Two-dimensional Dirac fermion in presence of an asymmetric vector potential

TL;DR

This paper presents an exactly solvable two-dimensional Dirac fermion model with an asymmetric Pöschl-Teller-like vector potential, analyzing its energy spectrum and scattering properties.

Contribution

It introduces a new solvable model of Dirac fermions with an asymmetric potential, connecting the problem to the Heun equation and hypergeometric functions.

Findings

Exact solutions for the wavefunctions are obtained.

The energy spectrum depends on longitudinal momentum and potential strength.

Scattering properties are characterized in the model.

Abstract

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 stationary equation is brought into the form of the Heun equation and its fundamental solutions are found as an irreducible combination of two Gauss hypergeometric functions. The energy spectrum and the scattering is studied in dependence on the conserved longitudinal momentum as well as on the strength of the coupling.