We study twisted bilayer WSe_2 within a continuum moiré model and introduce a method for treating finite geometries directly in the continuum framework, overcoming limitations associated with momentum-space formulations and Wannier obstructions. By projecting a confinement potential onto bulk moiré eigenstates, we obtain a real-space description of edge physics without lattice models. Applying this approach to nanoribbons, we demonstrate chiral edge modes consistent with bulk Chern numbers and reveal their moiré-scale character. In the magic-angle regime, these states are strongly localized, exhibit layer-polarized counter-propagating modes, and are electrically tunable via a displacement field, enabling control of localization, hybridization, and topological transitions. Our results establish a general framework for boundary physics in topological moiré materials.

The conventional description of transport through the interface between a normal conductor and a superconductor reduces the system to a one-dimensional problem treating Andreev reflection based on a zero-dimensional Sharvin-type point-contact model, and effectively neglects all considerations of device geometry. While this has been successful in systems where conductance in the normal material is in the diffusive transport regime, such an oversimplification of the problem fails in other transport regimes. In particular, when transport is ballistic as in a typical semiconductor-superconductor hybrid structure, geometrical effects are inherently important, and a proper description must consider a one-dimensional contact injecting into a two-dimensional ballistic cavity. We present a study of this regime and explore the bias-voltage dependence of Andreev transport in a cavity-type device comprised of a high-mobility HgTe quantum well side-contacted by one superconducting and one normal contact, each creating a one-dimensional interface. The enhanced conductance from Andreev transport features two finite-bias conductance peaks, observed at energies within the energy gap of the superconductor. Interestingly, these two peaks respond differently to the application of a perpendicular-to-plane magnetic field. Using a semiclassical model for the quantum transport within the cavity, we are able to attribute each peak to a different class of ballistic trajectories. One class is dominated by normal reflection, and its interference condition is independent of magnetic field, whereas the other one contains retroreflected Andreev processes at the superconductor interface. These create closed trajectories that are strongly suppressed by magnetic field due to Aharonov-Bohm and Doppler shift effects.

The search for scalable, electrically controlled qubits remains a central challenge in quantum technology. We introduce gate-defined moiré quantum dots as a promising platform for valley-based qubits. Moiré engineering resolves the central conflict of valley physics: momentum-space separation protects the states, while the enlarged moiré length scale allows smooth gates to mix them controllably. Dot geometry and confinement strength program valley hybridization, while a displacement field controls detuning, providing two noncommuting electrostatic axes for qubit control.

Simplified models with a minimal number of degrees of freedom have been a fruitful tool for gaining understanding of the essence of topological-insulator physics without the ballast of complications typical for band structures of these narrow-gap materials. The Bernevig-Hughes-Zhang model is such a minimal model, designed for describing the quantum spin Hall effect in HgTe quantum wells, more precisely, the transition between a trivial and topological phase as a function of the quantum well thickness. Since symmetry is central to the idea of quantum anomalies (e.g., the parity anomaly) in topological insulators, it is essential to identify them properly in these minimal models. In this work, we use dimensional reduction of three-dimensional point groups to the two-dimensional point groups appropriate for these quasi-two-dimensional minimal models, using the models for thin and thick layers of HgTe as examples. We determine the actions of crystal and time reversal operations on the basis states and the associated conserved quantum numbers, which aid the interpretation of the physics. While the usual effective models are invariant under the parity operation z -* -z, this symmetry is broken by electric fields along the z direction. We identify parity-odd contributions such as the well-known Rashba-type term in these effective models and show which quantum numbers remain conserved.

A topological invariant based on polar-decomposition of matrices correctly captures the topology of finite non-Hermitian chains exhibiting the non-Hermitian skin effect, provided that an appropriate crop-length parameter is chosen. This parameter, which sets the cutoff used in the calculation of the invariant, is usually chosen empirically and becomes especially important near topological phase transitions, where finite-size effects are strongest. Here we show that the required crop-length is controlled by physical decay (localization) lengths. For nearest-neighbor and pure longer-range hopping Hatano-Nelson-type chains, the crop-length is set mainly by a single localization length and is well approximated by a scalar multiple of that length. For more general longer-range hopping models, it is governed instead by a multichannel root structure of the characteristic polynomial. Random-forest regression captures finite-size and near-boundary corrections while preserving this decay-length interpretation. Trained on one set of Hamiltonians, the predictor accurately generalizes to unseen Hamiltonians and complex base energies, reproducing crop-lengths across full phase diagrams. We further show that the predictions learned from clean nearest-neighbor hopping chains remain stable under moderate hopping disorder. These results provide a practical and physically interpretable way to choose the crop-length, which in turn determines when the real-space invariant can reliably capture the topology of finite non-Hermitian chains.

We study the non-Hermitian topology of multi-terminal transport in a quantum spin-Hall device described by the Bernevig-Hughes-Zhang model. We show that breaking time-reversal symmetry alone does not imply non-reciprocal transport or a non-Hermitian conductance matrix. Instead, non-Hermitian topology arises only when transport becomes directionally imbalanced. We identify two distinct mechanisms that generate such a response: spin-selective coupling at the contacts and an out-of-plane Zeeman field that unbalances the counter-propagating helical edge modes. We show, for unpolarized leads, that the spin polarization-dependent response to Zeeman fields, provides a transport-based probe of the intrinsic spin polarization of the helical edge states. Moreover, we demonstrate that non-Hermitian skin effect is more sensitive than conductance elements to detect the spin polarization of the edge states. Our results clarify the conditions required for non-Hermitian topology in quantum spin-Hall transport and establish non-Hermitian skin effect as a diagnostic tool for spin-selective coupling and edge-state polarization.

We investigate thermal and non-local electrical transport in four-terminal Josephson junctions formed by a normal region coupled to two transverse chiral superconducting leads, supporting phases characterized by Chern numbers C=0, 1 and 2. We identify the conditions under which a single chiral Majorana mode (C=1) produces a robust half-quantized thermal conductance, while non-local electrical conductance remains strongly suppressed by particle-hole symmetry. Thermal conductance quantization occurs near a superconducting phase difference π, but only in the low-doping regime of the central region and in the intermediate- to long-junction limits. At finite Zeeman fields, the thermal response broadly follows the topology of the isolated superconducting leads for the C=1 phase while, in the C=2 phase, the thermal conductance generally deviates from quantization, depending on the momentum-space location of the Majorana modes. Our results establish clear criteria for probing chiral Majorana modes in Josephson junctions and highlight the essential role of momentum-space structure, finite-size geometry, and sample parameters in thermal transport.

This work focuses on the nondissipative, parity-odd spin transport of (2 + 1)-dimensional relativistic electrons, generated by torsion, and the torsional Hall viscosity H. We first determine H for massive Dirac fermions in the presence of a constant electromagnetic field. We predict that the magnetic field induces a contribution to H competing with the one originating from the Dirac mass. Moreover, we quantify the impact on H originating from the band structure deformation quadratic in momentum terms that was proposed by Bernevig-Hughes-Zhang (BHZ). We find that the BHZ deformation substantially enhances H in magnitude as measured in a domain wall configuration, when compared to the free Dirac fermion result. Nevertheless, the torsional Hall viscosity still discriminates between topologically trivial and nontrivial regimes. Our results, hence, pave the way for a deeper understanding of hydrodynamic spin transport and its possible verification in experiments.

Spin-momentum-locked edge states of quantum spin Hall insulators provide a compelling platform for spintronic applications, owing to their intrinsic protection against backscattering from non-magnetic disorder. This protection emerges from time-reversal symmetry, which pairs Kramers partners of helical edge modes with opposite spin and momentum, thereby strictly forbidding elastic single-particle backscattering within the pair. Yet, contrary to the idealized notion of linear edge bands, the non-monotonic dispersions of realistic materials can host multiple Kramers pairs, reintroducing backscattering channels between them without violating time-reversal symmetry. Here, we investigate inter-Kramers pair backscattering in the non-linear edge bands of the quantum spin Hall insulator indenene, highlighting a critical aspect of edge state stability. Using quasiparticle interference in scanning tunneling spectroscopy - a direct probe of backscattering - we observe intra-band coupling between different Kramers pairs, while energy regions with only a single Kramers pair remain strictly protected. Supported by theoretical analysis, our findings provide an unprecedented experimental demonstration of edge state backscattering fully consistent with their underlying topological protection. This insight has profound implications for numerous quantum spin Hall insulator candidates, emphasizing that the mere presence of gap-traversing edge modes does not inherently guarantee their protection against backscattering.

It has recently been shown that signatures of non-Hermitian topology can be realized in a conventional quantum Hall device connected to multiple current sources. These signatures manifest as robust current-voltage characteristics, dictated by the presence of a nontrivial, non-Hermitian topological invariant of the conductance matrix. Chiral edge states are believed to be responsible for this non-Hermitian response, similar to how they lead to a quantized Hall conductivity in the presence of a single current source. Here, we go beyond this paradigm, showing that multi-terminal conductance matrices can exhibit non-Hermitian topological phase transitions that cannot be traced back to the presence and directionality of a boundary-localized chiral mode. By performing quantum transport simulations in the quantum Hall regime of monolayer graphene, we find that when the chemical potential is swept across the zeroth Landau level, unavoidable device imperfections cause the appearance of an additional non-Hermitian phase of the conductance matrix. This highlights graphene as an ideal platform for the study of non-Hermitian topological phase transitions, and is a first step towards exploring how the geometry of quantum devices can be harnessed to produce robust, topologically-protected transport characteristics.

We study the thermoelectrical transport transverse to conventional and topological Josephson junctions with a central quantum dot (QD). For that purpose, we derive an effective resonant tunneling model where the QD is renormalized with an induced superconducting gap. By applying the Keldysh Green's function technique, we compute the local density of states as well as the transmission functions. In the latter case, we observe that the Andreev bound states forming on the QD are inverted if the junction has p-wave symmetry, meaning that electron and hole orbitals switch roles. We calculate the thermoelectric transport coefficients both analytically and numerically and show how the induced gaps and the band inversion are reflected in the electrical and heat conductance as well as the Seebeck coefficient, the latter experiencing a sign change in the topological case.

The software project kdotpy provides a Python application for simulating electronic band structures of semiconductor devices with k·p theory on a lattice. The application implements the widely used Kane model, capable of reliable predictions of transport and optical properties for a large variety of topological and non-topological materials with a zincblende crystal structure. The application automates the tedious steps of simulating band structures. The user inputs the relevant physical parameters on the command line, for example materials and dimensions of the device, magnetic field, and temperature. The program constructs the appropriate matrix Hamiltonian on a discretized lattice of spatial coordinates and diagonalizes it. The physical observables are extracted from the eigenvalues and eigenvectors and saved as output. The program is highly customizable with a large set of configuration options and material parameters.

The band inversion of topological materials in three spatial dimensions is intimately connected to the parity anomaly of 2D massless Dirac fermions, known from quantum field theory. At finite magnetic fields, the parity anomaly reveals itself as a non-zero spectral asymmetry, i.e., an imbalance between the number of conduction and valence band Landau levels, due to the unpaired zero Landau level. This work reports the realization of this 2D Dirac physics at a single surface of the 3D topological insulator (Hg,Mn)Te. An unconventional re-entrant sequence of quantized Hall plateaus in the measured Hall resistance can be directly related to the occurrence of spectral asymmetry in a single topological surface state. The effect should be observable in any topological insulator where the transport is dominated by a single Dirac surface state.

The unambiguous identification of Majorana zero modes (MZMs) is one of the most outstanding problems of condensed matter physics. Thermal transport provides a detection tool that is sensitive to these chargeless quasiparticles. We study thermoelectric transport between metallic leads transverse to a Josephson junction. The central double quantum dot hosts conventional or topological Andreev states that depend on the phase difference $\phi$. We show that the presence of MZMs can be identified by a significant amplification of both the electrical and thermal conductance at $\phi \approx \pi$ as well as the Seebeck coefficient at $\phi \approx 0$. We further investigate the robustness of our results against Cooper pair splitting processes.

The conformal anomaly indicates the breaking of conformal symmetry (angle-preserving transformations) in the quantum theory by quantum fluctuations and is a close cousin of the gravitational anomaly. We show, for the first time, that the conformal anomaly controls the variance of the local magnetization M loc at finite temperatures in spin chains and spin ladders. This effect is perceived at constant and variable temperature across the sample. The change of M loc induced by the conformal anomaly is of the order of 3-5% of the maximal spin at one Kelvin for DIMPY or CuPzN and increases linearly with temperature. Further, for a temperature gradient of 10% across the sample, the time-relaxation of the non-equilibrium M loc is of the order of nanoseconds. Thus, we believe that experimental techniques such as neutron scattering, nuclear magnetic resonance (NMR), spin noise and ultrafast laser pumping should pinpoint the presence of the conformal anomaly. There-fore, we pave the road to detect the conformal anomaly in spin observables of strongly interacting low-dimensional magnets.

Quantum devices characterized by non-Hermitian topology are predicted to show highly robust and potentially useful properties for precision sensing and signal amplification. However, realizing them has remained a daunting experimental task, as non-Hermiticity is often associated with gain and loss, which would require precise tailoring to produce the signatures of non-trivial topology. Here, instead of gain and loss, we use the non-reciprocity of quantum Hall edge states to directly observe non-Hermitian topology in a multi-terminal quantum Hall ring. Our transport measurements evidence a robust, non-Hermitian skin effect, characterized by currents and voltages showing an exponential profile that persists across Hall plateau transitions away from the regime of maximum non-reciprocity. Our observation of non-Hermitian topology in a quantum device introduces a scalable experimental approach to construct and investigate generic non-Hermitian systems.

The scattering of superconducting pairs by magnetic impurities on a superconducting surface leads to pairs of sharp in-gap resonances known as Yu-Shiba-Rusinov (YSR) bound states. Similar to the interference of itinerant electrons scattered by defects in normal metals, these resonances reveal a periodic texture around the magnetic impurity. The wavelength of these resonances is, however, often too short to be resolved even by methods capable of atomic resolution, i.e., scanning tunneling microscopy (STM). We combine a CO molecule with a superconducting cluster pre-attached to an STM tip to maximize both spatial and energy resolution, thus demonstrating the superior properties of such double-functionalized probes by imaging the spatial distribution of YSR states. Our approach reveals rich interference patterns of the hybridized YSR states of two Fe atoms on Nb(110), previously inaccessible with conventional STM probes. This advancement extends the capabilities of STM techniques, providing insights into superconducting phenomena at the atomic scale.

Quantum Hall phases have recently emerged as a platform to investigate non-Hermitian topology in condensed-matter systems. This platform is particularly interesting due to its tunability, which allows to modify the properties and topology of the investigated non-Hermitian phases by tuning external parameters of the system such as the magnetic field. Here, we show the tunability of non-Hermitian topology chirality in a graphene heterostructure using a gate voltage. By changing the charge carrier density, we unveil some novel properties specific to different quantum Hall regimes. First, we find that the best quantization of the non-Hermitian topological invariant is interestingly obtained at very high filling factor rather than on well-quantized quantum Hall plateaus. This is of particular importance for the efficient operation of devices based on non-Hermitian topology. Moreover, we observe an additional non-Hermitian topological phase in the insulating nu=0 quantum Hall plateau, which survives at lower fields than the opening of the nu=0 gap, confirming a recent prediction of a disorder-induced trivial phase. Our results evidence graphene as a promising platform for the study of non-Hermitian physics and of emergent phases in such topological devices.

Motivated by Hall viscosity measurements in graphene sheets, we study hydrodynamic transport of electrons in a channel of finite width in external electric and magnetic fields. We consider electric charge densities varying from close to the Dirac point up to the Fermi-liquid regime. We find two competing contributions to the hydrodynamic Hall and inverse Nernst signals that originate from the Hall viscous and Lorentz forces. This competition leads to a nonlinear dependence of the full signals on the magnetic field and even a cancellation at different critical field values for both signals. In particular, the hydrodynamic inverse Nernst signal in the Fermi-liquid regime is dominated by the Hall viscous contribution. We further show that a finite channel width leads to a suppression of the Lorenz ratio, while the magnetic field enhances this ratio. All of these effects are predicted in parameter regimes accessible in experiments.

The Callan-Harvey mechanism in 2+1 D Jackiw-Rebbi model is revisited. We analyzed Callan-Harvey anomaly inflow in the massive Chern insulator (quantum anomalous Hall system) subject to external electric field. In addition to the conventional current flowing from the bulk to edge due to parity anomaly, we considered the dissipation of the edge charge due to interaction with external bosonic bath in 2+1 D and due to external bath of photons in 3+1 D. In the case of 2+1 D bosonic bath, we found the new stationary state, which is defined by the balance between Callan-Harvey current and the outgoing flow caused by the dissipation processes. In the case of 3+1 D photon bath, we found a critical electric field, below which this balance state can be achieved, but above which there is no such a balance. Furthermore, we estimated the photon-mediated transition rate between 2+1 D bulk and 1+1 D topological edge state of the order of one ns$^{-1}$ (nanosecond) at the room temperature.