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Silicon Carbide (SiC) has several advantageous properties compared to Silicon (Si) that make it an appealing detector material, such as a larger charge carrier saturation velocity, bandgap, and thermal conductivity. While the current understanding of material and model parameters suffices to simulate unirradiated 4H-SiC devices using technical computer-aided design (TCAD), configurations to accurately predict performance degradation after high levels of irradiation due to induced defects acting as traps and recombination centers do not exist. Despite increasing efforts to characterize the introduction and nature of such defects in 4H-SiC, published results are often contradictory. This work presents a bulk radiation damage model for TCAD simulations based on measurements on 50 $\mu m$ 4H-SiC pad diodes, neutron-irradiated at various fluxes ranging from $5\times 10^{14}$ $n_{eq}/cm^2$ to $1\times 10^{16}$ $n_{eq}/cm^2$. The model accurately predicts internal electric shifts, such as flattening of the detector capacitance, degradation in charge collection efficiency (CCE), and signal detection capabilities under forward bias conditions up to high bias. It further introduces the EH$_4$ defect cluster as major lifetime killer and reinforces the assumption of the EH$_{6,7}$ deep-level defect to be of donor type., Comment: Proceeding of a Poster talk at the 16th Pisa Meeting on Advanced Detectors

We describe the planned near-term and potential longer-term upgrades of the Belle II detector at the SuperKEKB electron-positron collider operating at the KEK laboratory in Tsukuba, Japan. These upgrades will allow increasingly sensitive searches for possible new physics beyond the Standard Model in flavor, tau, electroweak and dark sector physics that are both complementary to and competitive with the LHC and other experiments., Comment: Editor: F. Forti 170 pages

The tetragonal heavy fermion compound CeRh2As2 has intriguing low temperature symmetry breaking phases whose nature is unclear. The unconventional superconducting phase is complemented by other normal state phases which presumably involve ordering of 4f electron multipoles supported by the Kramers doublets split by the tetragonal crystal electric field (CEF). The most striking aspect is the pronounced anisotropic H-T phase boundary for in-plane and out-of plane field direction. Using a localized 4f CEF model we demonstrate that its essential features can be understood as the result of competing low field easy-plane magnetic order and field-induced quadrupolar order of XY type. We present calculations based on a coupled multipole random-phase approximation (RPA) response function approach as well as a molecular field treatment in the ordered regime. We use an analytical approach for a reduced quasi-quartet model and numerical calculations for the complete CEF level scheme. We discuss the quantum critical properties as function of multipolar control parameters and explain the origin of a pronounced a-c anisotropy of the H-T phase diagram. Finally the field and temperature evolution of multipolar order parameters is derived and the high field phase diagram is predicted., Comment: 18 pages, 10 figures, to be published in Physical Review B

The silicon vertex detector (SVD) is installed at the heart of the Belle II experiment, taking data at the high-luminosity $B$-Factory SuperKEKB since 2019. The detector has shown a stable and above-99\% hit efficiency, with a large signal-to-noise in all sensors since the beginning of data taking. Cluster position and time resolution have been measured with 2020 and 2022 data and show excellent performance and stability. The effect of radiation damage is visible, but not affecting the performance. As the luminosity increases, higher machine backgrounds are expected and the excellent hit-time information in SVD can be exploited for background rejection. In particular, we have recently developed a novel procedure to select hits by grouping them event-by-event based on their time. This new procedure allows a significant reduction of the fake rate, while preserving the tracking efficiency, and it has therefore replaced the previous cut-based procedure. We have developed a method that uses the SVD hits to estimate the track time (previously unavailable) and the collision time. It has a similar precision to the estimate based on the drift chamber but its execution time is three orders of magnitude smaller, allowing a faster online reconstruction that is crucial in a high luminosity regime. The track time is a powerful information provided to analysis that allows, together with the above-mention grouping selection, to raise the occupancy limit above that expected at nominal luminosity, leaving room for a safety factor. Finally, in June 2022 the data taking of the Belle II experiment was stopped to install a new two-layer DEPFET detector (PXD) and upgrade components of the accelerator. The whole silicon tracker (PXD+SVD) has been extracted from Belle II, the new PXD installed, the detector closed and commissioned. We briefly describe the SVD results of this upgrade., Comment: 16$^{\text{th}}$ Topical Seminar on Innovative Particle and Radiation Detectors (IPRD23) 25--29 September 2023 Siena, Italy

We present a comparative investigation of singlet ground state induced magnetism for singlet, doublet and triplet excited CEF states of non-Kramers f-electrons relevant primarily for Pr- and U- based compounds. This type of magnetic order is of intrinsic quantum nature because it requires the superposition of singlet ground state with excited states due to non-diagonal matrix elements of the effective intersite exchange to generate local moments. In contrast to conventional magnets the local moments and their ordering appear simultaneously at the transition temperature. It is finite only if the control parameter proportional to the ratio of exchange strength to level splitting exceeds a critical value marking the quantum critical point of the models. We determine the dependence of transition temperature, saturation moment, renormalised level splitting, specific heat jumps and low-temperature susceptibility as function of control parameter. Furthermore the temperature dependence of these quantities is calculated for control parameters above and below the quantum critical point and the distinction to conventional magnetism is discussed. In addition we investigate the dynamical properties of the three models, deriving the magnetic exciton dispersion and their critical behaviour. In particular the conditions for true and arrested soft-mode behaviour at the ordering wave vector are identified., Comment: 22 pages, 10 figures

The extremely low dark current of silicon carbide (SiC) detectors, even after high-fluence irradiation, was utilized to develop a beam monitoring system for a wide range of particle rates, i.e., from the kHz to the GHz regime. The system is completely built from off-the-shelve components and is focused on compactness and simple deployment. Beam tests using a 50 um thick SiC detector reveal, that for low fluences, single particles can be detected and counted. For higher fluences, beam properties were extracted from beam cross sections using a silicon strip detector. Overall accurate results were achieved up to a particle rate of 109 particles per second.

Silicon carbide (SiC) is a wide band gap semiconductor and an attractive candidate for applications in harsh environments such as space, fusion, or future high luminosity colliders. Due to the large band gap, the leakage currents in SiC devices are extremely small, even after irradiation to very high fluences, enabling operation without cooling and at high temperatures. This study investigates the effect of neutron irradiation on 50$\mu$m p-n 4H-SiC diodes using current-voltage, capacitance-voltage, and charge collection efficiency (CCE) measurements up to neutron fluences of $1\times 10^{16}$ n$_{\text{eq}}$/cm$^2$. The leakage currents of the investigated devices remained extremely small, below 10 pA at 1.1 kV reverse bias. In the forward bias, a remarkable drop of the current was observed, which was attributed to an increased epi resistivity due to compensation of the epi layer doping by deep-level defects. The CCE was evaluated for alpha particles from a radioactive source, a 62.4 MeV proton beam at the MedAustron ion therapy center and using UV-TCT. The charge collection efficiency in reverse bias was shown to scale directly with the 1 MeV equivalent fluence $\Phi_{\text{eq}}$ as $\text{CCE} \propto \Phi_{\text{eq}}^{-0.63\pm0.01}$. A CCE better than 50% was able to be obtained for fluences up to $1 \times 10^{15}$ n$_{\text{eq}}$/cm$^2$. Because of the low currents in the forward direction, particle detection was also possible in forward bias, where the CCE was found to be increased relative to reverse bias. Furthermore, a significant dependency on the amount of injected charge was observed, with the CCE surpassing 100% in alpha and UV-TCT measurements, requiring further systematic investigation., Comment: 9 pages, 6 figures, to be published in the Proceedings Section of Journal of Instrumentation (JINST) as a proceeding of iWoRiD2023

The application of pressure as well as the successive substitution of Ru with Fe in the hidden order (HO) compound URu$_2$Si$_2$ leads to the formation of the large moment antiferromagnetic phase (LMAFM). Here we have investigated the substitution series URu$_{2-x}$Fe$_x$Si$_2$ from $x$\,=\,0.0 to 2.0 by U\,4$f$ core-level photoelectron spectroscopy and have observed non-monotonic changes in the spectra. The initial increase and subsequent decrease of the spectral weight of the 4$f$ core level satellite with increasing $x$ stands for a non-monotonic 5$f$ filling across the substitution series. The competition of chemical pressure and increase of the density of states at the Fermi energy, both due to substitution of Ru with Fe, can explain such a behavior. An extended Doniach phase diagram including the $x$ dependence of the density of states is proposed. Also in URu$_{2-x}$Fe$_x$Si$_2$ the ground state is a singlet or quasi-doublet state consisting of two singlets. Hence, the formation of magnetic order in the URu$_{2-x}$Fe$_x$Si$_2$ substitution series must be explained within a singlet magnetism model., Comment: 10 pages, 7 figures

Using high resolution tender-x-ray resonant inelastic scattering and hard-x-ray non-resonant inelastic scattering beyond the dipole limit we were able to detect electronic excitations in intermetallic UGa$_2$ that are highly atomic in nature. Analysis of the spectral lineshape reveals that the local $5f^2$ configuration characterizes the correlated nature of this ferromagnet. The orientation and directional dependence of the spectra indicate that the ground state is made of the $\Gamma_1$ singlet and/or $\Gamma_6$ doublet symmetry. With the ordered moment in the $ab$ plane, we infer that the magnetism originates from the higher lying $\Gamma_6$ doublet being mixed with the $\Gamma_1$ singlet due to inter-site exchange, qualifying UGa$_2$ to be a true quantum magnet. The ability to observe atomic excitations is crucial to resolve the on-going debate about the degree of localization versus itineracy in U intermetallics., Comment: 9 pages, 7 figures

We investigate the dispersive paramagnetic excitons on the honeycomb lattice that originate from the crystalline-electric field (CEF) split localized f-electron states in the paramagnetic state due to intersite exchange. We start with a symmetry analysis of possible Ising-type singlet-singlet and xy-type singlet-doublet models. The former supports only symmetric intersite-exchange while the latter additionally allows for antisymmetric Dzyaloshinski-Moriya (DM) exchange interactions. We calculate the closed expressions for magnetic exciton dispersion using both response function formalism and the bosonic Bogoliubov approach. We do this for the most general model that shows inversion symmetry breaking on the honeycomb lattice but also discuss interesting special cases. By calculating Berry curvatures and Chern numbers of paramagnetic excitons we show that the xy model supports nontrivial topological states in a wide range of parameters. This leads to the existence of excitonic topological edge states with Dirac dispersion lying in the zone boundary gap without the presence of magnetic order., Comment: 22 pages, 6 figures

The unique electrical and material properties of 4H-silicon-carbide (4H-SiC) make it a promising candidate material for high rate particle detectors. In contrast to the ubiquitously used silicon (Si), 4H-SiC offers a higher carrier saturation velocity and larger breakdown voltage, enabling a high intrinsic time resolution and mitigating pile-up effects. Additionally, as radiation hardness requirements grow more demanding, wide-bandgap materials such as 4H-SiC could offer better performance. In this work, the detector performance of 50 micron thick 4H-SiC p-in-n planar pad sensors was investigated at room temperature, using an 241Am alpha source at reverse biases of up to 1100 V. Samples subjected to neutron irradiation with fluences of up to 1e16/cm^2 were included in the study in order to quantify the radiation hardness properties of 4H-SiC. The obtained results are compared to previously performed UV-TCT studies. Samples exhibit a drop in charge collection efficiency (CCE) with increasing irradiation fluence, partially compensated at high reverse bias voltages far above full depletion voltage. A plateau of the collected charges is observed in accordance with the depletion of the volume the alpha particles penetrate for an unirradiated reference detector. For the neutron-irradiated samples, such a plateau only becomes apparent at higher reverse bias. For the highest investigated fluence, CCE behaves almost linearly with increasing reverse bias. Compared to UV-TCT measurements, the reverse bias required to deplete a sensitive volume covering full energy deposition is lower, due to the small penetration depth of the alpha particles. At the highest reverse bias, the measured CCE values agree well with earlier UV-TCT studies, with discrepancies between 1% and 5%., Comment: 10 pages (8 without references), 6 figures, 1 table, to be published in the Proceedings Section of Journal of Instrumentation (JINST) as a proceeding of iWoRiD2022

We investigate the magnetic excitation spectrum in the helical state of a noncentrosymmetric superconductor with inversion symmetry breaking and strong Rashba spin-orbit coupling. For this purpose, we derive the general expressions of the dynamical spin response functions under the presence of strong Rashba splitting of conduction bands, superconducting gap, and external field which lead to stabilization of Cooper pairs with finite overall momentum in a helical state. The latter is characterized by momentum space regions of paired and unpaired states with different quasiparticle dispersions. The magnetic response is determined by i) excitations within and between both paired and unpaired regions ii) anomalous coherence factors and iii) additional spin matrix elements due to helical Rashba spin texture of bands. We show that as a consequence typical correlated real space and spin space anisotropies appear in the dynamical susceptibility which would be observable as a characteristic fingerprint for a helical superconducting state in inelastic neutron scattering investigations., Comment: 18 pages, 5 figures

The Silicon Vertex Detector (SVD), with its four double-sided silicon strip sensor layers, is one of the two vertex sub-detectors of Belle II operating at SuperKEKB collider (KEK, Japan). Since 2019 and the start of the data taking, the SVD has demonstrated a reliable and highly efficient operation, even running in an environment with harsh beam backgrounds that are induced by the world's highest instantaneous luminosity. In order to provide the best quality track reconstruction with an efficient pattern recognition and track fit, and to correctly propagate the uncertainty on the hit's position to the track parameters, it is crucial to precisely estimate the resolution of the cluster position measurement. Several methods for estimating the position resolution directly from the data will be discussed., Comment: 4 pages, The 30th International Workshop on Vertex Detectors

We derive the dynamical magnetic response functions in the Fulde-Ferrell (FF) state of a superconductor with inversion symmetry. The pair momentum 2q is obtained by minimization of the condensation energy and the resulting quasiparticle states and spectral functions exhibit the segmentation into paired and unpaired regions due to the finite q. The dynamical magnetic susceptibility is then calculated in linear response formalism in the FF state with finite-q condensate resulting from s-wave or d-wave pairing. We show that quasiparticle excitations inside as well as between paired and unpaired segments contribute to the dynamical response. We discuss its dependence on frequency and momentum transfer which develops a characteristic symmetry-breaking parallel to q. Furthermore, we investigate the possible influence on Knight shift and in the case of d-wave pairing on the spin resonance formation in the FF state., Comment: 10 pages, 8 figures

We investigate the quasiparticle excitations in the FFLO- type helical state of a superconductor with inversion-symmetry breaking and strong Rashba spin-orbit coupling. We restrict to a state with single finite momentum of Cooper pairs in the helical phase that is determined by minimization of the condensation energy. We derive the dependence of quasiparticle dispersions on the Rashba coupling strength and external field. It leads to a peculiar momentum-space segmentation of the corresponding Rashba Fermi surface sheets which has not yet been observed experimentally. We show that it may be directly visualized by the method of quasiparticle interference that identifies the critical points of the segmented sheets and can map their evolution with field strength, bias voltage and Rashba coupling. We also indicate a strategy how to determine the finite Cooper-pair momentum from experimental quantities. This investigation has the potential for a more detailed microscopic understanding of the helical superconducting state under the influence of Rashba spin-orbit coupling., Comment: 12 pages, 7 figures

Hearing loss is a major health problem and psychological burden in humans. Mouse models offer a possibility to elucidate genes involved in the underlying developmental and pathophysiological mechanisms of hearing impairment. To this end, large-scale mouse phenotyping programs include auditory phenotyping of single-gene knockout mouse lines. Using the auditory brainstem response (ABR) procedure, the German Mouse Clinic and similar facilities worldwide have produced large, uniform data sets of averaged ABR raw data of mutant and wildtype mice. In the course of standard ABR analysis, hearing thresholds are assessed visually by trained staff from series of signal curves of increasing sound pressure level. This is time-consuming and prone to be biased by the reader as well as the graphical display quality and scale. In an attempt to reduce workload and improve quality and reproducibility, we developed and compared two methods for automated hearing threshold identification from averaged ABR raw data: a supervised approach involving two combined neural networks trained on human-generated labels and a self-supervised approach, which exploits the signal power spectrum and combines random forest sound level estimation with a piece-wise curve fitting algorithm for threshold finding. We show that both models work well, outperform human threshold detection, and are suitable for fast, reliable, and unbiased hearing threshold detection and quality control. In a high-throughput mouse phenotyping environment, both methods perform well as part of an automated end-to-end screening pipeline to detect candidate genes for hearing involvement. Code for both models as well as data used for this work are freely available., Comment: 41 pages, 17 figures

In 2019 the Belle II experiment started data taking at the asymmetric SuperKEKB collider (KEK, Japan) operating at the Y(4S) resonance. Belle II will search for new physics beyond the Standard Model by collecting an integrated luminosity of 50~ab$^{-1}$. The silicon vertex detector (SVD), consisting of four layers of double-sided silicon strip sensors, is one of the two vertex sub-detectors. The SVD extrapolates the tracks to the inner pixel detector (PXD) with enough precision to correctly identify hits in the PXD belonging to the track. In addition the SVD has standalone tracking capability and utilizes ionization to enhance particle identification in the low momentum region. The SVD is operating reliably and with high efficiency, despite exposure to the harsh beam background of the highest peak-luminosity collider ever built. High signal-to-noise ratio and hit efficiency have been measured, as well as the spatial resolution; all these quantities show excellent stability over time. Data-simulation agreement on cluster properties has recently been improved through a careful tuning of the simulation. The precise hit-time resolution can be exploited to reject out-of-time hits induced by beam background, which will make the SVD more robust against higher levels of background. During the first three years of running, radiation damage effects on strip noise, sensor currents and depletion voltage have been observed, as well as some coupling capacitor failure due to intense radiation bursts. None of these effects cause significant degradation in the detector performance., Comment: 7 pages, 5 figures, proceedings contribution at the 12th International Conference on Position Sensitive Detectors

The protected helical surface states in thin films of topological insulators (TI) are subject to inter-surface hybridisation. This leads to gap opening and spin texture changes as witnessed in photoemission and quasiparticle interference investigations. Theoretical studies show that universally the hybridisation energy exhibits exponential decay as well as sign oscillations as a function of film thickness, depending on the effective band parameters of the material. When a step is introduced in the TI film e.g. by profiling the substrate such that the hybridisation has different signs on both sides of the step, 1D bound states appear within the hybridisation gap which decay exponentially with distance from the step. The step bound states have linear dispersion and inherit the helical spin locking from the surface states and are therefore non-degenerate. When the substrate becomes an s-wave superconductor Majorana zero modes located at the step ends are created inside the superconducting gap. The proposed scenario involves just a suitably stepped interface of superconductor and TI and therefore may be a most simple device being able to host Majorana zero modes., Comment: 10 pages, 5 figures

The quantum magnetism in a three-singlet model (TSM) with singlet crystalline electric field (CEF) states interacting on a lattice is investigated, motivated by its appearance in compounds with 4f^2 and 5f^2 electronic structure. Contrary to conventional (semi-classical) magnetism there are no preformed moments above the ordering temperature Tm. They appear spontaneously as induced or excitonic moments due to singlet-singlet mixing at Tm. In most cases the transition is of second order, however for large matrix elements between the excited states it turns into a first order transition at a critical point. Furthermore we derive the excitonic mode spectrum and its quantum critical soft mode behaviour which leads to the criticality condition for induced order as expressed in terms of the control parameters of the TSM and discuss the distinctions to the previously known two-singlet case. We also derive the temperature dependence of order parameters for second and first order transitions and the exciton spectrum in the induced magnetic phase., Comment: 14 pages, 11 figures

In this paper we describe the implementation of semi-structured deep distributional regression, a flexible framework to learn conditional distributions based on the combination of additive regression models and deep networks. Our implementation encompasses (1) a modular neural network building system based on the deep learning library \pkg{TensorFlow} for the fusion of various statistical and deep learning approaches, (2) an orthogonalization cell to allow for an interpretable combination of different subnetworks, as well as (3) pre-processing steps necessary to set up such models. The software package allows to define models in a user-friendly manner via a formula interface that is inspired by classical statistical model frameworks such as \pkg{mgcv}. The packages' modular design and functionality provides a unique resource for both scalable estimation of complex statistical models and the combination of approaches from deep learning and statistics. This allows for state-of-the-art predictive performance while simultaneously retaining the indispensable interpretability of classical statistical models.

In Path Integral control problems a representation of an optimally controlled dynamical system can be formally computed and serve as a guidepost to learn a parametrized policy. The Path Integral Cross-Entropy (PICE) method tries to exploit this, but is hampered by poor sample efficiency. We propose a model-free algorithm called ASPIC (Adaptive Smoothing of Path Integral Control) that applies an inf-convolution to the cost function to speedup convergence of policy optimization. We identify PICE as the infinite smoothing limit of such technique and show that the sample efficiency problems that PICE suffers disappear for finite levels of smoothing. For zero smoothing this method becomes a greedy optimization of the cost, which is the standard approach in current reinforcement learning. We show analytically and empirically that intermediate levels of smoothing are optimal, which renders the new method superior to both PICE and direct cost-optimization., Comment: 23 pages, 5 figures, NeurIPS 2019 Optimization Foundations of Reinforcement Learning Workshop (OptRL 2019)

The application of pressure as well as the successive substitution of Ru with Fe in the hidden order (HO) compound URu$_2$Si$_2$ leads to the formation of the large moment antiferromagnetic phase (LMAFM). Here we have investigated the substitution series URu$_{2-x}$Fe$_x$Si$_2$ with $x$ = 0.2 and 0.3 with non-resonant inelastic x-ray scattering (NIXS) and 4$f$ core-level photoelectron spectroscopy with hard x-rays (HAXPES). NIXS shows that the substitution of Fe has no impact on the symmetry of the ground-state wave function. In HAXPES we find no shift of spectral weight that would be indicative for a change of the 5$f$-electron count. Consequently, changes in the exchange interaction $\cal{J}$ due to substitution must be minor so that the conjecture of chemical pressure seems unlikely. An alternative scenario is discussed, namely the formation of long range magnetic order due the substitution induced local enhancement of the magnetization in the vicinity of the $f$-electron ions while the overall electronic structure remains unchanged., Comment: 6 pages, 3 figures

Using inelastic x-ray scattering beyond the dipole limit and hard x-ray photoelectron spectroscopy we establish the dual nature of the U $5f$ electrons in UM$_2$Si$_2$ (M = Pd, Ni, Ru, Fe), regardless of their degree of delocalization. We have observed that the compounds have in common a local atomic-like state that is well described by the U $5f^2$ configuration with the $\Gamma_1^{(1)}$ and $\Gamma_2$ quasi-doublet symmetry. The amount of the U 5$f^3$ configuration, however, varies considerably across the UM$_2$Si$_2$ series, indicating an increase of U5$f$ itineracy in going from M=Pd to Ni to Ru, and to the Fe compound. The identified electronic states explain the formation of the very large ordered magnetic moments in UPd$_2$Si$_2$ and UNi$_2$Si$_2$, the availability of orbital degrees of freedom needed for the hidden order in URu$_2$Si$_2$ to occur, as well as the appearance of Pauli paramagnetism in UFe$_2$Si$_2$. A unified and systematic picture of the U$M_2$Si$_2$ compounds may now be drawn, thereby providing suggestions for new experiments to induce hidden order and/or superconductivity in U compounds with the tetragonal body-centered ThCr$_2$Si$_2$ structure.

The underscreened Kondo lattice consisting of a single twofold degenerate conduction band and a CEF split 4f-electron quasi-quartet has non-conventional quasiparticle dispersions obtained from the constrained mean-field theory. An additional genuinely heavy band is found in the main hybridization band gap of the upper and lower hybridzed bands whose heavy effective mass is controlled by the CEF splitting. Its presence should profoundly influence the dynamical optical and magnetic response functions. In the former, the onset of the optical conductivity is not the main hybridisation energy but the much lower Kondo energy scale which appears in the direct transitions to the additional heavy band. The dynamical magnetic response is also strongly modified by the in-gap heavy band which can lead to unconventional resonant excitations that may be interpreted as coherent CEF-Kondo lattice magnetic exciton bands. Their instability at low temperature signifies the onset of induced excitonic magnetism in the underscreened Kondo lattice., Comment: 12 pages, 8 figures

The protected surface states of topological insulators (TIs) form gapless Dirac cones corresponding non-degenerate eigenstates with helical spin polarisation. The presence of a warping term deforms the isotropic cone of the most simple model into snowflake Fermi surfaces as in Bi2Se3 and Bi2Te3. Their features have been identified in STM quasiparticle interference (QPI) experiments on isolated surfaces. Here we investigate the QPI spectrum for the TI thin-film geometry with finite tunnelling between the surface states. This leads to a dramatic change of spectrum due to gapping and a change in spin texture that should leave distinct signatures in the QPI pattern. We consider both normal and magnetic exchange scattering from the surface impurities and obtain the scattering t-matrix in Born approximation as well as the general closed solution. We show the expected systematic variation of QPI snowflake intensity features by varying film thickness and study, in particular, the influence on backscattering processes. We predict the variation of the QPI spectrum for Bi2Se3 thin films using the observed gap dependence from ARPES results., Comment: 16 pages, 13 figures

In contrast to magnetic order formed by electrons' dipolar moments, ordering phenomena associated with higher-order multipoles (quadrupoles, octupoles, etc.) are more difficult to characterize because of the limited choice of experimental probes that can distinguish different multipolar moments. The heavy-fermion compound CeB6 and its La-diluted alloys are among the best-studied realizations of the long-range-ordered multipolar phases, often referred to as "hidden order". Previously the hidden order in phase II was identified as primary antiferroquadrupolar (AFQ) and field-induced octupolar (AFO) order. Here we present a combined experimental and theoretical investigation of collective excitations in the phase II of CeB6. Inelastic neutron scattering (INS) in fields up to 16.5 T reveals a new high-energy mode above 14 T in addition to the low-energy magnetic excitations. The experimental dependence of their energy on the magnitude and angle of the applied magnetic field is compared to the results of a multipolar interaction model. The magnetic excitation spectrum in rotating field is calculated within a localized approach using the pseudo-spin presentation for the Gamma8 states. We show that the rotating-field technique at fixed momentum can complement conventional INS measurements of the dispersion at constant field and holds great promise for identifying the symmetry of multipolar order parameters and the details of inter-multipolar interactions that stabilize hidden-order phases., Comment: 15 pages with 13 figures + Supplemental Material

We review the cubic rare-earth boride series which displays diverse electronic states like localized 4f electron multiplets split by the crystal electric field (CEF), itinerant heavy-fermion quasiparticle bands of the Kondo lattice as well as gapped Kondo insulator or mixed-valent semiconductor states. Fairly exotic states may appear due to the 'hidden' order of multipoles carried by degenerate CEF multiplets, in addition to magnetic order present in many RB6 (R = rare earth) compounds. Most prominent are CeB6 and its La-diluted alloys which exhibit antiferro-quadrupolar and octupolar ordering enabled by the cubic G8 quartet state. The associated collective excitations are multipolar waves with a dispersion characteristic for the underlying order and accessible by inelastic neutron scattering. This localized multipolar-moment picture of R-borides is complemented by the itinerant Kondo-lattice approach. Collective spin exciton modes inside the hybridization gap around symmetry points of the Brillouin zone may appear. This has been observed in heavy-fermion metal CeB6 and in particular in the Kondo insulators YbB12 and SmB6. The latter is also the prime candidate for a strongly correlated topological insulator., Comment: 78 pages, 26 figures; book chapter in "Rare-Earth Borides" , ed. Dmytro S. Inosov

We present a study of the magnetic susceptibility $\chi_{mol}$ under variable hydrostatic pressure on single crystals of Cs$_2$CuCl$_{4-x}$Br$_x$. This includes the border compounds \textit{x} = 0 and 4, known as good realizations of the distorted triangular-lattice spin-1/2 Heisenberg antiferromagnet, as well as the isostructural stoichiometric systems Cs$_2$CuCl$_{3}$Br$_1$ and Cs$_2$CuCl$_{2}$Br$_2$. For the determination of the exchange coupling constants $J$ and $J^{\prime}$, $\chi_{mol}$ data were fitted by a $J-J^{\prime}$ model \cite{Schmidt2015}. Its application, validated for the border compounds, yields a degree of frustration $J^{\prime}$/$J$ = 0.47 for Cs$_2$CuCl$_3$Br$_1$ and $J^{\prime}$/$J$ $\simeq$ 0.63 - 0.78 for Cs$_2$CuCl$_2$Br$_2$, making these systems particular interesting representatives of this family. From the evolution of the magnetic susceptibility under pressure up to about 0.4\,GPa, the maximum pressure applied, two observations were made for all the compounds investigated here. First, we find that the overall energy scale, given by $J_c = (J^2$ + $J^{\prime 2}$)$^{1/2}$, increases under pressure, whereas the ratio $J^{\prime}$/$J$ remains unchanged in this pressure range. These experimental observations are in accordance with the results of DFT calculations performed for these materials. Secondly, for the magnetoelastic coupling constants, extraordinarily small values are obtained. We assign these observations to a structural peculiarity of this class of materials.

The crystal-field (CF) splitting of the $^6H_{5/2}$ Hund's rule ground state of Sm$^{3+}$ in the strongly correlated topological insulator SmB$_6$ has been determined with high resolution resonant inelastic x-ray scattering (RIXS) at the Sm M$_5$ edge. The valence selectivity of RIXS allows isolating the crystal-field-split excited multiplets of the Sm$^{3+}$ (4$f^5$) configuration from those of Sm$^{2+}$ (4$f^6$) in intermediate valent SmB$_6$. The very large energy range of RIXS allows the crystal-field analysis of a high lying multiplet at about 2.4\,eV that has the same total angular momentum $J$ as the ground state so that ambiguities due to the elastic tail can be avoided. We find that the $\Gamma_7$ doublet and $\Gamma_8$ quartet of the $^6H_{5/2}$ Hund's rule ground state are split by $\Delta^{CF}_{^6H_{5/2}}$\,=\,20$\pm$10\,meV which sets an upper limit for the 4$f$ band width. This indicates an extremely large mass renormalization from the band structure value, pointing out the need to consider the coefficients of fractional parentage for the hopping of the 4$f$ electrons., Comment: 8 pages, 6 figures

We report an experimental and theoretical study of the low-temperature specific heat $C$ and magnetic susceptibility $\chi$ of the layered anisotropic triangular-lattice spin-1/2 Heisenberg antiferromagnets Cs$_2$CuCl$_{4-x}$Br$_x$ with $x$ = 0, 1, 2, and 4. We find that the ratio $J'/J$ of the exchange couplings ranges from 0.32 to $\approx 0.78$, implying a change (crossover or quantum phase transition) in the materials' magnetic properties from one-dimensional (1D) behavior for $J'/J < 0.6$ to two-dimensional (2D) behavior for $J'/J \approx 0.78$ behavior. For $J'/J < 0.6$, realized for $x$ = 0, 1, and 4, we find a magnetic contribution to the low-temperature specific heat, $C_{\rm m} \propto T$, consistent with spinon excitations in 1D spin-1/2 Heisenberg antiferromagnets. Remarkably, for $x$ = 2, where $J'/J \approx 0.78$ implies a 2D magnatic character, we also observe $C_{\rm m} \propto T$. This finding, which contrasts the prediction of $C_{\rm m} \propto T^2$ made by standard spin-wave theories, shows that Fermi-like statistics also plays a significant role for the magnetic excitations in frustrated spin-1/2 2D antiferromagnets.

We study the quasiparticle spectrum in an underscreened Kondo-lattice (KL) model that involves a single spin degenerate conduction band and two crystalline-electric-field (CEF) split Kramers doublets coupled by both orbital-diagonal and non-diagonal exchange interactions. We find the three quasiparticle bands of the model using a constrained fermionic mean field approach. While two bands are similar to the one-orbital model a new genuinely heavy band inside the main hybridization gap appears in the quasiquartet model. Its dispersion is due to effective hybridization with conduction states but the bandwidth is controled by the size of the CEF splitting. Furthermore several new indirect and direct hybridztion gaps may be identified. By solving the selfconsistency equation we calculate the CEF- splitting and exchange dependence of effective Kondo low energy scale, hybridization gaps and band widths. We also derive the quasiparticle spectral densities and their partial orbital contributions. We suggest that the two-orbital KL model can exhibit mixed CEF/Kondo excitonic magnetism., Comment: 18pages, 12 figures, published version

Recently the influence of antisymmetric spin-orbit coupling has been studied in novel topological superconductors such as half-Heuslers and artificial hetero-structures. We investigate the effect of Rashba and/or Dresselhaus spin-orbit couplings on the band structure and topological properties of a two-dimensional noncentrosymetric superconductor. For this goal, the topological helical edge modes are analyzed for different spin-orbit couplings as well as for several superconducting pairing symmetries. To explore the transport properties, we examine the response of the spin-polarized edge states to an exchange field in a superconductor-ferromagnet heterostructure. The broken chiral symmetry causes the uni-directional currents at opposite edges., Comment: 10 pages, 7 figures

In quasi-2D quantum magnets the ratio of N\'eel temperature $T_\text N$ to Curie-Weiss temperature $\Theta_\text{CW}$ is frequently used as an empirical criterion to judge the strength of frustration. In this work we investigate how these quantities are related in the canonical quasi-2D frustrated square or triangular $J_1$-$J_2$ model. Using the self-consistent Tyablikov approach for calculating $T_\text N$ we show their dependence on the frustration control parameter $J_2/J_1$ in the whole N\'eel and columnar antiferromagnetic phase region. We also discuss approximate analytical results. In addition the field dependence of $T_\text N(H)$ and the associated possible reentrance behavior of the ordered moment due to quantum fluctuations is investigated. These results are directly applicable to a class of quasi-2D oxovanadate antiferromagnets. We give clear criteria to judge under which conditions the empirical frustration ratio $f=\Theta_\text{CW}/T_\text N$ may be used as measure of frustration strength in the quasi-2D quantum magnets., Comment: 16 pages, 14 figures, to appear in Physical Review B