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

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.