Related papers: Solvable Two-dimensional Dirac Equation with Matri…
The generalized tight-binding model, with the exact diagonalization method, is developed to investigate optical properties of graphene in five kinds of external fields. The quite large Hamiltonian matrix is transferred into the band-like…
We introduce and analyze numerical companion matrix methods for the reconstruction of hypersurfaces with crossings from smooth interpolants given unordered or, without loss of generality, value-sorted data. The problem is motivated by the…
Recently, a new quantum model - two-dimensional generalization of the Scarf II - was completely solved analytically by SUSY method for the integer values of parameter. Now, the same integrable model, but with arbitrary values of parameter,…
This paper aims at extending our previous work on the solution of the one-dimensional Dirac equation using the Tridiagonal Representation Approach (TRA). In the approach, we expand the spinor wavefunction in terms of suitable square…
In this study, firstly it is reviewed how the solutions of the Dirac-Weyl equation for a massless charge on the hyperboloid under perpendicular magnetic fields are obtained by using supersymmetric (SUSY) quantum mechanics methods. Then, the…
In this work, we have obtained the solutions of a massless fermion which is under the external magnetic field around a cosmic string for specific three potential models using supersymmetric quantum mechanics. The constant magnetic field,…
Although massless Dirac fermions in graphene constitute a centrosymmetric medium for in-plane excitations, their second-order nonlinear optical response is nonzero if the effects of spatial dispersion are taken into account. Here we present…
A generalized Dirac equation is derived in order to describe charge carriers moving in corrugated graphene, which is the case for temperatures above 10{\deg}K due to the presence of flexural phonons. Such interaction is taken into account…
We introduce the new, exactly solvable model of the two-dimensional Dirac fermion in presence of an asymmetric, P\"oschl-Teller-like vector potential. Utilizing the translation invariance of the system, the effective one-dimensional…
The quaternion Dirac equation in presence of generalized electromagnetic field has been discussed in terms of two gauge potentials of dyons. Accordingly, the supersymmetry has been established consistently and thereafter the one, two and…
We discuss the novel electronic properties of graphene under an external periodic scalar or vector potential, and the analytical and numerical methods used to investigate them. When graphene is subjected to a one-dimensional periodic scalar…
A two-dimensional periodic array of scatterers has been introduced to a single layer of graphene in the presence of an external magnetic field perpendicular to the graphene layer. The eigenvalue equation for such a system has been solved…
Any departure from graphene's flatness leads to the emergence of artificial gauge fields that act on the motion of the Dirac fermions through an associated pseudomagnetic field. Here, we demonstrate the tunability of strong gauge fields in…
We show that if the solutions to the (2+1)-dimensional massless Dirac equation for a given 1D potential are known, then they can be used to obtain the eigenvalues and eigenfunctions for the same potential, orientated at an arbitrary angle,…
We present a unified description of the quantum Hall effect in graphene on the basis of the 8-component Dirac Hamiltonian and the supersymmetric (SUSY) quantum mechanics. It is remarkable that the zero-energy state emerges because the…
The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The…
The dynamics of low energy electrons in general static strained graphene surface is modelled mathematically by the Dirac equation in curved space-time. In Cartesian coordinates, a parametrization of the surface can be straightforwardly…
A general discussion of graphene in external electromagnetic field is provided. In general, the formulation is not Lorentz invariant because of Zeeman energy. But it can be restored approxiamtely in the case of strong magnetic field, the…
This paper concerns the asymmetric transport associated with a low-energy interface Dirac model of graphene-type materials subject to external magnetic and electric fields. We show that the relevant physical observable, an interface…
In this paper, we examine the electron interaction within tilted anisotropic Dirac materials when subjected to external electric and magnetic fields possessing translational symmetry. Specifically, we focus on a distinct non-zero electric…