arXiv subjects

Vit Jakubsky

Publications and source records attributed to Vit Jakubsky.

At least 19 recordsLinked to original sources

arXiv2026

Super-Klein tunneling in 2D Lorentzian-type barriers in graphene

We introduce a two-dimensional model of spin-1/2 Dirac fermions in graphene subjected to a highly tunable electric field, which exhibits super-Klein tunneling. The electric field can be continuously interpolated between two limiting configurations: a uniform electrostatic Lorentzian barrier with translational invariance and a chain of well-separated electrostatic scatterers. We demonstrate that super-Klein tunneling arises naturally as a direct consequence of the intrinsic connection of the model to free-particle dynamics, a relation that is established through methods of supersymmetric quantum mechanics, which provide an elegant and analytically tractable framework. Besides the mentioned super-Klein tunneling, scale invariance of the model and invisibility of the potential for particles of specific energy are revealed, and possible routes toward experimental realization are discussed.

cond-mat.mes-hall↗

arXiv2025

SUSY transformation as the coupler of non-interacting systems

Quasi-one-dimensional chains of atoms can be effectively described by one-dimensional Dirac-type equation. Crystal structure of the chain is reflected by pseudo-spin of the quasi-particles. In the article, we present a simple framework where supersymmetric transformation is utilized to generate an interaction between two, initially non-interacting systems described by pseudo-spin-one Dirac-type equation. In the presented example, the transformation converts two asymptotically non-interacting atomic chains into a saw chain locally. The model possesses a flat band whose energy can be fine-tuned deliberately.

quant-ph↗

arXiv2024

Flat-band engineering of quasi-one-dimensional systems via supersymmetric transformations

We introduce a systematic method to spectrally design quasi-one-dimensional crystal models described by the Dirac equation in the low-energy regime. The method is based on the supersymmetric transformation applied to an initially known pseudo-spin-1/2 model. This allows extending the corresponding susy partner so that the new model describes a pseudo-spin-1 system. The spectral design allows the introduction of a flat-band and discrete energies at will into the new model. The results are illustrated in two examples where the Su-Schriefer-Heeger chain is locally converted into a stub lattice.

cond-mat.mes-hall↗

arXiv2023

Reflectionless pseudospin-1 Dirac systems via Darboux transformation and flat band solutions

This manuscript explores the Darboux transformation employed in the construction of exactly solvable models for pseudospin-one particles described by the Dirac-type equation. We focus on the settings where a flat band of zero energy is present in the spectrum of the initial system. Using the flat band state as one of the seed solutions substantially improves the applicability of the Darboux transformation, for it becomes necessary to ensure the Hermiticy of the new Hamiltonians. This is illustrated explicitly in four examples, where we show that the new Hamiltonians can describe quasi-particles in Lieb lattice with inhomogeneous hopping amplitudes.

quant-ph↗

arXiv2021

Dirac fermions in armchair graphene nanoribbons trapped by electric quantum dots

We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of a quantum-dot-type electrostatic potential. With the use of specific projection operators, we find exact solutions for some bound states that satisfy appropriate boundary conditions. We show that the energies of these bound states belong either to the gap of valence and conducting bands or they represent BIC's (bound states in the continuum) whose energies are embedded in the continuous spectrum.

cond-mat.mes-hall↗

arXiv2020

Super-Klein tunneling of Dirac fermions through electrostatic gratings in graphene

We use the Wick-rotated time-dependent supersymmetry to construct models of two-dimensional Dirac fermions in presence of an electrostatic grating. We show that there appears omnidirectional perfect transmission through the grating at specific energy. Additionally to being transparent for incoming fermions, the grating hosts strongly localized states.

cond-mat.mes-hall↗

arXiv2019

On the propagation of Dirac fermions in graphene with the strain-induced inhomogeneous Fermi velocity

We consider systems described by the two-dimensional Dirac equation where the Fermi velocity is inhomogeneous as a consequence of mechanical deformations. We show that the mechanical deformations can lead to deflection and focusing of the wave packets. The analogy with known reflectionless quantum systems is pointed out. Furthermore, with the use of the qualitative spectral analysis, we discuss how inhomogeneous strains can be used to create waveguides for valley polarized transport of partially dispersionless wave packets.

cond-mat.mes-hall↗

arXiv2017

Dispersionless wave packets in Dirac materials

We show that a wide class of quantum systems with translational invariance can host dispersionless, soliton-like, wave packets. We focus on the setting where the effective, two-dimensional Hamiltonian acquires the form of the Dirac operator. The proposed framework for construction of the dispersionless wave packets is illustrated on silicene-like systems with topologically nontrivial effective mass. Our analytical predictions are accompanied by a numerical analysis and possible experimental realizations are discussed.

cond-mat.mes-hall↗

arXiv2016

Confluent Crum-Darboux transformations in Dirac Hamiltonians with $PT$-symmetric Bragg gratings

We consider optical systems where propagation of light can be described by a Dirac-like equation with $PT$-symmetric Hamiltonian. In order to construct exactly solvable configurations, we extend the confluent Crum-Darboux transformation for the one-dimensional Dirac equation. The properties of the associated intertwining operators are discussed and the explicit form for higher-order transformations is presented. We utilize the results to derive a multi-parametric class of exactly solvable systems where the balanced gain and loss represented by the $PT$-symmetric refractive index can imply localization of the electric field in the material.

hep-th↗

arXiv2015

$PT$-symmetric invisible defects and confluent Darboux-Crum transformations

We show that confluent Darboux-Crum transformations with emergent Jordan states are an effective tool for the design of optical systems governed by the Helmholtz equation under the paraxial approximation. The construction of generic, asymptotically real and periodic, $PT$-symmetric systems with local complex periodicity defects is discussed in detail. We show how the decay rate of the defect is related with the energy of the bound state trapped by the defect. In particular, the bound states in the continuum are confined by the periodicity defects with power law decay. We show that these defects possess complete invisibility; the wave functions of the system coincide asymptotically with the wave functions of the undistorted setting. The general results are illustrated with explicit examples of reflectionless models and systems with one spectral gap. We show that the spectral properties of the studied models are reflected by Lax-Novikov-type integrals of motion and associated supersymmetric structures of bosonized and exotic nature.

hep-th↗

arXiv2015

Twisted kinks, Dirac transparent systems and Darboux transformations

Darboux transformations are employed in construction and analysis of Dirac Hamiltonians with pseudoscalar potentials. By this method, we build a four parameter class of reflectionless systems. Their potentials correspond to composition of complex kinks, also known as twisted kinks, that play an important role in the $1+1$ Gross-Neveu and Nambu-Jona-Lasinio field theories. The twisted kinks turn out to be multi-solitonic solutions of the integrable AKNS hierarchy. Consequently, all the spectral properties of the Dirac reflectionless systems are reflected in a non-trivial conserved quantity, which can be expressed in a simple way in terms of Darboux transformations. We show that the four parameter pseudoscalar systems reduce to well-known models for specific choices of the parameters. An associated class of transparent non-relativistic models described by matrix Schrödinger Hamiltonian is studied and the rich algebraic structure of their integrals of motion is discussed.

hep-th↗

arXiv2015

Qualitative analysis of trapped Dirac fermions in graphene

We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac operator, we obtain sufficient and necessary conditions for confinement of the quasi-particles. The rigorous theoretical results are illustrated on the realistic examples of the three classes of traps.

cond-mat.mes-hall↗

arXiv2014

Spectrally isomorphic Dirac systems: graphene in electromagnetic field

We construct the new one-dimensional Dirac Hamiltonians that are spectrally isomorphic (not isospectral) with the known exactly solvable models. Explicit formulas for their spectra and eigenstates are provided. The operators are utilized for description of Dirac fermions in graphene in presence of an inhomogeneous electromagnetic field. We discuss explicit, physically relevant, examples of spectrally isomorphic systems with both non-periodic and periodic electromagnetic barriers. In the latter case, spectrally isomorphic two- and three-gap systems associated with the Ablowitz-Kaup-Newell-Segur hierarchy are considered.

hep-th↗

arXiv2014

Soliton defects in one-gap periodic system and exotic supersymmetry

By applying Darboux-Crum transformations to the quantum one-gap Lame system, we introduce an arbitrary countable number of bound states into forbidden bands. The perturbed potentials are reflectionless and contain two types of soliton defects in the periodic background. The bound states with finite number of nodes are supported in the lower forbidden band by the periodicity defects of the potential well type, while the pulse type bound states in the gap have infinite number of nodes and are trapped by defects of the compression modulations nature. We investigate the exotic nonlinear N=4 supersymmetric structure in such paired Schrodinger systems, which extends an ordinary N=2 supersymmetry and involves two bosonic generators composed from Lax-Novikov integrals of the subsystems. One of the bosonic integrals has a nature of a central charge, and allows us to liaise the obtained systems with the stationary equations of the Korteweg-de Vries and modified Korteweg-de Vries hierarchies. This exotic supersymmetry opens the way for the construction of self-consistent condensates based on the Bogoliubov-de Gennes equations and associated with them new solutions to the Gross-Neveu model. They correspond to the kink or kink-antikink defects of the crystalline background in dependence on whether the exotic supersymmetry is unbroken or spontaneously broken.

hep-th↗

arXiv2014

Carbon nanotubes in almost homogeneous transverse magnetic field: exactly solvable model

A class of exactly solvable models describing carbon nanotubes in the presence of an external inhomogeneous magnetic field is considered. The framework of the continuum approximation is employed, where the motion of the charge carriers is governed by the Dirac- Weyl equation. The explicit solution of a particular example is provided. It is shown that these models possess nontrivial integrals of motion that establish N = 2 nonlinear supersymmetry in case of metallic and maximally semiconducting nanotubes. Remarkable stability of energy levels with respect to small fluctuations of longitudinal momentum is demonstrated

cond-mat.mes-hall↗

arXiv2013

Finite-gap twists of carbon nanotubes and an emergent hidden supersymmetry

We consider radially twisted nanotubes in the low-energy approximation where the dynamics is governed by a one-dimensional Dirac equation. The mechanical deformation of the nanotubes is reflected by the presence of an effective vector potential. We discuss twisted carbon and boron-nitride nanotubes, where deformations give rise to periodic and nonperiodic finite-gap Hamiltonians. The intimate relation of these systems with the integrable Ablowitz-Kaup-Newell-Segur hierarchy is exploited in the study of their spectral properties as well as in the computation of the (local) density of states. We show that a nonlinear hidden supersymmetry generated by local supercharges arises naturally in the finite-gap configurations of twisted nanotubes with time-reversal symmetry. The properties of the van Hove singularities are encoded in its structure.

cond-mat.mes-hall↗

arXiv2013

Applications of the potential algebras of the two-dimensional Dirac-like operators

Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of the Hamiltonian that close centrally extended so(3), so(2,1) or oscillator algebra. The algebraic framework is used in construction of physically interesting solvable models described by (2+1) dimensional Dirac equation. It is applied in description of open-cage fullerenes where the energies and wave functions of low-energy charge-carriers are computed. The potential algebras are also used in construction of shape-invariant, one-dimensional Dirac operators. We show that shape-invariance of the first-order operators is associated with the N=4 nonlinear supersymmetry which is represented by both local and nonlocal supercharges. The relation to the shape-invariant non-relativistic systems is discussed as well.

math-ph↗

arXiv2012

Supersymmetric twisting of carbon nanotubes

We construct exactly solvable models of twisted carbon nanotubes via supersymmetry, by applying the matrix Darboux transformation. We derive the Green's function for these systems and compute the local density of states. Explicit examples of twisted carbon nanotubes are produced, where the back-scattering is suppressed and bound states are present. We find that the local density of states decreases in the regions where the bound states are localized. Dependence of bound-state energies on the asymptotic twist of the nanotubes is determined. We also show that each of the constructed unextended first order matrix systems possesses a proper nonlinear hidden supersymmetric structure with a nontrivial grading operator.

hep-th↗