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Institute
- Institut für Theoretische Physik und Astrophysik (24) (remove)
The prediction and the experimental discovery of topological insulators has set the stage for a novel type of electronic devices. In contrast to conventional metals or semiconductors, this new class of materials exhibits peculiar transport properties at the sample surface, as conduction channels emerge at the topological boundaries of the system.
In specific materials with strong spin-orbit coupling, a particular form of a two-dimensional topological insulator, the quantum spin Hall state, can be observed.
Here, the respective one-dimensional edge channels are helical in nature, meaning that there is a locking of the spin orientation of an electron and its direction of motion.
Due to the symmetry of time-reversal, elastic backscattering off interspersed impurities is suppressed in such a helical system, and transport is approximately ballistic.
This allows in principle for the realization of novel energy-efficient devices, ``spintronic`` applications, or the formation of exotic bound states with non-Abelian statistics, which could be used for quantum computing.
The present work is concerned with the general transport properties of one-dimensional helical states. Beyond the topological protection mentioned above, inelastic backscattering can arise from various microscopic sources, of which the most prominent ones will be discussed in this Thesis. As it is characteristic for one-dimensional systems, the role of electron-electron interactions can be of major importance in this context.
First, we review well-established techniques of many-body physics in one dimension such as perturbative renormalization group analysis, (Abelian) bosonization, and Luttinger liquid theory. The latter allow us to treat electron interactions in an exact way.
Those methods then are employed to derive the corrections to the conductance in a helical transport channel, that arise from various types of perturbations.
Particularly, we focus on the interplay of Rashba spin-orbit coupling and electron interactions as a source of inelastic single-particle and two-particle backscattering. It is demonstrated, that microscopic details of the system, such as the existence of a momentum cutoff, that restricts the energy spectrum, or the presence of non-interacting leads attached to the system, can fundamentally alter the transport signature.
By comparison of the predicted corrections to the conductance to a transport experiment, one can gain insight about the microscopic processes and the structure of a quantum spin Hall sample.
Another important mechanism we analyze is backscattering induced by magnetic moments. Those findings provide an alternative interpretation of recent transport measurements in InAs/GaSb quantum wells.
Within gauge/gravity duality, we consider the local quench-like time evolution obtained by joining two 1+1-dimensional heat baths at different temperatures at time \(t\) = 0. A steady state forms and expands in space. For the 2+1-dimensional gravity dual, we find that the “shockwaves” expanding the steady-state region are of spacelike nature in the bulk despite being null at the boundary. However, they do not transport information. Moreover, by adapting the time-dependent Hubeny-Rangamani-Takayanagi prescription, we holographically calculate the entanglement entropy and also the mutual information for different entangling regions. For general temperatures, we find that the entanglement entropy increase rate satisfies the same bound as in the ‘entanglement tsunami’ setups. For small temperatures of the two baths, we derive an analytical formula for the time dependence of the entanglement entropy. This replaces the entanglement tsunami-like behaviour seen for high temperatures. Finally, we check that strong subadditivity holds in this time-dependent system, as well as further more general entanglement inequalities for five or more regions recently derived for the static case.
Blazars like Markarian 421 or Markarian 501 are active galactic nuclei (AGN), with their jets orientated towards the observer. They are among the brightest objects in the very high energy (VHE) gamma ray regime (>100 GeV). Their emitted gamma-ray fluxes are extremely variable, with changing activity levels on timescales between minutes, months, and even years. Several questions are part of the current research, such as the question of the emission regions or the engine of the AGN and the particle acceleration. A dedicated longterm monitoring program is necessary to investigate the properties of blazars in detail. A densely sampled and unbiased light curve allows for observation of both high and low states of the sources, and the combination with multi-wavelength observation could contribute to the answer of several questions mentioned above. FACT (First G-APD Cherenkov Telescope) is the first operational telescope using silicon photomultiplier (SiPM, also known as Geigermode—Avalanche Photo Diode, G-APD) as photon detectors. SiPM have a very homogenous and stable longterm performance, and allow operation even during full moon without any filter, leading to a maximal duty cycle for an Imaging Air Cherenkov Telescope (IACT). Hence, FACT is an ideal device for such a longterm monitoring of bright blazars. A small set of sources (e.g., Markarian 421, Markarian 501, 1ES 1959+650, and 1ES 2344+51.4) is currently being monitored. In this contribution, the FACT telescope and the concept of longterm monitoring of bright blazars will be introduced. The results of the monitoring program will be shown, and the advantages of densely sampled and unbiased light curves will be discussed.
Chromium dioxide CrO\(_2\) belongs to a class of materials called ferromagnetic half-metals, whose peculiar aspect is that they act as a metal in one spin orientation and as a semiconductor or insulator in the opposite one. Despite numerous experimental and theoretical studies motivated by technologically important applications of this material in spintronics, its fundamental properties such as momentumresolved electron dispersions and the Fermi surface have so far remained experimentally inaccessible because of metastability of its surface, which instantly reduces to amorphous Cr\(_2\)O\(_3\). In this work, we demonstrate that direct access to the native electronic structure of CrO\(_2\) can be achieved with soft-x-ray angle-resolved photoemission spectroscopy whose large probing depth penetrates through the Cr\(_2\)O\(_3\) layer. For the first time, the electronic dispersions and Fermi surface of CrO\(_2\) are measured, which are fundamental prerequisites to solve the long debate on the nature of electronic correlations in this material. Since density functional theory augmented by a relatively weak local Coulomb repulsion gives an exhaustive description of our spectroscopic data, we rule out strong-coupling theories of CrO\(_2\). Crucial for the correct interpretation of our experimental data in terms of the valence-band dispersions is the understanding of a nontrivial spectral response of CrO\(_2\) caused by interference effects in the photoemission process originating from the nonsymmorphic space group of the rutile crystal structure of CrO\(_2\).
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.
Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to the band-structure properties. Another known source of electronic localization in solids is the Coulomb repulsion in partially filled d or f orbitals, which leads to the formation of local magnetic moments. The combination of these two effects is usually considered of little relevance to strongly correlated materials. Here we show that it represents, instead, the underlying physical mechanism in two of the most important ferromagnets: nickel and iron. In nickel, the van Hove singularity has an unexpected impact on the magnetism. As a result, the electron–electron scattering rate is linear in temperature, in violation of the conventional Landau theory of metals. This is true even at Earth’s core pressures, at which iron is instead a good Fermi liquid. The importance of nickel in models of geomagnetism may have therefore to be reconsidered.
The electrodynamics of topological insulators (TIs) is described by modified Maxwell’s equations, which contain additional terms that couple an electric field to a magnetization and a magnetic field to a polarization of the medium, such that the coupling coefficient is quantized in odd multiples of α/4π per surface. Here we report on the observation of this so-called topological magnetoelectric effect. We use monochromatic terahertz (THz) spectroscopy of TI structures equipped with a semitransparent gate to selectively address surface states. In high external magnetic fields, we observe a universal Faraday rotation angle equal to the fine structure constant α=e\(^{2}\)/2E\(_{0}\)hc (in SI units) when a linearly polarized THz radiation of a certain frequency passes through the two surfaces of a strained HgTe 3D TI. These experiments give insight into axion electrodynamics of TIs and may potentially be used for a metrological definition of the three basic physical constants.
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.
Paramagnetic heavy fermion insulators consist of fully occupied quasiparticle bands inherent to Fermi liquid theory. The gap emergence below a characteristic temperature is the ultimate sign of coherence for a many-body system, which in addition can induce a non-trivial band topology. Here, we demonstrate a simple and efficient method to compare a model study and an experimental result for heavy fermion insulators. The temperature dependence of the gap formation in both local moment and mixed valence regimes is captured within the dynamical mean field (DMFT) approximation to the periodic Anderson model (PAM). Using the topological coherence temperature as the scaling factor and choosing the input parameter set within the mixed valence regime, we can unambiguously link the theoretical energy scales to the experimental ones. As a particularly important result, we find improved consistency between the scaled DMFT density of states and the photoemission near-gap spectra of samarium hexaboride (SmB\(_{6}\)).
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.
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.
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.
Just as photons are the quanta of light, plasmons are the quanta of orchestrated charge-density oscillations in conducting media. Plasmon phenomena in normal metals, superconductors, and doped semiconductors are often driven by long-wavelength Coulomb interactions. However, in crystals whose Fermi surface is comprised of disconnected pockets in the Brillouin zone, collective electron excitations can also attain a shortwave component when electrons transition between these pockets. In this work, we show that the band structure of monolayer transition-metal dichalcogenides gives rise to an intriguing mechanism through which shortwave plasmons are paired up with excitons. The coupling elucidates the origin for the optical sideband that is observed repeatedly in monolayers of WSe\(_2\) and WS\(_2\) but not understood. The theory makes it clear why exciton-plasmon coupling has the right conditions to manifest itself distinctly only in the optical spectra of electron-doped tungsten-based monolayers.
Low-energy spin excitations in any long-range ordered magnetic system in the absence of magnetocrystalline anisotropy are gapless Goldstone modes emanating from the ordering wave vectors. In helimagnets, these modes hybridize into the so-called helimagnon excitations. Here we employ neutron spectroscopy supported by theoretical calculations to investigate the magnetic excitation spectrum of the isotropic Heisenberg helimagnet \({ZnCr_2Se_4}\) with a cubic spinel structure, in which spin\(-3/2\) magnetic \({Cr^{3+}}\) ions are arranged in a geometrically frustrated pyrochlore sublattice. Apart from the conventional Goldstone mode emanating from the \((0~ 0~ {q_h})\) ordering vector, low-energy magnetic excitations in the single-domain proper-screw spiral phase show soft helimagnon modes with a small energy gap of \({∼0.17~ meV}\), emerging from two orthogonal wave vectors \(({q_h}~ 0~ 0)\) and \({(0~ {q_h}~ 0)}\) where no magnetic Bragg peaks are present. We term them pseudo-Goldstone magnons, as they appear gapless within linear spinwave theory and only acquire a finite gap due to higher-order quantum-fluctuation corrections. Our results are likely universal for a broad class of symmetric helimagnets, opening up a new way of studying weak magnon-magnon interactions with accessible spectroscopic methods.
A search for high-energy neutrino emission correlated with gamma-ray bursts outside the electromagnetic prompt-emission time window is presented. Using a stacking approach of the time delays between reported gamma-ray burst alerts and spatially coincident muon-neutrino signatures, data from the Antares neutrino telescope recorded between 2007 and 2012 are analysed. One year of public data from the IceCube detector between 2008 and 2009 have been also investigated. The respective timing profiles are scanned for statistically significant accumulations within 40 days of the Gamma Ray Burst, as expected from Lorentz Invariance Violation effects and some astrophysical models. No significant excess over the expected accidental coincidence rate could be found in either of the two data sets. The average strength of the neutrino signal is found to be fainter than one detectable neutrino signal per hundred gamma-ray bursts in the Antares data at 90% confidence level.
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.
High-energy jets recoiling against missing transverse energy (MET) are powerful probes of dark matter at the LHC. Searches based on large MET signatures require a precise control of the \({Z(ν\overline{ν})}+\) jet background in the signal region. This can be achieved by taking accurate data in control regions dominated by \(Z(ℓ^+ℓ^−)+\) jet, \(W(ℓν)+\) jet and \(γ+\) jet production, and extrapolating to the \({Z(ν\overline{ν})}+\) jet background by means of precise theoretical predictions. In this context, recent advances in perturbative calculations open the door to significant sensitivity improvements in dark matter searches. In this spirit, we present a combination of state-of-the-art calculations for all relevant \(V+\) jets processes, including throughout NNLO QCD corrections and NLO electroweak corrections supplemented by Sudakov logarithms at two loops. Predictions at parton level are provided together with detailed recommendations for their usage in experimental analyses based on the reweighting of Monte Carlo samples. Particular attention is devoted to the estimate of theoretical uncertainties in the framework of dark matter searches, where subtle aspects such as correlations across different \(V+\) jet processes play a key role. The anticipated theoretical uncertainty in the \({Z(ν\overline{ν})}+\) jet background is at the few percent level up to the TeV range.
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.
Advanced LIGO detected a significant gravitational wave signal (GW170104) originating from the coalescence of two black holes during the second observation run on January 4th, 2017. An all-sky high-energy neutrino follow-up search has been made using data from the Antares neutrino telescope, including both upgoing and downgoing events in two separate analyses. No neutrino candidates were found within ±500 s around the GW event time nor any time clustering of events over an extended time window of ±3 months. The non-detection is used to constrain isotropic-equivalent high-energy neutrino emission from GW170104 to less than ∼ 1.2 × \(10^{55}\) erg for a \(E^{−2}\) spectrum. This constraint is valid in the energy range corresponding to the 5–95% quantiles of the neutrino flux [3.2 TeV; 3.6 PeV], if the GW emitter was below the Antares horizon at the alert time.
We consider a scenario inspired by natural supersymmetry, where neutrino data is explained within a low-scale seesaw scenario. We extend the Minimal Supersymmetric Standard Model by adding light right-handed neutrinos and their superpartners, the R-sneutrinos, and consider the lightest neutralinos to be higgsino-like. We consider the possibilities of having either an R-sneutrino or a higgsino as lightest supersymmetric particle. Assuming that squarks and gauginos are heavy, we systematically evaluate the bounds on slepton masses due to existing LHC data.
The topic of this PhD thesis is the combination of topologically non-trivial phases with correlation effects stemming from Coulomb interaction between the electrons in a condensed matter system. Emphasis is put on both emerging benefits as well as hindrances, e.g. concerning the topological protection in the presence of strong interactions.
The physics related to topological effects is established in Sec. 2. Based on the topological band theory, we introduce topological materials including Chern insulators, topological insulators in two and three dimensions as well as Weyl semimetals. Formalisms for a controlled treatment of Coulomb correlations are presented in Sec. 3, starting with the topological field theory. The Random Phase Approximation is introduced as a perturbative approach, while in the strongly interacting limit the theory of quantum Hall ferromagnetism applies. Interactions in one dimension are special, and are treated through the Luttinger liquid description. The section ends with an overview of the expected benefits offered by the combination of topology and interactions, see Sec. 3.3.
These ideas are then elaborated in the research part. In Chap. II, we consider weakly interacting 2D topological insulators, described by the Bernevig-Hughes-Zhang model. This is applicable, e.g., to quantum well structures made of HgTe/CdTe or InAs/GaSb. The bulk band structure is here a mixture stemming from linear Dirac and quadratic Schrödinger fermions. We study the low-energy excitations in Random Phase Approximation, where a new interband plasmon emerges due to the combined Dirac and Schrödinger physics, which is absent in the separate limits. Already present in the undoped limit, one finds it also at finite doping, where it competes with the usual intraband plasmon. The broken particle-hole symmetry in HgTe quantum wells allows for an effective separation of the two in the excitation spectrum for experimentally accessible parameters, in the right range for Raman or electron loss spectroscopy. The interacting bulk excitation spectrum shows here clear differences between the topologically trivial and topologically non-trivial regime. An even stronger signal in experiments is expected from the optical conductivity of the system. It thus offers a quantitative way to identify the topological phase of 2D topological insulators from a bulk measurement.
In Chap. III, we study a strongly interacting system, forming an ordered, quantum Hall ferromagnetic state. The latter can arise also in weakly interacting materials with an applied strong magnetic field. Here, electrons form flat Landau levels, quenching the kinetic energy such that Coulomb interaction can be dominant. These systems define the class of quantum Hall topological insulators: topologically non-trivial states at finite magnetic field, where the counter-propagating edge states are protected by a symmetry (spatial or spin) other than time-reversal. Possible material realizations are 2D topological insulators like HgTe heterostructures and graphene. In our analysis, we focus on the vicinity of the topological phase transition, where the system is in a strongly interacting quantum Hall ferromagnetic state. The bulk and edge physics can be described by a nonlinear \sigma-model for the collective order parameter of the ordered state. We find that an emerging, continuous U(1) symmetry offers topological protection. If this U(1) symmetry is preserved, the topologically non-trivial phase persists in the presence of interactions, and we find a helical Luttinger liquid at the edge. The latter is highly tunable by the magnetic field, where the effective interaction strength varies from weakly interacting at zero field, K \approx 1, to diverging interaction strength at the phase transition, K -> 0.
In the last Chap. IV, we investigate whether a Weyl semimetal and a 3D topological insulator phase can exist together at the same time, with a combined, hybrid surface state at the joint boundaries. An overlap between the two can be realized by Coulomb interaction or a spatial band overlap of the two systems. A tunnel coupling approach allows us to derive the hybrid surface state Hamiltonian analytically, enabling a detailed study of its dispersion relation. For spin-symmetric coupling, new Dirac nodes emerge out of the combination of a single Dirac node and a Fermi arc. Breaking the spin symmetry through the coupling, the dispersion relation is gapped and the former Dirac node gets spin-polarized. We propose experimental realizations of the hybrid physics, including compressively strained HgTe as well as heterostructures of topological insulator and Weyl semimetal materials, connected to each other, e.g., by Coulomb interaction.
The thesis deals with the automated generation and efficient evaluation of scattering amplitudes in general relativistic quantum field theories at one-loop order in perturbation theory. At the
present time we lack signals beyond the Standard Model which, in the past, have guided the
high-energy physics community, and ultimately led to the discovery of new physics phenomena.
In the future, precision tests could acquire this guiding role by systematically probing the Standard Model and constraining Beyond the Standard Model theories. As current experimental
constraints strongly favour Standard Model-like theories, only small deviations with respect to the Standard Model are expected which need to be studied in detail. The required precision
demands one-loop corrections in all future analyses, ideally in a fully automated way, allowing
to test a variety of observables in different models and in an effective field theory approach.
In the process of achieving this goal we have developed an enhanced version of the tool
Recola and on this basis the generalization Recola2. These tools represent fully automated
tree- and one-loop-amplitude providers for the Standard Model, or in the case of Recola2
for general models. Concerning the algorithm, we use a purely numerical and fully recursive
approach allowing for extreme calculations of yet unmatched complexity. Recola has led to the first computation involving 9-point functions. Beyond the Standard Model theories and Effective Field theories are integrated into the Recola2 framework as model files. Renormalized model files are produced with the newly developed tool Rept1l, which can perform the renormalization in a fully automated way, starting from nothing but Feynman rules. In view of validation, we have extended Recola2 to new gauges such as the Background-Field Method and the class of Rxi gauges. In particular, the Background-Field Method formulation for new theories serves as an automated validation, and is very useful in practical calculations and the formulation of renormalization conditions. We have applied the system to produce the first results for Higgs-boson production in Higgs strahlung and vector-boson fusion in the Two-Higgs-Doublet Model and the Higgs-Singlet Extension of the Standard Model. All in all, we have laid the foundation for an automated generation and computation of one-loop amplitudes within a large class of phenomenologically interesting theories. Furthermore, we enable the use of our system via a very flexible and dynamic control which does not require any intermediate intervention.
Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enable the detection of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency f\(_{J}\) rather than conventional emission at f\(_{J}\). Here, we report direct measurement of rf emission spectra on Josephson junctions made of HgTe-based gate-tunable topological weak links. The emission spectra exhibit a clear signal at half the Josephson frequency f\(_{J}\)/2. The linewidths of emission lines indicate a coherence time of 0.3–4 ns for the f\(_{J}\)/2 line, much shorter than for the f\(_{J}\) line (3–4 ns). These observations strongly point towards the presence of topological gapless Andreev bound states and pave the way for a future HgTe-based platform for topological quantum computation.
We 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.