Semiclassical theory of potential scattering for massless Dirac fermions

TL;DR

This paper develops a semiclassical (WKB) framework to analyze potential scattering of massless Dirac fermions in two dimensions, covering different energy and incident angle regimes, with extensions near normal incidence.

Contribution

It introduces a semiclassical approach using comparison equations for Dirac fermion scattering, improving predictions near normal incidence where standard methods fail.

Findings

Good agreement with numerical calculations

Effective extension of WKB method near normal incidence

Unified description of scattering regimes

Abstract

In this paper we study scattering of two-dimensional massless Dirac fermions by a potential that depends on a single Cartesian variable. Depending on the energy of the incoming particle and its angle of incidence, there are three different regimes of scattering. To find the reflection and transmission coefficients in these regimes, we apply the Wentzel-Kramers-Brillouin (WKB), also called semiclassical, approximation. We use the method of comparison equations to extend our prediction to nearly normal incidence, where the conventional WKB method should be modified due to the degeneracy of turning points. We compare our results to numerical calculations and find good agreement.