arXiv subjects

József Cserti

Publications and source records attributed to József Cserti.

At least 19 recordsLinked to original sources

arXiv2025

General theory of perturbation of infinite resistor networks

The effective resistance between any two nodes in a perturbed resistor network is determined by removing multiple bonds from an infinite resistor lattice. We have developed an efficient method for calculating the Green operator of the Laplacian for such perturbed networks, which is directly related to the two-point resistance. Unlike the recursive techniques that remove bonds one at a time, our approach handles all bond modifications simultaneously. To demonstrate the versatility of our method, several analytical and numerical examples are presented. In addition, we computed bond current distributions to gain deeper insight into the nature of resistor perturbations. We emphasize that our method has a broad range of applications, including condensed matter physics describing the quantum mechanical effects of impurities in crystal lattices, recently emerging topoelectronics, the study of vibrations in spring networks, and problems involving random walks.

math-ph↗

arXiv2025

Line defects in infinite networks of resistors

We study infinite resistor networks perturbed by line defects, in which the resistances are periodically modified along a single line. Using the Sherman-Morrison identity applied to the reciprocal-space representation of the lattice Green's function, we develop a general analytical framework for computing the equivalent resistance between arbitrary nodes. The resulting expression is a one-dimensional integral that is evaluated exactly in special cases. While our analysis is carried out for the square lattice, the method readily extends to other lattice geometries and networks with general impedances. Therefore, this framework is useful for studying the boundary behavior of topolectrical circuits, which serve as classical analogs of topological insulators.

cond-mat.dis-nn↗

arXiv2024

Snell's law in multirefringent systems

In anisotropic crystals, Maxwell's equations permit only birefringence for the propagation of light. Notwithstanding, multirefringent systems comprising more than two propagating modes exist, such as in electron optics and photonic crystals. It has been demonstrated that in such systems, the propagation of waves in the short wavelength limit results in the formation of anomalous caustics. To calculate these caustic curves, we generalized Snell's law valid for reflection and refraction in multirefringent systems possessing more than one propagating mode. The emergence of anomalous caustics in the wave function patterns obtained from rigorous quantum mechanical calculations in electron-optical systems is confirmed. These calculations were performed on electron scattering from circularly gated potential regions applied to multilayer rhombohedral graphene. Our results may generate further work to explore more complex phenomena in multirefringent systems.

cond-mat.mes-hall↗

arXiv2023

Differential scattering cross section of the non-Abelian Aharonov-Bohm effect in multiband systems

We develop a unified treatment of the non-Abelian Aharonov-Bohm (AB) effect in isotropic multiband systems, namely, the scattering of particles on a gauge field corresponding to a noncommutative Lie group. We present a complex contour integral representation of the scattering states for such systems, and, using their asymptotic form, we calculate the differential scattering cross section. The angular dependence of the cross section turns out to be the same as that obtained originally by Aharonov and Bohm in their seminal paper, but this time it depends on the polarization of the incoming plane wave. As an application of our theory, we perform the contour integrals for the wave functions explicitly and calculate the corresponding cross section for three non-trivial isotropic multiband systems relevant to condensed matter and particle physics. To have a deeper insight into the nature of the scattering, we plot the probability and current distributions for different incoming waves. This paper is a generalization of our recent results on the Abelian AB effect providing an extension of exactly solvable AB scattering problems.

quant-ph↗

arXiv2023

Unified Description of the Aharonov-Bohm Effect in Isotropic Multiband Electronic Systems

We present a unified treatment of the Aharonov--Bohm (AB) effect for two-dimensional multiband electronic systems possessing isotropic band structures. We propose an integral representation of the AB scattering state of an electron scattered by an infinitely thin solenoid. Moreover, we derive the asymptotic form of the AB scattering state and obtain the differential cross section from that. We found a remarkable result, namely that this cross section is {\it the same for all isotropic systems} and agrees with that obtained first by Aharonov and Bohm for spinless free particle systems. To demonstrate the generality of our theory, we consider several specific multiband systems relevant to condensed matter physics.

cond-mat.mes-hall↗

arXiv2022

General formalism for calculating the thermal efficiency of thermodynamic cycles defined in a $p-V$ diagram

We develop a general method for calculating the thermal efficiency of arbitrary thermodynamic cycles defined in the pressure-volume ($p-V$) diagram. To demonstrate how effective our approach is, we calculate the thermal efficiency of ideal gas engines for a few non-trivial cycles in the $p-V$ diagram, including a circular shape, a heart shape, a cycloid of Ceva, and a star-shaped curve. We determine the segments along the cycle where heat is absorbed or released from the heat engine. Our method can be applied to any gas model, and, as an example, we present the results for the van der Waals gas.

cond-mat.stat-mech↗

arXiv2020

Current distribution in magnetically confined 2DEG: semiclassical and quantum mechanical treatment

In the ballistic regime we study both semiclassically and quantum mechanically the electron's dynamics in two-dimensional electron gas (2DEG) in the presence of an inhomogeneous magnetic field applied perpendicular to the plane. The magnetic field is constant inside four separate circular regions which are located at the four corners of a square of side length larger than the diameter of the circles, while outside the circles the magnetic field is zero. We carry out the stability analysis of the periodic orbits and for given initial conditions numerically calculate the two-dimensional invariant torus embedded in the four-dimensional phase space. Applying the Bohr--Sommerfeld and the Einstein--Brillouin--Keller semiclassical quantization methods we obtain the energy levels for different magnetic field strengths. We also perform exact quantum calculations solving numerically the discretized version of the Schrödinger equation. In our calculations, we consider only those bound states that are localized to the neighborhood of the four magnetic disks. We show that the semiclassical results are in good agreement with those found from our quantum calculations. Moreover, the current distribution and the phase of the different wave functions enable us to deduce the two quantum numbers $n_1$ and $n_2$ characterizing the energy levels in the semiclassical methods. Finally, we present two examples in which the quantum state shows a similar structure to the previous states, but these are special in the following sense. One of them is a scar state localized to the neighborhood of the periodic orbit while this orbit is already unstable. In the case of the other state, the current density is circulating in two rings in opposite direction. Thus, it is not consistent with the classical motion in the neighborhood of the periodic orbit.

cond-mat.mes-hall↗

arXiv2020

Competition of trivial and topological phases in patterned graphene based heterostructures

We explore the effect of mechanical strain on the electronic spectrum of patterned graphene based heterostructures. We focus on the competition of Kekulé-O type distortion favoring a trivial phase and commensurate Kane-Mele type spin-orbit coupling generating a topological phase. We derive a simple low-energy Dirac Hamiltonian incorporating the two gap promoting mechanisms and include terms corresponding to uniaxial strain. The derived effective model explains previous ab initio results through a simple physical picture. We show that while the trivial gap is sensitive to mechanical distortions, the topological gap stays resilient.

cond-mat.mes-hall↗

arXiv2020

Quantum interference and nonequilibrium Josephson current in molecular Andreev interferometers

We study the quantum interference (QI) effects in three-terminal Andreev interferometers based on polyaromatic hydrocarbons (PAH's) under non-equilibrium conditions. The Andreev interferometer consists of a PAH coupled to two superconducting and one normal conducting terminals. We calculate the current measured in the normal lead as well as the current between the superconducting terminals under non-equilibrium conditions. We show that both the QI arising in the PAH cores and the bias voltage applied to a normal contact have a fundamental effect on the charge distribution associated with the Andreev Bound States (ABS's). QI can lead to a peculiar dependence of the normal current on the superconducting phase difference that was not observed in earlier studies of mesoscopic Andreev interferometers. We explain our results by an induced asymmetry in the spatial distribution of the electron- and hole-like quasiparticles. The non-equilibrium charge occupation induced in the central PAH core can result in a $π$ transition in the current-phase relation of the supercurrent for large enough applied bias voltage on the normal lead. The asymmetry in the spatial distribution of the electron- and hole-like quasiparticles might be used to split Cooper pairs and hence to produce entangled electrons in four terminal setups.

cond-mat.mes-hall↗

arXiv2019

Magic number theory of superconducting proximity effects and Wigner delay times in graphene-like molecules

When a single molecule is connected to external electrodes by linker groups, the connectivity of the linkers to the molecular core can be controlled to atomic precision by appropriate chemical synthesis. Recently, the connectivity dependence of the electrical conductance and Seebeck coefficient of single molecules has been investigated both theoretically and experimentally. Here we study the connectivity dependence of the Wigner delay time of single-molecule junctions and the connectivity dependence of superconducting proximity effects, which occur when the external electrodes are replaced by superconductors. Although absolute values of transport properties depend on complex and often uncontrolled details of the coupling between the molecule and electrodes, we demonstrate that ratios of transport properties can be predicted using tables of 'magic numbers,' which capture the connectivity dependence of superconducting proximity effects and Wigner delay times within molecules. These numbers are calculated easily, without the need for large-scale computations. For normal-molecule-superconducting junctions, we find that the electrical conductance is proportional to the fourth power of their magic numbers, whereas for superconducting-molecule-superconducting junctions, the critical current is proportional to the square of their magic numbers. For more conventional normal-molecule-normal junctions, we demonstrate that delay time ratios can be obtained from products of magic number tables.

cond-mat.mes-hall↗

arXiv2018

Topological and trivial magnetic oscillations in nodal loop semimetals

Nodal loop semimetals are close descendants of Weyl semimetals and possess a topologically dressed band structure. We argue by combining the conventional theory of magnetic oscillation with topological arguments that nodal loop semimetals host coexisting topological and trivial magnetic oscillations. These originate from mapping the topological properties of the extremal Fermi surface cross sections onto the physics of two dimensional semi Dirac systems, stemming from merging two massless Dirac cones. By tuning the chemical potential and the direction of magnetic field, a sharp transition is identified separating purely trivial oscillations, arising from the Landau levels of a normal two dimensional (2D) electron gas, to a phase where oscillations of topological and trivial origin coexist, originating from 2D massless Dirac and semi Dirac points, respectively. These could in principle be directly identified in current experiments.

cond-mat.str-el↗

arXiv2016

Frequency dependent magneto-optical conductivity in the generalized $α- T_3$ model

We have studied a generalized three band crossing model in 2D, the generalized $α- T_3$ lattice, ranging from the pseudospin-1 Dirac equation through a quadratic+flat band touching to the pseudospin-1/2 Dirac equation. A general method is presented to determine the operator form of the Green's function, being gauge and representation independent. This yields the Landau level structure in a quantizing magnetic field and the longitudinal and transversal magneto-optical conductivities of the underlying system Although the magneto-optical selection rules allow for many transitions between Landau levels, the dominant one stems from exciting a particle from/to the flat band to/from a propagating band. The Hall conductivity from each valley is rational (not quantized at all), in agreement with Berry phase considerations, though their sum is always integer quantized.

cond-mat.mes-hall↗

arXiv2016

Magnetic field oscillations of the critical current in long ballistic graphene Josephson junctions

We study the Josephson current in long ballistic superconductor-monolayer graphene-superconductor junctions. As a first step, we have developed an efficient computational approach to calculate the Josephson current in tight-binding systems. This approach can be particularly useful in the long junction limit, which has hitherto attracted less theoretical interest but has recently become experimentally relevant. We use this computational approach to study the dependence of the critical current on the junction geometry, doping level, and an applied perpendicular magnetic field. In zero magnetic field we find a good qualitative agreement with the recent experiment of Ben Shalom et al. (Reference[12]) for the length dependence of the critical current. For highly doped samples our numerical calculations show a broad agreement with the results of the quasiclassical formalism. In this case the critical current exhibits Fraunhofer-like oscillations as a function of the magnetic field. However, for lower doping levels, where the cyclotron orbit becomes comparable to the characteristic geometrical length scales of the system, deviations from the results of the quasiclassical formalism appear. We argue that due to the exceptional tunability and long mean free path of graphene systems a new regime can be explored where geometrical and dynamical effects are equally important to understand the magnetic field dependence of the critical current.

cond-mat.mes-hall↗

arXiv2016

Transfer matrix approach for the Kerr and Faraday rotation in layered nanostructures

To study the optical rotation of the polarization of light incident on multilayer systems consisting of atomically thin conductors and dielectric multilayers we present a general method based on transfer matrices. The transfer matrix of the atomically thin conducting layer is obtained using the Maxwell equations. We derive expressions for the Kerr (Faraday) rotation angle and for the ellipticity of the reflected (transmitted) light as a function of the incident angle and polarization of the light. The method is demonstrated by calculating the Kerr (Faraday) angle for bilayer graphene in the quantum anomalous Hall state placed on the top of dielectric multilayers. The optical conductivity of the bilayer graphene is calculated in the framework of a four-band model.

cond-mat.mes-hall↗

arXiv2015

Multiple scattering theory for superconducting heterostructures

We generalize the screened Korringa-Kohn-Rostoker (SKKR) method for solving the corresponding Kohn-Sham-Bogoliubov-de Gennes (KSBdG) equations for surfaces and interfaces. As an application of the newly developed theory we study the quasiparticle spectrum of Au overlayers on a Nb(100) host. We find that, within the superconducting gap region, the quasiparticle spectrum consists of Andreev bound states (ABS) with a dispersion which is closely connected to the underlying electronic structure of the overlayer. We also find that the spectrum has a strongly k-dependent induced gap. The properties of the gap is discussed in relation to the thickness of the overlayer, and it is shown that certain states do not participate in the Andreev scattering process.

cond-mat.supr-con↗

arXiv2013

Diverging dc conductivity due to a flat band in disordered pseudospin-1 Dirac-Weyl fermions

Several lattices, such as the dice or the Lieb lattice, possess Dirac cones and a flat band crossing the Dirac point, whose effective model is the pseudospin-1 Dirac-Weyl equation. We investigate the fate of the flat band in the presence of disorder by focusing on the density of states (DOS) and dc conductivity. While the central hub-site does not reveal the presence of the flat band, the sublattice resolved DOS on the non-central sites exhibits a narrow peak with height ~ 1/\sqrt{g} with g the dimensionless disorder variance. Although the group velocity is zero on the flat band, the dc conductivity diverges as ln(1/g) with decreasing disorder due to interband transitions around the band touching point between the propagating and the flat band. Generalizations to higher pseudospin are given.

cond-mat.mes-hall↗

arXiv2012

Intraband electron focusing in bilayer graphene

We propose an implementation of a valley selective electronic Veselago lens in bilayer graphene. We demonstrate that in the presence of an appropriately oriented potential step, low-energy electrons radiating from a point source can be re-focused coherently within the same band. The phenomenon is due to the trigonal warping of the band structure that leads to a negative refraction index. We show that the interference pattern can be controlled by an external mechanical strain.

cond-mat.mes-hall↗

arXiv2011

Effect of the band structure topology on the minimal conductivity for bilayer graphene with symmetry breaking

Using the Kubo formula we develop a general and simple expression for the minimal conductivity in systems described by a two by two Hamiltonian. As an application we derive an analytical expression for the minimal conductivity tensor of bilayer graphene as a function of a complex parameter $w$ related to recently proposed symmetry breaking mechanisms resulting from electron-electron interaction or strain applied to the sample. The number of Dirac points changes with varying parameter w, this directly affect the minimal conductivity. Our analytic expression is confirmed using an independent calculation based on Landauer approach and we find remarkably good agreement between the two methods. We demonstrate that the minimal conductivity is very sensitive to the change of the parameter $w$ and the orientation of the electrodes with respect to the sample. Our results show that the minimal conductivity is closely related to the topology of the low energy band structure.

cond-mat.mes-hall↗