arXiv subjects

Viktor Könye

Publications and source records attributed to Viktor Könye.

At least 19 recordsLinked to original sources

arXiv2026

Synthetic horizons in an atomic chain: Horizon-induced effects and connections to quantum Hall systems

We investigate the sine model, a one-dimensional tight-binding Hamiltonian with position-dependent sinusoidal hopping, and demonstrate the formation of synthetic horizons where electronic wave packets exhibit exponential slowdown. Interestingly, using the exact transformation between this model and the Harper equation, we find that analogous semiclassical horizons can emerge in a quantum Hall setup within the Harper-equation representation and at half-filling for specific values of the magnetic flux. The Harper equation describes the eigenstates of a square-lattice tight-binding model subjected to a perpendicular magnetic field, as a family of one-dimensional problems parametrized by a conserved transverse quasi-momentum. We demonstrate the correspondence between the sine and Harper models by comparing their semiclassical phase-space portraits and by numerically studying wave-packet dynamics in both models. Furthermore, by applying sudden quenches to the sine model's hopping profile, we observe the emergence of states with an effective thermal Fermi-Dirac distribution characterized by a corresponding Unruh temperature. Our numerical calculations reveal a non-universal behavior of this temperature, suggesting the involvement of mechanisms beyond a simple low-energy description.

cond-mat.mes-hall↗

arXiv2026

Machine learning prediction of the convergence criterion for a topological invariant of finite non-Hermitian chains

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.

cond-mat.mes-hall↗

arXiv2026

Robust Signatures of Fragile Topology

Some topological phases of matter are called fragile. They do not generically host protected gapless boundary states and they can be trivialized by adding additional valence bands. Here we show that fragile topology nevertheless has robust signatures: it yields bulk Dirac cones in two-dimensional materials with arbitrarily many bands. In systems with time-reversal and twofold rotation symmetry, we establish a fragile topological index which guarantees the presence of gap closing points in the band structure. We test this prediction using first-principles calculations in five materials and find that all of them host such Dirac points, suggesting that this is a widespread phenomenon. Our results provide a robust spectroscopic signature of fragile topology which can be directly accessed in experiment. Further, they enable an alternate method for finding Dirac cones in ab-initio simulations, and may be used as a route towards identifying materials with nonlinear transport properties.

cond-mat.mes-hall↗

arXiv2026

Multipolar Piezoelectricity and Anisotropic Surface Transport in Alterelectrics

Altermagnets are an emergent class of materials combining features of ferro- and antiferro-magnetic materials. They have spin-separated bands normally associated with ferromagnets, but a vanishing net magnetization. Moreover the symmetries giving rise to $d$-wave altermagnetism can provide them with a particular anisotropic, quadrupolar (i.e. with equal and opposite values when strained in perpendicular directions) piezomagnetism. Observing that the same symmetries provide a natural place to look for hyberbolic wave dispersion, this raises the question which properties are intrinsically linked to magnetism and which are determined by the symmetry. Here, we disentangle these concepts by introducing an alternative to altermagnets, based on electric polarization. These alterelectrics display quadrupolar piezoelectricity and a hyperbolic dispersion, which we demonstrate conceptually within a simplified model as well as a first-principles material realization. We furthermore establish that a counterpart of the spin-separated bands is formed by surface modes which allow for surface dependent anisotropic electronic transport analogous to the spintronic applications proposed for altermagnets.

cond-mat.mtrl-sci↗

arXiv2025

Non-Hermitian topological devices with Chern insulators

Multi-terminal topological devices are a new generation of electronic devices with quantized properties robust against imperfections. In magnetic topological insulators, dissipationless edge states give functional devices in zero magnetic field, of interest for quantum metrology (resistance standard) or topological electronics (Chern networks). Here we show that a new generation of simple quantum circuits (disk, ring) with non-Hermitian topology, based on the interconnection of 1D Chern states in the quantum anomalous Hall regime, can have a much stronger quantization of their invariant than that of the Chern invariant itself, when measured in a non-metrology grade setup - that is, in industry-relevant conditions. Remarkably, the chirality-related topological skin effect is realized without the need of a magnetic field or an electrical gate, with a record degree of localization for a quantum Hall device. This new type of topological quantum devices based on magnets, with an exponential response that can be switched at small magnetic fields (about 200mT), can operate at liquid-Helium temperature with a good quantization and have some potential as cryogenic sensors for applications in high-precision impedance or magnetic field measurements.

cond-mat.mes-hall↗

arXiv2025

Non-unitary Time Evolution via the Chebyshev Expansion Method

The Chebyshev expansion method is a well-established technique for computing the time evolution of quantum states, particularly in Hermitian systems with a bounded spectrum. Here, we show that the applicability of the Chebyshev expansion method extends well beyond this constraint: It remains valid across the entire complex plane and is thus suitable for arbitrary non-Hermitian matrices. We identify that numerical rounding errors are the primary source of errors encountered when applying the method outside the conventional spectral bounds, and they are not caused by fundamental limitations. By carefully selecting the spectral radius and the time step, we show how these errors can be effectively suppressed, enabling accurate time evolution calculations in non-Hermitian systems. We derive an analytic upper bound for the rounding error, which serves as a practical guideline for selecting time steps in numerical simulations. As an application, we illustrate the performance of the method by computing the time evolution of wave packets in the Hatano-Nelson model.

cond-mat.mes-hall↗

arXiv2025

Non-Hermitian topology of transport in the quantum Hall phases in graphene

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.

cond-mat.mes-hall↗

arXiv2025

Self-consistent surface superconductivity in time-reversal symmetric Weyl semimetals

Weyl semimetals host topologically protected surface states, the so-called Fermi arcs, that have a penetration depth into the bulk that depends on surface-momentum, and diverges at the Weyl points. It has recently been observed in PtBi$_2$ that such Fermi arc states can become superconducting, with a critical temperature larger than that of the bulk. Here we introduce a general variational method that captures the interplay between surface and bulk superconductivity, for any bulk Hamiltonian that harbors (topological) surface states with varying penetration depth. From the self-consistent solutions we establish that the surface state localization length of Weyl semimetals leads to characteristic features in the surface superconductivity, with a gap depending on surface momentum and a penetration length for the order parameter that is temperature-dependent due to competition with the bulk superconductivity.

cond-mat.supr-con↗

arXiv2025

Effects of Berry Curvature and Orbital Magnetic Moment in the Magnetothermoelectric Transport of Bloch Electron Systems

Thermoelectric transport coefficients up to linear order in the applied magnetic field are microscopically studied using Kubo-Luttinger linear response theory and thermal Green's functions. We derive exact formulas for the thermoelectric conductivity and thermal conductivity in the limit of small relaxation rates for Bloch electrons in terms of Bloch wave functions, which show that the Sommerfeld-Bethe relationship holds. Our final formula contains the Berry curvature contributions as well as the orbital magnetic moment contributions, that arise naturally from the microscopic theory. We show that generalized $f$-sum rules containing the Berry curvature and orbital magnetic moment play essential roles in taking into account the interband effects of the magnetic field. As an application, we study a model of a gapped Dirac electron system with broken time-reversal symmetry and show the presence of a linear magnetothermopower in such systems.

cond-mat.mes-hall↗

arXiv2024

Lack of near-sightedness principle in non-Hermitian systems

The non-Hermitian skin effect is a phenomenon in which an extensive number of states accumulates at the boundaries of a system. It has been associated to nontrivial topology, with nonzero bulk invariants predicting its appearance and its position in real space. Here, we demonstrate that the non-Hermitian skin effect has weaker bulk-edge correspondence than topological insulators: when translation symmetry is broken by a single non-Hermitian impurity, skin modes are depleted at the boundary and accumulate at the impurity site, without changing any bulk invariant. Similarly, a single non-Hermitian impurity may deplete the states from a region of Hermitian bulk.

cond-mat.mes-hall↗

arXiv2024

Stability of Weyl node merging processes under symmetry constraints

Changes in the number of Weyl nodes in Weyl semimetals occur through merging processes, usually involving a pair of oppositely charged nodes. More complicated processes involving multiple Weyl nodes are also possible, but they typically require fine tuning and are thus less stable. In this work, we study how symmetries affect the allowed merging processes and their stability, focusing on the combination of a two-fold rotation and time-reversal ($C_2\mathcal{T}$) symmetry. We find that, counter-intuitively, processes involving a merging of three nodes are more generic than processes involving only two nodes. Our work suggests that multi-Weyl-merging may be observed in a large variety of quantum materials, and we discuss SrSi$_2$ and bilayer graphene as potential candidates

cond-mat.mes-hall↗

arXiv2024

Non-Hermitian topology in the quantum Hall effect of graphene

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.

cond-mat.mes-hall↗

arXiv2024

Phase transitions of wave packet dynamics in disordered non-Hermitian systems

Disorder can localize the eigenstates of one-dimensional non-Hermitian systems, leading to an Anderson transition with a critical exponent of 1. We show that, due to the lack of energy conservation, the dynamics of individual, real-space wave packets follows a different behavior. Both transitions between localization and unidirectional amplification, as well as transitions between distinct propagating phases become possible. The critical exponent of the transition equals $1/2$ in propagating-propagating transitions.

cond-mat.mes-hall↗

arXiv2023

Non-Hermitian topological ohmmeter

Measuring large electrical resistances forms an essential part of common applications such as insulation testing, but suffers from a fundamental problem: the larger the resistance, the less sensitive a canonical ohmmeter is. Here we develop a conceptually different electronic sensor by exploiting the topological properties of non-Hermitian matrices, whose eigenvalues can show an exponential sensitivity to perturbations. The ohmmeter is realized in an multi-terminal, linear electric circuit with a non-Hermitian conductance matrix, where the target resistance plays the role of the perturbation. We inject multiple currents and measure a single voltage in order to directly obtain the value of the resistance. The relative accuracy of the device increases exponentially with the number of terminals, and for large resistances outperforms a standard measurement by over an order of magnitude. Our work paves the way towards leveraging non-Hermitian conductance matrices in high-precision sensing.

cond-mat.mes-hall↗

arXiv2023

Observation of non-Hermitian topology in a multi-terminal quantum Hall device

Quantum devices characterized by non-Hermitian topology are predicted to show highly robust and potentially useful properties, but realizing them has remained a daunting experimental task. This is because non-Hermiticity is often associated with gain and loss, which would require precise tailoring to produce the signatures of nontrivial topology. Here, instead of gain/loss, we use the nonreciprocity of the 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: currents and voltages show an exponential profile, which persists also 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.

cond-mat.mes-hall↗

arXiv2022

Anisotropic optics and gravitational lensing of tilted Weyl fermions

We show that tilted Weyl semimetals with a spatially varying tilt of the Weyl cones provide a platform for studying analogues to problems in anisotropic optics as well as curved spacetime. Considering particular tilting profiles, we numerically evaluate the time evolution of electronic wave packets and their current densities. We demonstrate that electron trajectories in such systems can be obtained from Fermat's principle in the presence of an inhomogeneous, anisotropic effective refractive index. On the other hand, we show how the electrons dynamics reveal gravitational features and use them to simulate gravitational lensing around a synthetic black hole. These results bridge optical and gravitational analogies in Weyl semimetals, suggesting novel pathways for experimental solid-state electron optics.

cond-mat.mes-hall↗

arXiv2022

Nontrivial gapless electronic states at the stacking faults of weak topological insulators

Lattice defects such as stacking faults may obscure electronic topological features of real materials. In fact, defects are a source of disorder that can enhance the density of states and conductivity of the bulk of the system and they break crystal symmetries that can protect the topological states. On the other hand, in recent years it has been shown that lattice defects can act as a source of nontrivial topology. Motivated by recent experiments on three-dimensional (3D) topological systems such as Bi$_2$TeI and Bi$_{14}$Rh$_3$I$_9$, we examine the effect of stacking faults on the electronic properties of weak topological insulators (WTIs). Working with a simple model consisting of a 3D WTI formed by weakly-coupled two-dimensional (2D) topological layers separated by trivial spacers, we find that 2D stacking faults can carry their own, topologically nontrivial gapless states. Depending on the WTI properties, as well as the way in which the stacking fault is realized, the latter can form a topologically protected 2D semimetal, but also a 2D topological insulator which is embedded in the higher-dimensional WTI bulk. This suggests the possibility of using stacking faults in real materials as a source of topologically nontrivial, symmetry-protected conducting states.

cond-mat.mes-hall↗

arXiv2022

Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice

To simulate the dynamics of massless Dirac fermions in curved spacetimes with one, two, and three spatial dimensions we construct tight-binding Hamiltonians with spatially varying hoppings. These models represent tilted Weyl semimetals where the tilting varies with position, in a manner similar to the light cones near the horizon of a black hole. We illustrate the gravitational analogies in these models by numerically evaluating the propagation of wave packets on the lattice and then comparing them to the geodesics of the corresponding curved spacetime. We also show that the motion of electrons in these spatially varying systems can be understood through the conservation of energy and the quasi-conservation of quasimomentum. This picture is confirmed by calculations of the scattering matrix, which indicate an exponential suppression of any noncontinuous change in the quasimomentum. Finally, we show that horizons in the lattice models can be constructed also at finite energies using specially designed tilting profiles.

cond-mat.mes-hall↗