer layer structure.
Strong metallic signatures are found for In high coverage films \( (\Theta_{ML}\approx3\) to \(2\) ML\() \) by
scanning tunneling spectroscopy (STS) and angle-resolved photoelectron spectroscopy (ARPES),
which form a \( (7\times7) \), \( (6\times4\sqrt{3}) \), and \( (4\sqrt{3}\times4\sqrt{3}) \) surface reconstruction. In all these In phases
electrons follow the nearly-free electron model. Similar to the Al films, thermal treatments could
not obtain the buffer layer system.
Surprisingly, in the course of this investigation a triangular In lattice featuring a \( (1\times1) \)
periodicity is observed to host massive Dirac-like bands at \( K/K^{\prime} \) in ARPES. Based on this
strong electronic similarity with graphene at the Brillouin zone boundary, this new structure is
referred to as \textit{indenene}. An extensive theoretical analysis uncovers the emergence of an electronic
honeycomb network based on triangularly arranged In \textit{p} orbitals. Due to strong atomic spin-orbit
coupling and a comparably small substrate-induced in-plane inversion symmetry breaking this
material system is rendered topologically non-trivial. In indenene, the topology is intimately
linked to a bulk observable, i.e., the energy-dependent charge accumulation sequence within the
surface unit cell, which is experimentally exploited in STS to confirm the non-trivial topological
character. The band gap at \( K/K^{\prime} \), a signature of massive Dirac fermions, is estimated by
ARPES to approximately 125 meV. Further investigations by X-ray standing wave, STM, and
LEED confirm the structural properties of indenene. Thus, this thesis presents the growth and
characterization of the novel quantum spin Hall insulator material indenene.
Breaking inversion symmetry in crystalline solids enables the formation of spin-polarized electronic states by spin-orbit coupling without the need for magnetism. A variety of interesting physical phenomena related to this effect have been intensively investigated in recent years, including the Rashba effect, topological insulators and Weyl semimetals. In this work, the interplay of inversion symmetry breaking and spin-orbit coupling and, in particular their general influence on the character of electronic states, i.e., on the spin and orbital degrees of freedom, is investigated experimentally. Two different types of suitable model systems are studied: two-dimensional surface states for which the Rashba effect arises from the inherently broken inversion symmetry at the surface, and a Weyl semimetal, for which inversion symmetry is broken in the three-dimensional crystal structure. Angle-resolved photoelectron spectroscopy provides momentum-resolved access to the spin polarization and the orbital composition of electronic states by means of photoelectron spin detection and dichroism with polarized light. The experimental results shown in this work are also complemented and supported by ab-initio density functional theory calculations and simple model considerations.
Altogether, it is shown that the breaking of inversion symmetry has a decisive influence on the Bloch wave function, namely, the formation of an orbital angular momentum. This mechanism is, in turn, of fundamental importance both for the physics of the surface Rashba effect and the topology of the Weyl semimetal TaAs.
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.
Ratios of top-quark pair to \(Z\)-boson cross sections measured from proton-proton collisions at the LHC centre-of-mass energies of \(\sqrt{s}\) = 13 TeV, 8 TeV, and 7 TeV are presented by the ATLAS Collaboration. Single ratios, at a given \(\sqrt{s}\) for the two processes and at different \(\sqrt{s}\) for each process, as well as double ratios of the two processes at different \(\sqrt{s}\), are evaluated. The ratios are constructed using previously published ATLAS measurements of the \({t\overline{t}}\) and \(Z\)-boson production cross sections, corrected to a common phase space where required, and a new analysis of \(Z\) → ℓ\(^+\)ℓ\(^-\) where ℓ = \(e, µ\) at \(\sqrt{s}\) = 13 TeV performed with data collected in 2015 with an integrated luminosity of 3.2 fb\(^−1\). Correlations of systematic uncertainties are taken into account when evaluating the uncertainties in the ratios. The correlation model is also used to evaluate the combined cross section of the \(Z\) → \(e\)\(^+\)\(e\)\(^−\) and the \(Z\) → \(µ\)\(^+\)\(µ\)\(^−\) channels for each \(\sqrt{s}\) value. The results are compared to calculations performed at next-to-next-to-leading-order accuracy using recent sets of parton distribution functions. The data demonstrate significant power to constrain the gluon distribution function for the Bjorken-\(x\) values near 0.1 and the light-quark sea for \(x\) < 0.02.
Same- and opposite-sign charge asymmetries are measured in lepton+jets \({t\overline{t}}\) events in which a \(b\)-hadron decays semileptonically to a soft muon, using data corresponding to an integrated luminosity of 20.3 fb\(^{−1}\) from proton-proton collisions at a centre-of-mass energy of \(\sqrt{s}\) = 8 TeV collected with the ATLAS detector at the Large Hadron Collider at CERN. The charge asymmetries are based on the charge of the lepton from the top-quark decay and the charge of the soft muon from the semileptonic decay of a \(b\)-hadron and are measured in a fiducial region corresponding to the experimental acceptance. Four CP asymmetries (one mixing and three direct) are measured and are found to be compatible with zero and consistent with the Standard Model.
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.
A measurement of the \(ZZ\) production cross section in the \(ℓ^−ℓ^+ℓ^{′−}ℓ^{′+}\) and \(ℓ^−ℓ^+{ν\overline{ν}}\) channels (ℓ = e, µ) in proton-proton collisions at \(\sqrt{s}\) = 8TeV at the Large Hadron Collider at CERN, using data corresponding to an integrated luminosity of 20.3 fb\(^{−1}\) collected by the ATLAS experiment in 2012 is presented. The fiducial cross sections for \(ZZ\) → \(ℓ^−ℓ^+ℓ^{′−}ℓ^{′+}\) and \(ZZ\) → \(ℓ^−ℓ^+{ν\overline{ν}}\) are measured in selected phase-space regions. The total cross section for \(ZZ\) events produced with both \(Z\) bosons in the mass range 66 to 116GeV is measured from the combination of the two channels to be 7.3 ± 0.4(stat) ± 0.3 (syst)\(^{−0.2}_{−0.1}\) (lumi) pb, which is consistent with the Standard Model prediction of 6.6\(^{+0.7}_{−0.6}\) pb. The differential cross sections in bins of various kinematic variables are presented. The differential event yield as a function of the transverse momentum of the leading \(Z\) boson is used to set limits on anomalous neutral triple gauge boson couplings in \(ZZ\) production.
A measurement of the \({t\overline{t}}Z\) and \({t\overline{t}}W\) production cross sections in final states with either two same-charge muons, or three or four leptons (electrons or muons) is presented. The analysis uses a data sample of proton–proton collisions at \(\sqrt{s}\) = 13 TeV recorded with the ATLAS detector at the Large Hadron Collider in 2015, corresponding to a total integrated luminosity of 3.2 fb\(^{−1}\). The inclusive cross sections are extracted using likelihood fits to signal and control regions, resulting in \(\sigma_{{t\overline{t}}Z}\) = 0.9 ± 0.3 pb and \(\sigma_{{t\overline{t}}W}\) = 1.5 ± 0.8 pb, in agreement with the Standard Model predictions.
Realization and Spectroscopy of the Quantum Spin Hall Insulator Bismuthene on Silicon Carbide
(2022)
Topological matter is one of the most vibrant research fields of contemporary solid state physics since the theoretical prediction of the quantum spin Hall effect in graphene in 2005. Quantum spin Hall insulators possess a vanishing bulk conductivity but symmetry-protected, helical edge states that give rise to dissipationless charge transport.
The experimental verification of this exotic state of matter in 2007 lead to a boost of research activity in this field, inspired by possible ground-breaking future applications.
However, the use of the quantum spin Hall materials available to date is limited to cryogenic temperatures owing to their comparably small bulk band gaps.
In this thesis, we follow a novel approach to realize a quantum spin Hall material with a large energy gap and epitaxially grow bismuthene, i.e., Bi atoms adopting a honeycomb lattice, in a \((\sqrt{3}\times\sqrt{3})\) reconstruction on the semiconductor SiC(0001). In this way, we profit both from the honeycomb symmetry as well as the large spin-orbit coupling of Bi, which, in combination, give rise to a topologically non-trivial band gap on the order of one electronvolt.
An in-depth theoretical analysis demonstrates that the covalent bond between the Si and Bi atoms is not only stabilizing the Bi film but is pivotal to attain the quantum spin Hall phase.
The preparation of high-quality, unreconstructed SiC(0001) substrates sets the basis for the formation of bismuthene and requires an extensive procedure in ultra-pure dry H\(_2\) gas. Scanning tunneling microscopy measurements unveil the (\(1\times1\)) surface periodicity and smooth terrace planes, which are suitable for the growth of single Bi layers by means of molecular beam epitaxy. The chemical configuration of the resulting Bi film and its oxidation upon exposure to ambient atmosphere are inspected with X-ray photoelectron spectroscopy.
Angle-resolved photoelectron spectroscopy reveals the excellent agreement of probed and calculated band structure. In particular, it evidences a characteristic Rashba-splitting of the valence bands at the K point. Scanning tunneling spectroscopy probes signatures of this splitting, as well, and allows to determine the full band gap with a magnitude of \(E_\text{gap}\approx0.8\,\text{eV}\).
Constant-current images and local-density-of-state maps confirm the presence of a planar honeycomb lattice, which forms several domains due to different, yet equivalent, nucleation sites of the (\(\sqrt{3}\times\sqrt{3}\))-Bi reconstruction.
Differential conductivity measurements demonstrate that bismuthene edge states evolve at atomic steps of the SiC substrate. The probed, metallic local density of states is in agreement with the density of states expected from the edge state's energy dispersion found in density functional theory calculations - besides a pronounced dip at the Fermi level.
By means of temperature- and energy-dependent tunneling spectroscopy it is shown that the spectral properties of this suppressed density of states are successfully captured in the framework of the Tomonaga-Luttinger liquid theory and most likely originate from enhanced electronic correlations in the edge channel.
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.
Measurements of top quark spin observables in \(t\overline{t}\) events are presented based on 20.2 fb\(^{−1}\) of \(\sqrt{s}\) = 8 TeV proton-proton collisions recorded with the ATLAS detector at the LHC. The analysis is performed in the dilepton final state, characterised by the presence of two isolated leptons (electrons or muons). There are 15 observables, each sensitive to a different coefficient of the spin density matrix of \(t\overline{t}\) production, which are measured independently. Ten of these observables are measured for the first time. All of them are corrected for detector resolution and acceptance effects back to the parton and stable-particle levels. The measured values of the observables at parton level are compared to Standard Model predictions at next-to-leading order in QCD. The corrected distributions at stable-particle level are presented and the means of the distributions are compared to Monte Carlo predictions. No significant deviation from the Standard Model is observed for any observable.
We present charged-particle distributions sensitive to the underlying event, measured by the ATLAS detector in proton-proton collisions at a centre-of-mass energy of 13 TeV, in low-luminosity Large Hadron Collider fills corresponding to an integrated luminosity of 1.6 nb\(^{−1}\). The distributions were constructed using charged particles with absolute pseudorapidity less than 2.5 and with transverse momentum greater than 500 MeV, in events with at least one such charged particle with transverse momentum above 1 GeV. These distributions characterise the angular distribution of energy and particle flows with respect to the charged particle with highest transverse momentum, as a function of both that momentum and of charged-particle multiplicity. The results have been corrected for detector effects and are compared to the predictions of various Monte Carlo event generators, experimentally establishing the level of underlying-event activity at LHC Run 2 energies and providing inputs for the development of event generator modelling. The current models in use for UE modelling typically describe this data to 5% accuracy, compared with data uncertainties of less than 1%.
A measurement of the \(t\)-channel single-top-quark and single-top-antiquark production cross-sections in the lepton+jets channel is presented, using 3.2 fb\(^{−1}\) of proton-proton collision data at a centre-of-mass energy of 13 TeV, recorded with the ATLAS detector at the LHC in 2015. Events are selected by requiring one charged lepton (electron or muon), missing transverse momentum, and two jets with high transverse momentum, exactly one of which is required to be \(b\)-tagged. Using a binned maximum-likelihood fit to the discriminant distribution of a neural network, the cross-sections are determined to be \({σ(tq)}\) = 156 ± 5 (stat.) ± 27 (syst.) ± 3 (lumi.) pb for single top-quark production and \(σ(\overline{t}q)\) = 91 ± 4 (stat.) ± 18 (syst.) ± 2 (lumi.) pb for single top-antiquark production, assuming a top-quark mass of 172.5 GeV. The cross-section ratio is measured to be \(R_{t}\) = \(σ(tq)/σ(\overline{t}q)\) = 1.72 ± 0.09 (stat.) ± 0.18 (syst.). All results are in agreement with Standard Model predictions.
This work consists of two parts. On the one hand, it describes simulation and
measurement of the effect of contaminations of the detector gas on the performance
of particle detectors, with special focus on Micromegas detectors. On the other
hand, it includes the setup of a production site for the finalization of drift panels
which are going to be used in the ATLAS NSW. The first part augments these
two parts to give an introduction into the theoretical foundations of gaseous particle
detectors.
Two-dimensional triangular lattices of group IV adatoms on semiconductor substrates provide a rich playground for the investigation of Mott-Hubbard physics. The possibility to combine various types of adatoms and substrates makes members of this material class versatile model systems to study the influence of correlation strength, band filling and spin-orbit coupling on the electronic structure - both experimentally and with dedicated many-body calculation techniques. The latter predict exotic ground states such as chiral superconductivity or spin liquid behavior for these frustrated lattices, however, experimental confirmation is still lacking. In this work, three different systems, namely the \(\alpha\)-phases of Sn/SiC(0001), Pb/Si(111), and potassium-doped Sn/Si(111) are investigated with scanning tunneling microscopy and photoemission spectroscopy in this regard. The results are potentially relevant for spintronic applications or quantum computing.
For the novel group IV triangular lattice Sn/SiC(0001), a combined experimental and theoretical study reveals that the system features surprisingly strong electronic correlations because they are boosted by the substrate through its partly ionic character and weak screening capabilities. Interestingly, the spectral function, measured for the first time via angle-resolved photoemission, does not show any additional superstructure beyond the intrinsic \(\sqrt{3} \times \sqrt{3} R30^{\circ}\) reconstruction, thereby raising curiosity regarding the ground-state spin pattern.
For Pb/Si(111), preceding studies have noted a phase transition of the surface reconstruction from \(\sqrt{3} \times \sqrt{3} R30^{\circ}\) to \(3 \times 3\) at 86 K. In this thesis, investigations of the low-temperature phase with high-resolution scanning tunneling microscopy and spectroscopy unveil the formation of a charge-ordered ground state. It is disentangled from a concomitant structural rearrangement which is found to be 2-up/1-down, in contrast to previous predictions. Applying an extended variational cluster approach, a phase diagram of local and nonlocal Coulomb interactions is mapped out. Based on a comparison of theoretical spectral functions with scattering vectors found via quasiparticle interference, Pb/Si(111) is placed in said phase diagram and electronic correlations are found to be the driving force of the charge-ordered state.
In order to realize a doped Mott insulator in a frustrated geometry, potassium was evaporated onto the well-known correlated Sn/Si(111) system. Instead of the expected insulator-to-metal transition, scanning tunneling spectroscopy data indicates that the electronic structure of Sn/Si(111) is only affected locally around potassium atoms while a metallization is suppressed. The potassium atoms were found to be adsorbed on empty \(T_4\) sites of the substrate which eventually leads to the formation of two types of K-Sn alloys with a relative potassium content of 1/3 and 1/2, respectively. Complementary measurements of the spectral function via angle-resolved photoemission reveal that the lower Hubbard band of Sn/Si(111) gradually changes its shape upon potassium deposition. Once the tin and potassium portion on the surface are equal, this evolution is complete and the system can be described as a band insulator without the need to include Coulomb interactions.
To probe the \(W tb\) vertex structure, top-quark and \(W\)-boson polarisation observables are measured from \(t\)-channel single-top-quark events produced in proton-proton collisions at a centre-of-mass energy of 8 TeV. The dataset corresponds to an integrated luminosity of 20.2 fb\(^{−1}\), recorded with the ATLAS detector at the LHC. Selected events contain one isolated electron or muon, large missing transverse momentum and exactly two jets, with one of them identified as likely to contain a \(b\)-hadron. Stringent selection requirements are applied to discriminate \(t\)-channel single-top-quark events from background. The polarisation observables are extracted from asymmetries in angular distributions measured with respect to spin quantisation axes appropriately chosen for the top quark and the \(W\) boson. The asymmetry measurements are performed at parton level by correcting the observed angular distributions for detector effects and hadronisation after subtracting the background contributions. The measured top-quark and \(W\)-boson polarisation values are in agreement with the Standard Model predictions. Limits on the imaginary part of the anomalous coupling \(g_R\) are also set from model independent measurements.
The production of a \(Z\) boson and a photon in association with a high-mass dijet system is studied using 20.2 fb\(^{−1}\) of proton-proton collision data at a centre-of-mass energy of \(\sqrt{s}\) = 8 TeV recorded with the ATLAS detector in 2012 at the Large Hadron Collider. Final states with a photon and a Z boson decaying into a pair of either electrons, muons, or neutrinos are analysed. Electroweak and total \(pp\) → \(Zγjj\) cross-sections are extracted in two fiducial regions with different sensitivities to electroweak production processes. Quartic couplings of vector bosons are studied in regions of phase space with an enhanced contribution from pure electroweak production, sensitive to vector-boson scattering processes \(V V → Zγ\). No deviations from Standard Model predictions are observed and constraints are placed on anomalous couplings parameterized by higher-dimensional operators using effective field theory.
A search for direct top squark pair production resulting in events with either a same-flavour opposite-sign dilepton pair with invariant mass compatible with a \(Z\) boson or a pair of jets compatible with a Standard Model (SM) Higgs boson (\(h\)) is presented. Requirements on the missing transverse momentum, together with additional selections on leptons, jets, jets identified as originating from \(b\)-quarks are imposed to target the other decay products of the top squark pair. The analysis is performed using proton-proton collision data at \(\sqrt{s}\) = 13 TeV collected with the ATLAS detector at the LHC in 2015–2016, corresponding to an integrated luminosity of 36.1 fb\(^{-1}\). No excess is observed in the data with respect to the SM predictions. The results are interpreted in two sets of models. In the first set, direct production of pairs of lighter top squarks (\(\tilde{t}_1\)) with long decay chains involving \(Z\) or Higgs bosons is considered. The second set includes direct pair production of the heavier top squark pairs (\(\tilde{t}_2\)) decaying via \(\tilde{t}_2\) → \(Z\tilde{t}_1\) or \(\tilde{t}_2\) → \(h\tilde{t}_1\). The results exclude at 95% confidence level \(\tilde{t}_2\) and \(\tilde{t}_1\) masses up to about 800 GeV, extending the exclusion region of supersymmetric parameter space covered by previous LHC searches.
A measurement of the splitting scales occuring in the \(k_t\) jet-clustering algorithm is presented for final states containing a \(Z\) boson. The measurement is done using 20.2 fb\(^{−1}\) of proton-proton collision data collected at a centre-of-mass energy of \(\sqrt{s} = 8\) TeV by the ATLAS experiment at the LHC in 2012. The measurement is based on charged-particle track information, which is measured with excellent precision in the \(p_T\) region relevant for the transition between the perturbative and the non-perturbative regimes. The data distributions are corrected for detector effects, and are found to deviate from state-of-the-art predictions in various regions of the observables.
Inclusive jet production cross-sections are measured in proton-proton collisions at a centre-of-mass energy of \(\sqrt{s} = 8\) TeV recorded by the ATLAS experiment at the Large Hadron Collider at CERN. The total integrated luminosity of the analysed data set amounts to 20.2 fb\(^{−1}\). Double-differential cross-sections are measured for jets defined by the anti-\(k_t\) jet clustering algorithm with radius parameters of \(R\) = 0.4 and \(R\) = 0.6 and are presented as a function of the jet transverse momentum, in the range between 70 GeV and 2.5 TeV and in six bins of the absolute jet rapidity, between 0 and 3.0. The measured cross-sections are compared to predictions of quantum chromodynamics, calculated at next-to-leading order in perturbation theory, and corrected for non-perturbative and electroweak effects. The level of agreement with predictions, using a selection of different parton distribution functions for the proton, is quantified. Tensions between the data and the theory predictions are observed.
A search for new phenomena in final states characterized by high jet multiplicity, an isolated lepton (electron or muon) and either zero or at least three \(b\)-tagged jets is presented. The search uses 36.1 fb\(^{−1}\) of \(\sqrt{s}=13\) TeV proton-proton collision data collected by the ATLAS experiment at the Large Hadron Collider in 2015 and 2016. The dominant sources of background are estimated using parameterized extrapolations, based on observables at medium jet multiplicity, to predict the \(b\)-tagged jet multiplicity distribution at the higher jet multiplicities used in the search. No significant excess over the Standard Model expectation is observed and 95% confidence-level limits are extracted constraining four simplified models of \(R\)-parity-violating supersymmetry that feature either gluino or top-squark pair production. The exclusion limits reach as high as 2.1 TeV in gluino mass and 1.2 TeV in top-squark mass in the models considered. In addition, an upper limit is set on the cross-section for Standard Model \(t\overline{t}t\overline{t}\) production of 60 fb (6.5 × the Standard Model prediction) at 95% confidence level. Finally, model-independent limits are set on the contribution from new phenomena to the signal-region yields.
The top-quark mass is measured in the all-hadronic top-antitop quark decay channel using proton-proton collisions at a centre-of-mass energy of \(\sqrt{s}=8\) TeV with the ATLAS detector at the CERN Large Hadron Collider. The data set used in the analysis corresponds to an integrated luminosity of 20.2 fb\(^{−1}\). The large multi-jet background is modelled using a data-driven method. The top-quark mass is obtained from template fits to the ratio of the three-jet to the dijet mass. The three-jet mass is obtained from the three jets assigned to the top quark decay. From these three jets the dijet mass is obtained using the two jets assigned to the W boson decay. The top-quark mass is measured to be 173.72 ± 0.55 (stat.) ± 1.01 (syst.) GeV.
This article presents searches for the \({Zγ}\) decay of the Higgs boson and for narrow high-mass resonances decaying to \(Z\)γ, exploiting \(Z\) boson decays to pairs of electrons or muons. The data analysis uses 36.1 fb\(^{−1}\) of \({pp}\) collisions at \(\sqrt{s}=13\) recorded by the ATLAS detector at the CERN Large Hadron Collider. The data are found to be consistent with the expected Standard Model background. The observed (expected — assuming Standard Model \({pp} → H → {Z}γ\) production and decay) upper limit on the production cross section times the branching ratio for \({pp} → H → {Z}γ\) is 6.6. (5.2) times the Standard Model prediction at the 95% confidence level for a Higgs boson mass of 125.09 GeV. In addition, upper limits are set on the production cross section times the branching ratio as a function of the mass of a narrow resonance between 250 GeV and 2.4 TeV, assuming spin-0 resonances produced via gluon-gluon fusion, and spin-2 resonances produced via gluon-gluon or quark-antiquark initial states. For high-mass spin-0 resonances, the observed (expected) limits vary between 88 fb (61 fb) and 2.8 fb (2.7 fb) for the mass range from 250 GeV to 2.4 TeV at the 95% confidence level.
Inclusive and differential fiducial cross sections of Higgs boson production in proton-proton collisions are measured in the \(H\) → \({ZZ^*}\) → \(4{ℓ}\) decay channel. The proton-proton collision data were produced at the Large Hadron Collider at a centre-of-mass energy of 13 TeV and recorded by the ATLAS detector in 2015 and 2016, corresponding to an integrated luminosity of 36.1 fb\(^{−1}\). The inclusive fiducial cross section in the \(H\) → \({ZZ^*}\) → \(4{ℓ}\) decay channel is measured to be 3.62 ± 0.50(stat)\(^{+0.25}_{− 0.20}\) (sys) fb, in agreement with the Standard Model prediction of 2.91 ± 0.13 fb. The cross section is also extrapolated to the total phase space including all Standard Model Higgs boson decays. Several differential fiducial cross sections are measured for observables sensitive to the Higgs boson production and decay, including kinematic distributions of jets produced in association with the Higgs boson. Good agreement is found between data and Standard Model predictions. The results are used to put constraints on anomalous Higgs boson interactions with Standard Model particles, using the pseudo-observable extension to the kappa-framework.
This article presents a search for flavour-changing neutral currents in the decay of a top quark into an up-type (\({q = c, u}\)) quark and a Higgs boson, where the Higgs boson decays into two photons. The proton-proton collision data set analysed amounts to 36.1 fb\(^{−1}\) at \(\sqrt{s} = 13\) TeV collected by the ATLAS experiment at the LHC. Top quark pair events are searched for, where one top quark decays into \(qH\) and the other decays into \(bW\). Both the hadronic and leptonic decay modes of the \(W\) boson are used. No significant excess is observed and an upper limit is set on the \({t → cH}\) branching ratio of 2.2 × 10\(^{−3}\) at the 95% confidence level, while the expected limit in the absence of signal is 1.6 × 10\(^{−3}\). The corresponding limit on the \(tcH\) coupling is 0.090 at the 95% confidence level. The observed upper limit on the \({t → uH}\) branching ratio is 2.4 × 10\(^{−3}\).
A measurement of \(b\)-hadron pair production is presented, based on a data set corresponding to an integrated luminosity of 11.4 fb\(^{−1}\) of proton-proton collisions recorded at \(\sqrt{s}=8\) TeV with the ATLAS detector at the LHC. Events are selected in which a \(b\)-hadron is reconstructed in a decay channel containing \(J/ψ → μμ\), and a second \(b\)-hadron is reconstructed in a decay channel containing a muon. Results are presented in a fiducial volume defined by kinematic requirements on three muons based on those used in the analysis. The fiducial cross section is measured to be 17.7 ± 0.1(stat.) ± 2.0(syst.) nb. A number of normalised differential cross sections are also measured, and compared to predictions from the PHYTHIA8, HERWIG++, MADGRAPH5_AMC@NLO+PYTHIA8 and SHERPA event generators, providing new constraints on heavy flavour production.
A search is presented for the pair production of heavy vector-like \(T\) quarks, primarily targeting the \(T\) quark decays to a \(W\) boson and a \(b\)-quark. The search is based on 36.1 fb\(^{−1}\) of \(pp\) collisions at \(\sqrt{s}=13\) TeV recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Data are analysed in the lepton-plus-jets final state, including at least one \(b\)-tagged jet and a large-radius jet identified as originating from the hadronic decay of a high-momentum \(W\) boson. No significant deviation from the Standard Model expectation is observed in the reconstructed \(T\) mass distribution. The observed 95% confidence level lower limit on the \(T\) mass are 1350 GeV assuming 100% branching ratio to \(Wb\). In the SU(2) singlet scenario, the lower mass limit is 1170 GeV. This search is also sensitive to a heavy vector-like \(B\) quark decaying to \(Wt\) and other final states. The results are thus reinterpreted to provide a 95% confidence level lower limit on the \(B\) quark mass at 1250 GeV assuming 100% branching ratio to \(Wt\); in the SU(2) singlet scenario, the limit is 1080 GeV. Mass limits on both \(T\) and \(B\) production are also set as a function of the decay branching ratios. The 100% branching ratio limits are found to be applicable to heavy vector-like \(Y\) and \(X\) production that decay to \(Wb\) and \(Wt\), respectively.
A search is conducted for new resonant and non-resonant high-mass phenomena in dielectron and dimuon final states. The search uses 36.1 fb\(^{−1}\) of proton-proton collision data, collected at \(\sqrt{s}=13\) TeV by the ATLAS experiment at the LHC in 2015 and 2016. No significant deviation from the Standard Model prediction is observed. Upper limits at 95% credibility level are set on the cross-section times branching ratio for resonances decaying into dileptons, which are converted to lower limits on the resonance mass, up to 4.1 TeV for the E\(_6\)-motivated \(Z^′_χ\). Lower limits on the \({qqℓℓ}\) contact interaction scale are set between 2.4 TeV and 40 TeV, depending on the model.
The cross section of a top-quark pair produced in association with a photon is measured in proton-proton collisions at a centre-of-mass energy of \(\sqrt{s} = 8\) TeV with 20.2 fb\(^{−1}\) of data collected by the ATLAS detector at the Large Hadron Collider in 2012. The measurement is performed by selecting events that contain a photon with transverse momentum \(p_T\) > 15 GeV, an isolated lepton with large transverse momentum, large missing transverse momentum, and at least four jets, where at least one is identified as originating from a \(b\)-quark. The production cross section is measured in a fiducial region close to the selection requirements. It is found to be 139 ± 7 (stat.) ± 17 (syst.) fb, in good agreement with the theoretical prediction at next-to-leading order of 151 ± 24 fb. In addition, differential cross sections in the fiducial region are measured as a function of the transverse momentum and pseudorapidity of the photon.
Measurements of differential cross-sections of top-quark pair production in fiducial phase-spaces are presented as a function of top-quark and \(t\overline{t}\) system kinematic observables in proton-proton collisions at a centre-of-mass energy of \(\sqrt{s}\) = 13 TeV. The data set corresponds to an integrated luminosity of 3.2 fb\(^{−1}\), recorded in 2015 with the ATLAS detector at the CERN Large Hadron Collider. Events with exactly one electron or muon and at least two jets in the final state are used for the measurement. Two separate selections are applied that each focus on different top-quark momentum regions, referred to as resolved and boosted topologies of the \(t\overline{t}\) final state. The measured spectra are corrected for detector effects and are compared to several Monte Carlo simulations by means of calculated \(χ^2\) and \(p\)-values.
A search for the supersymmetric partners of the Standard Model bottom and top quarks is presented. The search uses 36.1 fb\(^{−1}\) of \(pp\) collision data at \(\sqrt{s}\) = 13 TeV collected by the ATLAS experiment at the Large Hadron Collider. Direct production of pairs of bottom and top squarks (\(\overline{b}_1\) and \(\overline{t}_1\)) is searched for in final states with \(b\)-tagged jets and missing transverse momentum. Distinctive selections are defined with either no charged leptons (electrons or muons) in the final state, or one charged lepton. The zero-lepton selection targets models in which the \(\overline{b}_1\) is the lightest squark and decays via \(\overline{b}_1\) → \(b\overline{χ}^0_1\), where \(\overline{χ}^0_1\) is the lightest neutralino. The one-lepton final state targets models where bottom or top squarks are produced and can decay into multiple channels, \(\overline{b}_1\) → \(b\overline{χ}^0_1\) and \(\overline{b}_1\) → \(t\overline{χ}^±_1\), or \(\overline{t}_1\) → \(t\overline{χ}^0_1\) and \(\overline{t}_1\) → \(b\overline{χ}^±_1\), where \(\overline{χ}^±_1\) is the lightest chargino and the mass difference \(m_{\overline{χ}^±_1}\) − \(m_{\overline{χ}^0_1}\) is set to 1 GeV. No excess above the expected Standard Model background is observed. Exclusion limits at 95% confidence level on the mass of third-generation squarks are derived in various supersymmetry-inspired simplified models.
We explore a cosmology where the Big Bang singularity is replaced by a condensation event of interacting strings. We study the transition from an uncontrolled, chaotic soup (“before”) to a clearly interacting “real world”. Cosmological inflation scenarios do not fit current observations and are avoided. Instead, long-range interactions inside this crystallization event limit growth and crystal symmetries ensure the same laws of nature and basic symmetries over our domain. Tiny mis-arrangements present nuclei of superclusters and galaxies and crystal structure leads to the arrangement of dark (halo regions) and normal matter (galaxy nuclei) so convenient for galaxy formation. Crystals come and go, allowing an evolutionary cosmology where entropic forces from the quantum soup “outside” of the crystal try to dissolve it. These would correspond to dark energy and leads to a big rip scenario in 70 Gy. Preference of crystals with optimal growth and most condensation nuclei for the next generation of crystals may select for multiple self-organizing processes within the crystal, explaining “fine-tuning” of the local “laws of nature” (the symmetry relations formed within the crystal, its “unit cell”) to be particular favorable for self-organizing processes including life or even conscious observers in our universe.
Independent of cosmology, a crystallization event may explain quantum-decoherence in general: The fact, that in our macroscopic everyday world we only see one reality. This contrasts strongly with the quantum world where you have coherence, a superposition of all quantum states. We suggest that a “real world” (so our everyday macroscopic world) happens only in our domain, i.e. inside a crystal. “Outside” of our domain and our observable universe there is the quantum soup of boiling quantum foam and superposition of all possibilities. In our crystallized world the vacuum no longer boils but is cooled down by the crystallization event and hence is 10**20 smaller, exactly as observed in our everyday world. As we live in a “solid” state, within a crystal, the different quanta which build our world have all their different states nicely separated. This theory postulates there are only n quanta and m states available for them (there is no Everett-like ever splitting multiverse after each decision). In the solid state we live in, there is decoherence, the states are nicely separated. The arrow of entropy for each edge of the crystal forms one fate, one worldline or clear development of a world, while the layers of the crystal are different system states.
Some mathematical leads from loop quantum gravity point to required interactions and potentials. A complete mathematical treatment of this unified theory is far too demanding currently. Interaction potentials for strings or membranes of any dimension allow a solid state of quanta, so allowing decoherence in our observed world are challenging to calculate. However, if we introduce here the heuristic that any type of physical interaction of strings corresponds just to a type of calculation, there is already since 1898 the Hurwitz theorem showing that then only 1D, 2D, 4D and 8D (octonions) allow complex or hypercomplex number calculations. No other hypercomplex numbers and hence dimensions or symmetries are possible to allow calculations without yielding divisions by zero. However, the richest solution allowed by the Hurwitz theorem, octonions, is actually the observed symmetry of our universe, E8.
The projects presented in this thesis cover the examination of the electronic and structural properties of organic thin films at noble metal-organic interfaces. Angle-resolved photoemission spectroscopy is used as the primary investigative tool due to the connection of the emitted photoelectrons to the electronic structure of the sample. The surveyed materials are of relevance for fundamental research and practical applications on their own, but also serve as archetypes for the photoemission techniques presented throughout the four main chapters of this thesis. The techniques are therefore outlined with their adaptation to other systems in mind and a special focus on the proper description of the final state.
The most basic description of the final state that is still adequate for the evaluation of photoemission data is a plane wave. Its simplicity enables a relatively intuitive interpretation of photoemission data, since the initial and final state are related to one another by a Fourier transform and a geometric factor in this approximation. Moreover, the initial states of some systems can be reconstructed in three dimensions by combining photoemission measurements at various excitation energies. This reconstruction can even be carried out solely based on experimental data by using suitable iterative algorithms.
Since the approximation of the final state in the photoemission process by a plane wave is not valid in all instances, knowledge on the limitations of its applicability is indispensable. This can be gained by a comparison to experimental data as well as calculations with a more detailed description of the photoemission final state. One possible appraoch is based on independently emitting atoms where the coherent superposition of partial, atomic final states produces the total final state. This approach can also be used for more intricate studies on organic thin films. To this end, experimental data can be related to theoretical calculations to gain extensive insights into the structural and electronic properties of molecules in organic thin films.
A search is presented for particles that decay producing a large jet multiplicity and invisible particles. The event selection applies a veto on the presence of isolated electrons or muons and additional requirements on the number of \(b\)-tagged jets and the scalar sum of masses of large-radius jets. Having explored the full ATLAS 2015-2016 dataset of LHC proton-proton collisions at \(\sqrt{s}\) = 13 TeV, which corresponds to 36.1 fb\(^{−1}\) of integrated luminosity, no evidence is found for physics beyond the Standard Model. The results are interpreted in the context of simplified models inspired by R-parity-conserving and R-parity-violating supersymmetry, where gluinos are pair-produced. More generic models within the phenomenological minimal supersymmetric Standard Model are also considered.
A search for pair production of a scalar partner of the top quark in events with four or more jets plus missing transverse momentum is presented. An analysis of 36.1 fb\(^{−1}\) of \(\sqrt{s}\) = 13 TeV proton-proton collisions collected using the ATLAS detector at the LHC yields no significant excess over the expected Standard Model background. To interpret the results a simplified supersymmetric model is used where the top squark is assumed to decay via \(\tilde{t}_1\) → \(t^{(∗)}\)\(\tilde{χ}^0_1\) and \(\tilde{t}_1\) → \(b\tilde{χ}^±_1\) → \({bW}^{(∗)}\tilde{χ}^0_1\), where \(\tilde{χ}^0_1\) (\(\tilde{χ}^±_1\)) denotes the lightest neutralino (chargino). Exclusion limits are placed in terms of the top-squark and neutralino masses. Assuming a branching ratio of 100% to \(t\tilde{χ}^0_1\), top-squark masses in the range 450–1000 GeV are excluded for \(\tilde{χ}^0_1\) masses below 160 GeV. In the case where \(m_{\tilde{t}_1}\) ∼ \(m_t\) + \(m_{\tilde{χ}^0_1}\), top-squark masses in the range 235–590 GeV are excluded.
This paper presents a measurement of the triple-differential cross section for the Drell-Yan process \({Z/γ^*}\) → ℓ\(^+\)ℓ\(^-\) where ℓ is an electron or a muon. The measurement is performed for invariant masses of the lepton pairs, \(m_{ℓℓ}\) , between 46 and 200 GeV using a sample of 20.2 fb\(^{−1}\) of \(pp\) collisions data at a centre-of-mass energy of \(\sqrt{s}\) = 8 TeV collected by the ATLAS detector at the LHC in 2012. The data are presented in bins of invariant mass, absolute dilepton rapidity, |\(y_{ℓℓ}\)|, and the angular variable cos \(θ^*\) between the outgoing lepton and the incoming quark in the Collins-Soper frame. The measurements are performed in the range |\(y_{ℓℓ}\)| < 2.4 in the muon channel, and extended to |\(y_{ℓℓ}\)| < 3.6 in the electron channel. The cross sections are used to determine the \(Z\) boson forward-backward asymmetry as a function of |\(y_{ℓℓ}\)| and \(m_{ℓℓ}\) . The measurements achieve high-precision, below the percent level in the pole region, excluding the uncertainty in the integrated luminosity, and are in agreement with predictions. These precision data are sensitive to the parton distribution functions and the effective weak mixing angle.
A search for the decay of the Standard Model Higgs boson into a \({b\overline{b}}\) pair when produced in association with a \(W\) or \(Z\) boson is performed with the ATLAS detector. The analysed data, corresponding to an integrated luminosity of 36.1 fb\(^{−1}\), were collected in proton-proton collisions in Run 2 of the Large Hadron Collider at a centre-of-mass energy of 13 TeV. Final states containing zero, one and two charged leptons (electrons or muons) are considered, targeting the decays \(Z\) → \({νν}\), \(W\) → \({ℓν}\) and \(Z\) → \({ℓℓ}\). For a Higgs boson mass of 125 GeV, an excess of events over the expected background from other Standard Model processes is found with an observed significance of 3.5 standard deviations, compared to an expectation of 3.0 standard deviations. This excess provides evidence for the Higgs boson decay into b-quarks and for its production in association with a vector boson. The combination of this result with that of the Run 1 analysis yields a ratio of the measured signal events to the Standard Model expectation equal to 0.90 ± 0.18(stat.)\(^{+0.21}_{−0.19}\)(syst.). Assuming the Standard Model production cross-section, the results are consistent with the value of the Yukawa coupling to \(b\)-quarks in the Standard Model.
The electroweak production and subsequent decay of single top quarks in the \(t\)-channel is determined by the properties of the \({Wtb}\) vertex, which can be described by the complex parameters of an effective Lagrangian. An analysis of a triple-differential decay rate in \(t\)-channel production is used to simultaneously determine five generalised helicity fractions and phases, as well as the polarisation of the produced top quark. The complex parameters are then constrained. This analysis is based on 20.2 fb\(^{−1}\) of proton-proton collision data at a centre-of-mass energy of 8 TeV collected with the ATLAS detector at the LHC. The fraction of decays containing transversely polarised \(W\) bosons is measured to be \(f_1\) = 0.30 ± 0.05. The phase between amplitudes for transversely and longitudinally polarised \(W\) bosons recoiling against left-handed \(b\)-quarks is measured to be \(\delta\)_ = 0.002\(\pi^{+0.016\pi}_{+0.017\pi}\), giving no indication of CP violation. The fractions of longitudinal or transverse \(W\) bosons accompanied by right-handed \(b\)-quarks are also constrained. Based on these measurements, limits are placed at 95% CL on the ratio of the complex coupling parameters Re [\({g_R/V_L}\) \(\in\) [−0.12, 0.17] and Im [\({g_R/V_L}\) \(\in\) [−0.07, 0.06]. Constraints are also placed on the ratios |\({V_R}/{V_L}\)| and |\({g_L}/{V_L}\)|. In addition, the polarisation of single top quarks in the \(t\)-channel is constrained to be \(P\) > 0.72 (95% CL). None of the above measurements make assumptions about the value of any of the other parameters or couplings and all of them are in agreement with the Standard Model.
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.
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.
Quantitative Electron Paramagnetic Resonance Studies of Charge Transfer in Organic Semiconductors
(2020)
In the present work we investigated various charge transfer processes, as they appear in the versatile world of organic semiconductors by probing the spin states of the corresponding charge carrier species via electron paramagnetic resonance (EPR) spectroscopy. All studied material systems are carbon-based compounds, either belonging to the group of polymers, fullerenes, or single-wall carbon nanotubes (SWNTs).
In the first instance, we addressed the change of the open circuit voltage (Voc) with the fullerene blend stoichiometry in fullerene-based solar cells for organic photovoltaics (OPV). The voltage depends strongly on the energy separation between the lowest unoccupied molecular orbital (LUMO) of the donor and the highest occupied molecular orbital (HOMO) of the acceptor. By exploiting the Gaussian distribution of the charge carriers in a two-level system, and thus also their spins in the EPR experiment, it could be shown that the LUMOs get closer by a few to a few hundred meV when going from pure fullerene materials to a fullerene mixture. The reason for this strong energetic effect is likely the formation of a fullerene alloy.
Further, we investigated the chemical doping mechanism of SWNTs with a (6,5)-chirality and their behaviour under optical excitation. In order to determine the unintentional (pre)-doping of SWNTs, EPR spectra of the raw material as well as after different purification steps were recorded. This facilitated the determination of nanotube defects and atmospheric p-doping as the causes of the measured EPR signals. In order to deliberately transfer additional charge carriers to the nanotubes, we added the redox-active substance AuCl3 where we determined an associated doping-yield of (1.5±0.2)%. In addition, a statistical occupation model was developed which can be used to simulate the distribution of EPR active, i.e. unpaired and localised charge carriers on the nanotubes.
Finally, we investigated the charge transfer behaviour of (6,5)-SWNTs together with the polymer P3HT and the fullerene PC60BM after optical excitation.
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.
In the past decades correlated-electron physics due to strong Coulomb interactions and topological physics caused by band inversion often induced by strong spin-orbit coupling have been the workhorses of solid state research.
While commonly considered as disparate phenomena, it was realized in the early 2010s that the interplay between the comparably strong Coulomb and spin-orbit interactions in the $5d$ transition metal oxides may result in hitherto unforeseen properties.
The layered perovskite Sr$\textsubscript{2}$IrO$\textsubscript{4}$ has attracted special attention due to the observation of an unconventional Mott-insulating phase and predictions of exotic superconductivity.
Less is known about its three-dimensional counterpart SrIrO$\textsubscript{3}$, since rather than the cubic perovskite structure it adopts the thermodynamically stable hexagonal polymorph thereof.
This thesis therefore sets out to establish the synthesis of epitaxially stabilized perovskite SrIrO$\textsubscript{3}$ by pulsed laser deposition and to investigate its electronic and magnetic structure by state-of-the-art x-ray spectroscopy techniques.
In this endeavor the appropriate thermodynamic conditions for the growth of high-quality SrIrO$\textsubscript{3}$ are identified with a focus on the prevention of cation off-stoichiometry and the sustainment of layer-by-layer growth.
In the thus-optimized films the cubic perovskite symmetry is broken by a tetragonal distortion due to epitaxial strain and additional cooperative rotations of the IrO$\textsubscript{6}$ octahedra.
As a consequence of the thermodynamic instability of the IrO$\textsubscript{2}$ surface layer, the films unexpectedly undergo a conversion to a SrO termination during growth.
In an attempt to disentangle the interplay between spin-orbit and Coulomb interaction the three-dimensional electronic structure of perovskite SrIrO$\textsubscript{3}$ is investigated in a combined experimental and theoretical approach using soft x-ray angle-resolved photoelectron spectroscopy and \textit{ab initio} density functional theory calculations.
The experimentally found metallic ground state hosts coherent quasiparticle peaks with a well-defined Fermi surface and is theoretically described by a single half-filled band with effective total angular momentum $J_\text{eff} = 1/2$ only upon incorporation of a sizeable local Coulomb repulsion and -- to a lesser extent -- the broken cubic crystal symmetry in the film.
Upon reduction of the SrIrO$\textsubscript{3}$ thickness below a threshold of four unit cells the scales are tipped in favor of a Mott-insulating phase as the on-site Coulomb repulsion surmounts the diminishing kinetic energy upon transition into the two-dimensional regime.
Concomitantly, a structural transition occurs because the corner-shared octahedral network between substrate and film imposes constraints upon the IrO$\textsubscript{6}$ octahedral rotations in the thin-film limit.
The striking similarity between the quasi-two-dimensional spin-orbit-induced Mott insulator Sr$\textsubscript{2}$IrO$\textsubscript{4}$ and SrO-terminated SrIrO$\textsubscript{3}$ in the monolayer limit underlines the importance of dimensionality for the metal-insulator transition and possibly opens a new avenue towards the realization of exotic superconductivity in iridate compounds.
Whether the analogy between SrIrO$\textsubscript{3}$ in the two-dimensional limit and its Ruddlesden-Popper bulk counterparts extends to their complex magnetic properties ultimately remains an open question, although no indications for a remanent (anti)ferromagnetic order were found.
The unprecedented observation of an x-ray magnetic circular dichroism at the O~$K$-absorption edge of iridium oxides in an external magnetic field promises deeper insights into the intricate connection between the $J_\text{eff} = 1/2$ pseudospin state, its hybridization with the oxygen ligand states and the magnetic order found in the Ruddlesden-Popper iridates.
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.
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.
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.
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.
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 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.
The dependence of the rate of proton–proton interactions on the centre-of-mass collision energy, √s, is of fundamental importance for both hadron collider physics and particle astrophysics. The dependence cannot yet be calculated from first principles; therefore, experimental measurements are needed. Here we present the first measurement of the inelastic proton–proton interaction cross-section at a centre-of-mass energy, √s, of 7 TeV using the ATLAS detector at the Large Hadron Collider. Events are selected by requiring hits on scintillation counters mounted in the forward region of the detector. An inelastic cross-section of 60.3±2.1 mb is measured for ξ>5×10−6, where ξ is calculated from the invariant mass, MX, of hadrons selected using the largest rapidity gap in the event. For diffractive events, this corresponds to requiring at least one of the dissociation masses to be larger than 15.7 GeV.
The measurement of the mass of the $W$ boson is currently one of the most promising precision analyses of the Standard Model, that could ultimately reveal a hint for new physics.
The mass of the $W$ boson is determined by comparing the $W$ boson, which cannot be reconstructed directly, to the $Z$ boson, where the full decay signature is available. With the help of Monte Carlo simulations one can extrapolate from the $Z$ boson to the $W$ boson.
Technically speaking, the measurement of the $W$ boson mass is performed by comparing data taken by the ATLAS experiment to a set of calibrated Monte Carlo simulations, which reflect different mass hypotheses.\
A dedicated calibration of the reconstructed objects in the simulations is crucial for a high precision of the measured value.
The comparison of simulated $Z$ boson events to reconstructed $Z$ boson candidates in data allows to derive event weights and scale factors for the calibration.
This thesis presents a new approach to reweight the hadronic recoil in the simulations. The focus of the calibration is on the average hadronic activity visible in the mean of the scalar sum of the hadronic recoil $\Sigma E_T$ as a function of pileup. In contrast to the standard method, which directly reweights the scalar sum, the dependency to the transverse boson momentum is less strongly affected here.
The $\Sigma E_T$ distribution is modeled first by means of its pileup dependency. Then, the remaining differences in the resolution of the vector sum of the hadronic recoil are scaled. This is done separately for the parallel and the pterpendicular component of the hadronic recoil with respect to the reconstructed boson.
This calibration was developed for the dataset taken by the ATLAS experiment at a center of mass energy of $8\,\textrm{TeV}$ in 2012. In addition, the same reweighting procedure is applied to the recent dataset with a low pileup contribution, the \textit{lowMu} runs at $5\,\textrm{TeV}$ and at $13\,\textrm{TeV}$, taken by ATLAS in November 2017. The dedicated aspects of the reweighting procedure are presented in this thesis. It can be shown that this reweighting approach improves the agreement between data and the simulations effectively for all datasets.
The uncertainties of this reweighting approach as well as the statistical errors are evaluated for a $W$ mass measurement by a template fit to pseudodata for the \textit{lowMu} dataset. A first estimate of these uncertainties is given here. For the pfoEM algorithm a statistical uncertainty of $17\,\text{MeV}$ for the $5\,\textrm{TeV}$ dataset and of $18\,\text{MeV}$ for the $13\,\textrm{TeV}$ are found for the $W \rightarrow \mu \nu$ analysis. The systematic uncertainty introduced by the resolution scaling has the largest effect, a value of $15\,\text{MeV}$ is estimated for the $13\,\textrm{TeV}$ dataset in the muon channel.
The quest for finding a unifying theory for both quantum theory and gravity lies at the heart of much of the research in high energy physics. Although recent years have witnessed spectacular experimental confirmation of our expectations from Quantum Field Theory and General Relativity, the question of unification remains as a major open problem. In this context, the perturbative aspects of quantum black holes represent arguably the best of our knowledge of how to proceed in this pursue.
In this thesis we investigate certain aspects of quantum gravity in 2 + 1 dimensional anti-de Sitter space (AdS3), and its connection to Conformal field theories in 1 + 1 dimensions (CFT2), via the AdS/CFT correspondence.
We study the thermodynamics properties of higher spin black holes. By focusing on the spin-4 case, we show that black holes carrying higher spin charges display a rich phase diagram in the grand canonical ensemble, including phase transitions of the Hawking-Page type, first order inter-black hole transitions, and a second order critical point.
We investigate recent proposals on the connection between bulk codimension-1 volumes and computational complexity in the CFT. Using Tensor Networks we provide concrete evidence of why these bulk volumes are related to the number of gates in a quantum circuit, and exhibit their topological properties. We provide a novel formula to compute this complexity directly in terms of entanglement entropies, using techniques from Kinematic space.
We then move in a slightly different direction, and study the quantum properties of black holes via de Functional Renormalisation Group prescription coming from Asymptotic safety. We avoid the arbitrary scale setting by restricting to a narrower window in parameter space, where only Newton’s coupling and the cosmological constant are allowed to vary. By one assumption on the properties of Newton’s coupling, we find black hole solutions explicitly. We explore their thermodynamical properties, and discover that very large black holes exhibit very unusual features.
The paper presents studies of Bose–Einstein Correlations (BEC) for pairs of like-sign charged particles measured in the kinematic range p\(_{T}\) > 100 MeV and |η| < 2.5 in proton collisions at centre-of-mass energies of 0.9 and 7 TeV with the ATLAS detector at the CERN Large Hadron Collider. The integrated luminosities are approximately 7 μb\(^{−1}\), 190 μb\(^{−1}\) and 12.4 nb\(^{−1}\) for 0.9 TeV, 7 TeV minimum-bias and 7 TeV high-multiplicity data samples, respectively. The multiplicity dependence of the BEC parameters characterizing the correlation strength and the correlation source size are investigated for charged-particle multiplicities of up to 240. A saturation effect in the multiplicity dependence of the correlation source size parameter is observed using the high-multiplicity 7 TeV data sample. The dependence of the BEC parameters on the average transverse momentum of the particle pair is also investigated.
A search for the Standard Model Higgs boson produced in association with a top-quark pair, t\(\overline{t}\)H, is presented. The analysis uses 20.3 fb\(^{−1}\) of pp collision data at \(\sqrt {s}\) = 8 TeV, collected with the ATLAS detector at the Large Hadron Collider during 2012. The search is designed for the H→b\(\overline{b}\) decay mode and uses events containing one or two electrons or muons. In order to improve the sensitivity of the search, events are categorised according to their jet and b-tagged jet multiplicities. A neural network is used to discriminate between signal and background events, the latter being dominated by t\(\overline{t}\)+jets production. In the single-lepton channel, variables calculated using a matrix element method are included as inputs to the neural network to improve discrimination of the irreducible t\(\overline{t}\)+b\(\overline{b}\) background. No significant excess of events above the background expectation is found and an observed (expected) limit of 3.4 (2.2) times the Standard Model cross section is obtained at 95 % confidence level. The ratio of the measured t\(\overline{t}\)H signal cross section to the Standard Model expectation is found to be μ = 1.5 ± 1.1 assuming a Higgs boson mass of 125 GeV.
Two searches for supersymmetric particles in final states containing a same-flavour opposite-sign lepton pair, jets and large missing transverse momentum are presented. The proton–proton collision data used in these searches were collected at a centre-of-mass energy \(\sqrt {s}\) = 8 TeV by the ATLAS detector at the Large Hadron Collider and corresponds to an integrated luminosity of 20.3 fb\(^{−1}\). Two leptonic production mechanisms are considered: decays of squarks and gluinos with Z bosons in the final state, resulting in a peak in the dilepton invariant mass distribution around the Z-boson mass; and decays of neutralinos (e.g. \(\tilde{χ}\)\(^{0}_{2}\) → ℓ\(^{+}\)ℓ\(^{−}\)\(\tilde{χ}\)\(^{0}_{1}\)), resulting in a kinematic endpoint in the dilepton invariant mass distribution. For the former, an excess of events above the expected Standard Model background is observed, with a significance of three standard deviations. In the latter case, the data are well-described by the expected Standard Model background. The results from each channel are interpreted in the context of several supersymmetric models involving the production of squarks and gluinos.
This paper reports on a search for narrow resonances in diboson production in the ℓℓq\(\overline{q}\) final state using pp collision data corresponding to an integrated luminosity of 20 fb\(^{−1}\) collected at \(\sqrt {s}\) = 8 TeV with the ATLAS detector at the Large Hadron Collider. No significant excess of data events over the Standard Model expectation is observed. Upper limits at the 95 % confidence level are set on the production cross section times branching ratio for Kaluza–Klein gravitons predicted by the Randall–Sundrum model and for Extended Gauge Model W′ bosons. These results lead to the exclusion of mass values below 740 and 1590 GeV for the graviton and W′ boson respectively.
A search is presented for narrow diboson resonances decaying to WW or WZ in the final state where one W boson decays leptonically (to an electron or a muon plus a neutrino) and the other W/Z boson decays hadronically. The analysis is performed using an integrated luminosity of 20.3 fb\(^{−1}\) of pp collisions at \(\sqrt {s}\) = 8 TeV collected by the ATLAS detector at the large hadron collider. No evidence for resonant diboson production is observed, and resonance masses below 700 and 1490 GeV are excluded at 95 % confidence level for the spin-2 Randall–Sundrum bulk graviton G\(^{*}\) with coupling constant of 1.0 and the extended gauge model W′ boson respectively.
Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb\(^{−1}\) of \(\sqrt {s}\) = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between E\(^{miss}_{T}\) > 150 GeV and E\(^{miss}_{T}\) > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presented.
Many extensions of the Standard Model predict the existence of charged heavy long-lived particles, such as R-hadrons or charginos. These particles, if produced at the Large Hadron Collider, should be moving non-relativistically and are therefore identifiable through the measurement of an anomalously large specific energy loss in the ATLAS pixel detector. Measuring heavy long-lived particles through their track parameters in the vicinity of the interaction vertex provides sensitivity to metastable particles with lifetimes from 0.6 ns to 30 ns. A search for such particles with the ATLAS detector at the Large Hadron Collider is presented, based on a data sample corresponding to an integrated luminosity of 18.4 fb\(^{−1}\) of pp collisions at \(\sqrt {s}\) = 8 TeV. No significant deviation from the Standard Model background expectation is observed, and lifetime-dependent upper limits on R-hadrons and chargino production are set. Gluino R-hadrons with 10 ns lifetime and masses up to 1185 GeV are excluded at 95 % confidence level, and so are charginos with 15 ns lifetime and masses up to 482 GeV.
A search for the production of single-top-quarks in association with missing energy is performed in proton–proton collisions at a centre-of-mass energy of \(\sqrt {s}\) =8 TeV with the ATLAS experiment at the large hadron collider using data collected in 2012, corresponding to an integrated luminosity of 20.3 fb\(^{−1}\). In this search, the W boson from the top quark is required to decay into an electron or a muon and a neutrino. No deviation from the standard model prediction is observed, and upper limits are set on the production cross-section for resonant and non-resonant production of an invisible exotic state in association with a right-handed top quark. In the case of resonant production, for a spin-0 resonance with a mass of 500 GeV, an effective coupling strength above 0.15 is excluded at 95 % confidence level for the top quark and an invisible spin-1/2 state with mass between 0 and 100 GeV. In the case of non-resonant production, an effective coupling strength above 0.2 is excluded at 95 % confidence level for the top quark and an invisible spin-1 state with mass between 0 and 657 GeV.
A search for Higgs boson decays to invisible particles is performed using 20.3 fb\(^{−1}\) of pp collision data at a centre-of-mass energy of 8 TeV recorded by the ATLAS detector at the Large Hadron Collider. The process considered is Higgs boson production in association with a vector boson (V = W or Z) that decays hadronically, resulting in events with two or more jets and large missing transverse momentum. No excess of candidates is observed in the data over the background expectation. The results are used to constrain VH production followed by H decaying to invisible particles for the Higgs boson mass range 115 < m\(_{H}\) < 300 GeV. The 95 % confidence-level observed upper limit on σ\(_{VH}\) × BR(H → inv.) varies from 1.6 pb at 115 GeV to 0.13 pb at 300 GeV. Assuming Standard Model production and including the gg → H contribution as signal, the results also lead to an observed upper limit of 78 % at 95 % confidence level on the branching ratio of Higgs bosons decays to invisible particles at a mass of 125 GeV.
A search for Higgs boson pair production pp → hh is performed with 19.5 fb\(^{−1}\) of proton–proton collision data at \(\sqrt {s}\) = 8 TeV, which were recorded by the ATLAS detector at the Large Hadron Collider in 2012. The decay products of each Higgs boson are reconstructed as a high-momentum b\(\overline{b}\) system with either a pair of small-radius jets or a single large-radius jet, the latter exploiting jet substructure techniques and associated b-tagged track-jets. No evidence for resonant or non-resonant Higgs boson pair production is observed. The data are interpreted in the context of the Randall–Sundrum model with a warped extra dimension as well as the two-Higgs-doublet model. An upper limit on the cross-section for pp → G\(^{*}_{KK}\) → hh → b\(\overline{b}\)b\(\overline{b}\) of 3.2(2.3) fb is set for a Kaluza–Klein graviton G\(^{*}_{KK}\) mass of 1.0(1.5) TeV, at the 95 % confidence level. The search for non-resonant Standard Model hh production sets an observed 95 % confidence level upper limit on the production cross-section σ(pp → hh → b\(\overline{b}\)b\(\overline{b}\)) of 202 fb, compared to a Standard Model prediction of σ(pp → hh → b\(\overline{b}\)b\(\overline{b}\)) = 3.6±0.5 fb.
A search for heavy long-lived multi-charged particles is performed using the ATLAS detector at the LHC. Data collected in 2012 at \(\sqrt {s}\) = 8 TeV from pp collisions corresponding to an integrated luminosity of 20.3 fb\(^{−1}\) are examined. Particles producing anomalously high ionisation, consistent with long-lived massive particles with electric charges from |q| = 2e to |q| = 6e are searched for. No signal candidate events are observed, and 95 % confidence level cross-section upper limits are interpreted as lower mass limits for a Drell–Yan production model. The mass limits range between 660 and 785 GeV.
A search is presented for the direct pair production of a chargino and a neutralino pp → \(\tilde{χ}\)\(^{±}_{1}\)\(\tilde{χ}\)\(^{0}_{2}\), where the chargino decays to the lightest neutralino and the W boson, \(\tilde{χ}\)\(^{±}_{1}\)→\(\tilde{χ}\)\(^{0}_{1}\)(W\(^{±}\)→ℓ\(^{±}\)ν), while the neutralino decays to the lightest neutralino and the 125 GeV Higgs boson, \(\tilde{χ}\)\(^{0}_{2}\)→\(\tilde{χ}\)\(^{0}_{1}\)(h→bb/γγ/ℓ\(^{±}\)νqq). The final states considered for the search have large missing transverse momentum, an isolated electron or muon, and one of the following: either two jets identified as originating from bottom quarks, or two photons, or a second electron or muon with the same electric charge. The analysis is based on 20.3 fb\(^{-1}\) of \(\sqrt {s}\) = 8 TeV proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with the Standard Model expectations, and limits are set in the context of a simplified supersymmetric model.
This article reports on a search for dark matter pair production in association with bottom or top quarks in 20.3 fb\(^{−1}\) of pp collisions collected at \(\sqrt {s}\) = 8 TeV by the ATLAS detector at the LHC. Events with large missing transverse momentum are selected when produced in association with high-momentum jets of which one or more are identified as jets containing b-quarks. Final states with top quarks are selected by requiring a high jet multiplicity and in some cases a single lepton. The data are found to be consistent with the Standard Model expectations and limits are set on the mass scale of effective field theories that describe scalar and tensor interactions between dark matter and Standard Model particles. Limits on the dark-matter–nucleon cross-section for spin-independent and spin-dependent interactions are also provided. These limits are particularly strong for low-mass dark matter. Using a simplified model, constraints are set on the mass of dark matter and of a coloured mediator suitable to explain a possible signal of annihilating dark matter.
A search for a new resonance decaying to a W or Z boson and a Higgs boson in the ℓℓ/ℓν/νν+b\(\overline{b}\) final states is performed using 20.3 fb\(^{−1}\) of pp collision data recorded at \(\sqrt {s}\) = 8 TeV with the ATLAS detector at the Large Hadron Collider. The search is conducted by examining the WH / ZH invariant mass distribution for a localized excess. No significant deviation from the Standard Model background prediction is observed. The results are interpreted in terms of constraints on the Minimal Walking Technicolor model and on a simplified approach based on a phenomenological Lagrangian of Heavy Vector Triplets.
Search for W' → tb → qqbb decays in pp collisions at \(\sqrt {s}\) = 8 TeV with the ATLAS detector
(2015)
A search for a massive W′ gauge boson decaying to a top quark and a bottom quark is performed with the ATLAS detector in pp collisions at the LHC. The dataset was taken at a centre-of-mass energy of \(\sqrt {s}\) = 8 TeV and corresponds to 20.3 fb\(^{−1}\) of integrated luminosity. This analysis is done in the hadronic decay mode of the top quark, where novel jet substructure techniques are used to identify jets from high-momentum top quarks. This allows for a search for high-mass W′ bosons in the range 1.5–3.0 TeV. b-tagging is used to identify jets originating from b-quarks. The data are consistent with Standard Model background-only expectations, and upper limits at 95 % confidence level are set on the W′ → tb cross section times branching ratio ranging from 0.16 pb to 0.33 pb for left-handed W′ bosons, and ranging from 0.10 pb to 0.21 pb for W′ bosons with purely right-handed couplings. Upper limits at 95 % confidence level are set on the W′-boson coupling to tb as a function of the W′ mass using an effective field theory approach, which is independent of details of particular models predicting a W′ boson.
The performance of the ATLAS muon trigger system is evaluated with proton–proton collision data collected in 2012 at the Large Hadron Collider at a centre-of-mass energy of 8 TeV. It is primarily evaluated using events containing a pair of muons from the decay of Z bosons. The efficiency of the single-muon trigger is measured for muons with transverse momentum 25 < p\(_{T}\) < 100GeV, with a statistical uncertainty of less than 0.01 % and a systematic uncertainty of 0.6 %. The pT range for efficiency determination is extended by using muons from decays of J/ψ mesons, W bosons, and top quarks. The muon trigger shows highly uniform and stable performance. The performance is compared to the prediction of a detailed simulation.
The production of a Z boson in association with a J/ψ meson in proton–proton collisions probes the production mechanisms of quarkonium and heavy flavour in association with vector bosons, and allows studies of multiple parton scattering. Using 20.3fb\(^{−1}\) of data collected with the ATLAS experiment at the LHC in pp collisions at \(\sqrt {s}\) = 8 TeV, the first measurement of associated Z+J/ψ production is presented for both prompt and non-prompt J/ψ production, with both signatures having a significance in excess of 5σ. The inclusive production cross-sections for Z boson production (analysed in μ\(^{+}\)μ\(^{−}\) or e\(^{+}\)e\(^{−}\) decay modes) in association with prompt and non-prompt J/ψ(→μ\(^{+}\)μ\(^{−}\)) are measured relative to the inclusive production rate of Z bosons in the same fiducial volume to be (36.8±6.7±2.5)×10\(^{−7}\) and (65.8±9.2±4.2)×10\(^{−7}\) respectively. Normalised differential production cross-section ratios are also determined as a function of the J/ψ transverse momentum. The fraction of signal events arising from single and double parton scattering is estimated, and a lower limit of 5.3 (3.7)mb at 68 (95)% confidence level is placed on the effective cross-section regulating double parton interactions.
Measurements of the W production cross sections in association with jets with the ATLAS detector
(2015)
This paper presents cross sections for the production of a W boson in association with jets, measured in proton–proton collisions at \(\sqrt {s}\) = 7 TeV with the ATLAS experiment at the large hadron collider. With an integrated luminosity of 4.6 fb\(^{−1}\), this data set allows for an exploration of a large kinematic range, including jet production up to a transverse momentum of 1 TeV and multiplicities up to seven associated jets. The production cross sections for W bosons are measured in both the electron and muon decay channels. Differential cross sections for many observables are also presented including measurements of the jet observables such as the rapidities and the transverse momenta as well as measurements of event observables such as the scalar sums of the transverse momenta of the jets. The measurements are compared to numerous QCD predictions including next-to-leading-order perturbative calculations, resummation calculations and Monte Carlo generators.
Double-differential three-jet production cross-sections are measured in proton–proton collisions at a centre-of-mass energy of \(\sqrt {s}\) = 7 TeV using the ATLAS detector at the large hadron collider. The measurements are presented as a function of the three-jet mass (m\(_{jjj}\)), in bins of the sum of the absolute rapidity separations between the three leading jets (|Y\(^{*}\)|). Invariant masses extending up to 5 TeV are reached for 8 < |Y\(^{*}\)| < 10. These measurements use a sample of data recorded using the ATLAS detector in 2011, which corresponds to an integrated luminosity of 4.51 fb\(^{-1}\). Jets are identified using the anti-k\(_{t}\) algorithm with two different jet radius parameters, R = 0.4 and R = 0.6. The dominant uncertainty in these measurements comes from the jet energy scale. Next-to-leading-order QCD calculations corrected to account for non-perturbative effects are compared to the measurements. Good agreement is found between the data and the theoretical predictions based on most of the available sets of parton distribution functions, over the full kinematic range, covering almost seven orders of magnitude in the measured cross-section values.
The mass of the top quark is measured in a data set corresponding to 4.6 fb\(^{-1}\) of proton–proton collisions with centre-of-mass energy \(\sqrt {s}\)=7 TeV collected by the ATLAS detector at the LHC. Events consistent with hadronic decays of top–antitop quark pairs with at least six jets in the final state are selected. The substantial background from multijet production is modelled with data-driven methods that utilise the number of identified b-quark jets and the transverse momentum of the sixth leading jet, which have minimal correlation. The top-quark mass is obtained from template fits to the ratio of three-jet to dijet mass. The three-jet mass is calculated from the three jets produced in a top-quark decay. Using these three jets the dijet mass is obtained from the two jets produced in the W boson decay. The top-quark mass obtained from this fit is thus less sensitive to the uncertainty in the energy measurement of the jets. A binned likelihood fit yields a top-quark mass of m\(_{t}\)= 175.1 ± 1.4 (stat.) ± 1.2 (syst.) GeV.
The top quark mass was measured in the channels t\(\overline{t}\) → lepton+jets and t\(\overline{t}\) → dilepton (lepton = e,μ) based on ATLAS data recorded in 2011. The data were taken at the LHC with a proton–proton centre-of-mass energy of \(\sqrt {s}\) = 7 TeV and correspond to an integrated luminosity of 4.6 fb\(^{-1}\). The t\(\overline{t}\) → lepton+jets analysis uses a three-dimensional template technique which determines the top quark mass together with a global jet energy scale factor (JSF), and a relative b-to-light-jet energy scale factor(bJSF), where the terms b-jets and light-jets refer to jets originating from b-quarks and u, d, c, s-quarks or gluons, respectively. The analysis of the t\(\overline{t}\) → dilepton channel exploits a one-dimensional template method using the m\(_{lb}\) observable, defined as the average invariant mass of the two lepton+b-jet pairs in each event. The top quark
mass is measured to be 172.33±0.75(stat + JSF + bJSF)±1.02(syst) GeV, and 173.79 ± 0.54(stat) ± 1.30(syst) GeV in the t\(\overline{t}\) → lepton+jets and t\(\overline{t}\) → dilepton channels, respectively. The combination of the two results yields m\(_{top}\) =172.99 ± 0.48(stat) ± 0.78(syst) GeV, with a total uncertainty of 0.91 GeV.
A measurement of W boson production in lead-lead collisions at \(\sqrt {^{S}NN}\)=2.76 TeV is presented. It is based on the analysis of data collected with the ATLAS detector at the LHC in 2011 corresponding to an integrated luminosity of 0.14 nb\(^{-1}\) and 0.15 nb\(^{-1}\) in the muon and electron decay channels, respectively. The differential production yields and lepton charge asymmetry are each measured as a function of the average number of participating nucleons ⟨N\(_{part}\)⟩ and absolute pseudorapidity of the charged lepton. The results are compared to predictions based on next-to-leading-order QCD calculations. These measurements are, in principle, sensitive to possible nuclear modifications to the parton distribution functions and also provide information on scaling of W boson production in multi-nucleon systems.
The jet energy scale (JES) and its systematic uncertainty are determined for jets measured with the ATLAS detector using proton–proton collision data with a centre-of-mass energy of \(\sqrt {s}\)=7 TeV corresponding to an integrated luminosity of 4.7 fb\(^{-1}\). Jets are reconstructed from energy deposits forming topological clusters of calorimeter cells using the anti-k\(_t\) algorithm with distance parameters R=0.4 or R=0.6, and are calibrated using MC simulations. A residual JES correction is applied to account for differences between data and MC simulations. This correction and its systematic uncertainty are estimated using a combination of in situ techniques exploiting the transverse momentum balance between a jet and a reference object such as a photon or a Z boson, for 20≤p\(^{jet}_{T}\)<1000 GeV and pseudorapidities |η|<4.5. The effect of multiple proton–proton interactions is corrected for, and an uncertainty is evaluated using in situ techniques. The smallest JES uncertainty of less than 1 % is found in the central calorimeter region (|η|<1.2) for jets with 55≤p\(^{jet}_{T}\)<500 GeV. For central jets at lower p\(_{T}\), the uncertainty is about 3 %. A consistent JES estimate is found using measurements of the calorimeter response of single hadrons in proton–proton collisions and test-beam data, which also provide the estimate for p\(^{jet}_{T}\)>1 TeV. The calibration of forward jets is derived from dijet p\(_{T}\) balance measurements. The resulting uncertainty reaches its largest value of 6 % for low-p\(_{T}\) jets at |η|=4.5. Additional JES uncertainties due to specific event topologies, such as close-by jets or selections of event samples with an enhanced content of jets originating from light quarks or gluons, are also discussed. The magnitude of these uncertainties depends on the event sample used in a given physics analysis, but typically amounts to 0.5–3 %.
This paper describes the trigger and offline reconstruction, identification and energy calibration algorithms for hadronic decays of tau leptons employed for the data collected from pp collisions in 2012 with the ATLAS detector at the LHC center-of-mass energy \(\sqrt {s}\)=8 TeV. The performance of these algorithms is measured in most cases with Z decays to tau leptons using the full 2012 dataset, corresponding to an integrated luminosity of 20.3 fb\(^{-1}\). An uncertainty on the offline reconstructed tau energy scale of 2–4 %, depending on transverse energy and pseudorapidity, is achieved using two independent methods. The offline tau identification efficiency is measured with a precision of 2.5 % for hadronically decaying tau leptons with one associated track, and of 4 % for the case of three associated tracks, inclusive in pseudorapidity and for a visible transverse energy greater than 20 GeV. For hadronic tau lepton decays selected by offline algorithms, the tau trigger identification efficiency is measured with a precision of 2–8 %, depending on the transverse energy. The performance of the tau algorithms, both offline and at the trigger level, is found to be stable with respect to the number of concurrent proton–proton interactions and has supported a variety of physics results using hadronically decaying tau leptons at ATLAS.
Studies of the spin and parity quantum numbers of the Higgs boson in the WW\(^{*}\)→eνμν final state are presented, based on proton–proton collision data collected by the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 20.3 fb\(^{-1}\) at a centre-of-mass energy of \(\sqrt {s}\)=8 TeV. The Standard Model spin-parity J\(^{CP}\)=0\(^{++}\) hypothesis is compared with alternative hypotheses for both spin and CP. The case where the observed resonance is a mixture of the Standard-Model-like Higgs boson and CP-even (J\(^{CP}\)=0\(^{++}\)) or CP-odd (J\(^{CP}\)=0\(^{+-}\)) Higgs boson in scenarios beyond the Standard Model is also studied. The data are found to be consistent with the Standard Model prediction and limits are placed on alternative spin and CP hypotheses, including CP mixing in different scenarios.
Measurements of the ZZ and WW final states in the mass range above the 2m\(_Z\) and 2m\(_W\) thresholds provide a unique opportunity to measure the off-shell coupling strength of the Higgs boson. This paper presents constraints on the off-shell Higgs boson event yields normalised to the Standard Model prediction (signal strength) in the ZZ→4ℓ, ZZ→2ℓ2ν and WW→eνμν final states. The result is based on pp collision data collected by the ATLAS experiment at the LHC, corresponding to an integrated luminosity of 20.3 fb\(^{-1}\) at a collision energy of \(\sqrt {s}\)=8 TeV. Using the CL\(_S\) method, the observed 95 % confidence level (CL) upper limit on the off-shell signal strength is in the range 5.1–8.6, with an expected range of 6.7–11.0. In each case the range is determined by varying the unknown gg→ZZ and gg→WW background K-factor from higher-order quantum chromodynamics corrections between half and twice the value of the known signal K-factor. Assuming the relevant Higgs boson couplings are independent of the energy scale of the Higgs boson production, a combination with the on-shell measurements yields an observed (expected) 95 % CL upper limit on Γ\(_H\)/Γ\(^{SM}_{H}\) in the range 4.5–7.5 (6.5–11.2) using the same variations of the background K-factor. Assuming that the unknown gg→VV background K-factor is equal to the signal K-factor, this translates into an observed (expected) 95 % CL upper limit on the Higgs boson total width of 22.7 (33.0) MeV.
This Letter reports a measurement of the exclusive γγ→ℓ\(^{+}\)ℓ\(^{−}\) (ℓ=e, μℓ=e, μ) cross-section in proton–proton collisions at a centre-of-mass energy of 7 TeV by the ATLAS experiment at the LHC, based on an integrated luminosity of 4.6 fb\(^{−1}\). For the electron or muon pairs satisfying exclusive selection criteria, a fit to the dilepton acoplanarity distribution is used to extract the fiducial cross-sections. The cross-section in the electron channel is determined to be \(^{excl.}_{γγ→e^{+}e^{-}}\)=0.428 ± 0.035 (stat.) ± 0.018 (syst.) pb for a phase–space region with invariant mass of the electron pairs greater than 24 GeV, in which both electrons have transverse momentum p\(_{T}\)>12 GeV and pseudorapidity |η|<2.4. For muon pairs with invariant mass greater than 20 GeV, muon transverse momentum p\(_{T}\)>10 GeV and pseudorapidity |η|<2.4, the cross-section is determined to be \(^{excl.}_{γγ→μ^{+}μ^{-}}\) =0.628 ± 0.032 (stat.) ± 0.021 (syst.) pb. When proton absorptive effects due to the finite size of the proton are taken into account in the theory calculation, the measured cross-sections are found to be consistent with the theory prediction.
A search for the associated production of the Higgs boson with a top quark pair is performed in multilepton final states using 20.3 fb\(^{−1}\) of proton–proton collision data recorded by the ATLAS experiment at \(\sqrt {s}\)=8 TeV at the Large Hadron Collider. Five final states, targeting the decays H→WW\(^{*}\), ττ, and ZZ\(^{*}\), are examined for the presence of the Standard Model (SM) Higgs boson: two same-charge light leptons (e or μ) without a hadronically decaying τ lepton; three light leptons; two same-charge light leptons with a hadronically decaying τ lepton; four light leptons; and one light lepton and two hadronically decaying τ leptons. No significant excess of events is observed above the background expectation. The best fit for the t\(\overline{t}\)H production cross section, assuming a Higgs boson mass of 125 GeV, is 2.1\(^{+1.4}_{-1.2}\) times the SM expectation, and the observed (expected) upper limit at the 95% confidence level is 4.7 (2.4) times the SM rate. The p-value for compatibility with the background-only hypothesis is 1.8σ; the expectation in the presence of a Standard Model signal is 0.9σ.
The distribution and orientation of energy inside jets is predicted to be an experimental handle on colour connections between the hard-scatter quarks and gluons initiating the jets. This Letter presents a measurement of the distribution of one such variable, the jet pull angle. The pull angle is measured for jets produced in t\(\overline{t}\) events with one W boson decaying leptonically and the other decaying to jets using 20.3 fb\(^{−1}\) of data recorded with the ATLAS detector at a centre-of-mass energy of \(\sqrt {s}\)=8 TeV at the LHC. The jet pull angle distribution is corrected for detector resolution and acceptance effects and is compared to various models.
High transverse momentum jets produced in pp collisions at a centre of mass energy of 7 TeV are used to measure the transverse energy–energy correlation function and its associated azimuthal asymmetry. The data were recorded with the ATLAS detector at the LHC in the year 2011 and correspond to an integrated luminosity of 158 pb\(^{-1}\). The selection criteria demand the average transverse momentum of the two leading jets in an event to be larger than 250 GeV. The data at detector level are well described by Monte Carlo event generators. They are unfolded to the particle level and compared with theoretical calculations at next-to-leading-order accuracy. The agreement between data and theory is good and provides a precision test of perturbative Quantum Chromodynamics at large momentum transfers. From this comparison, the strong coupling constant given at the Z boson mass is determined to be αs(m\(_{Z}\))=0.1173±0.0010 (exp.) \(^{+0.0065}_{−0.0026}\) (theo.).
An observation of the View the Λ\(^0_b\)→ψ(2S)Λ\(^0\) decay and a comparison of its branching fraction with that of the Λ\(^0_b\)→J/ψΛ\(^0\) decay has been made with the ATLAS detector in proton–proton collisions at \(\sqrt {s}\)=8 TeV at the LHC using an integrated luminosity of 20.6 fb\(^{-1}\). The J/ψJ/ψ and ψ(2S) mesons are reconstructed in their decays to a muon pair, while the Λ\(^0\)→pπ\(^-\) decay is exploited for the Λ\(^0\) baryon reconstruction. The Λ\(^0_b\) baryons are reconstructed with transverse momentum p\(_T\)>10 GeV pT>10 GeV and pseudorapidity |η|<2.1. The measured branching ratio of the Λ\(^0_b\)→ψ(2S)Λ\(^0\) and Λ\(^0_b\)→J/ψΛ\(^0\) decays is Γ(Λ\(^0_b\)→ψ(2S)Λ\(^0\))/Γ(Λ\(^0_b\)→J/ψΛ\(^0\))=0.501±0.033(stat)±0.019(syst), lower than the expectation from the covariant quark model.
Despite its history of more than one hundred years, the phenomenon of
superconductivity has not lost any of its allure. During that time the concept
and perception of the superconducting state - both from an experimental and
theoretical point of view - has evolved in way that has
triggered increasing interest. What was initially believed to simply be the
disappearance of electrical resistivity, turned out to be a universal and
inevitable result of quantum statistics, characterized by many more
aspects apart from its zero resistivity. The insights of
BCS-theory eventually helped to uncover its deep connection to particle physics
and consequently led to the formulation of the Anderson-Higgs-mechanism. The
very core of this theory is the concept of gauge symmetry (breaking). Within the
framework of condensed-matter theory, gauge invariance is only one of several
symmetry groups which are crucial for the description and classification of
superconducting states. \\
In this thesis, we employ time-reversal, inversion, point group and spin
symmetries to investigate and derive possible Hamiltonians featuring spin-orbit
interaction in two and three spatial dimensions.
In particular, this thesis aims at a generalization of existing numerical
concepts to open up the path to spin-orbit coupled (non)centrosymmetric
superconductors in multi-orbital models.
This is done in a two-fold way: On the one hand, we formulate - based on the
Kohn-Luttinger effect - the perturbative renormalization group in the
weak-coupling limit. On the other hand, we define the spinful flow equations of
the effective action in the framework of functional renormalization, which is
valid for finite interaction strength as well. Both perturbative and functional
renormalization groups produce a low-energy effective (spinful) theory that
eventually gives rise to a particular superconducting state, which is investigated
on the level of the irreducible two-particle vertex. The symbiotic relationship
between both perturbative and functional renormalization can be traced back to
the fact that, while the perturbative renormalization at infinitesimal coupling
is only capable of dealing with the Cooper instability, the functional
renormalization can investigate a plethora of instabilities both in the
particle-particle and particle-hole channels. \\
Time-reversal and inversion are the two key symmetries, which are being used to
discriminate between two scenarios. If both time-reversal and inversion symmetry
are present, the Fermi surface will be two-fold degenerate and characterized by a
pseudospin degree of freedom. In contrast, if inversion symmetry is broken, the
Fermi surface will be spin-split and labeled by helicity. In both cases, we
construct the symmetry allowed states in the particle-particle as well as the
particle-hole channel. The methods presented are formally unified and implemented
in a modern object-oriented reusable and extendable C++ code.
This methodological implementation is employed to one member of both families of
pseudospin and helicity characterized systems. For the pseudospin case, we choose
the intriguing matter of strontium ruthenate, which has been heavily
investigated for already twenty-four years, but still keeps puzzling researchers.
Finally, as the helicity based application, we consider the oxide heterostructure
LaAlO$_{3}$/SrTiO$_{3}$, which became famous for its highly mobile two-
dimensional electron gas and is suspected to host topological superconductivity.