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Semiclassical theory of potential scattering for massless Dirac fermions

Authors
  • Reijnders, K. J. A.
  • Tudorovskiy, T.
  • Katsnelson, M. I.
Type
Published Article
Publication Date
Apr 29, 2013
Submission Date
Jun 13, 2012
Identifiers
DOI: 10.1016/j.aop.2013.03.001
Source
arXiv
License
Yellow
External links

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.

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