Event

Talk
Semiclassical theory of potential scattering for massless Dirac fermions
Dr. Timur Tudorovskiy (Radboud University, Nijmegen)
16 Jan 2013, 16:00 – 17:00

Two-dimensional massless Dirac fermions are effective charge carriers in graphene and topological insulators. The potential scattering for these particles drastically differs from the conventional one. The most pronounced example, illustrating the difference, is the Klein paradox, i.e. the total transmission of the Dirac fermion normally incident on any one-dimensional potential barrier.
We present a systematic semiclassical theory of potential scattering for massless Dirac fermions under the assumption that the potential depends on a single Cartesian variable. We
distinguish three different regimes of scattering. To find the reflection and transmission coeffcients in these regimes, we apply the Wentzel-Kramers-Brillouin (WKB), or semiclassical,
approximation. We use the method of comparison equations to extend our prediction to nearly normal incidence, where the conventional WKB method should be modified due to the degeneracy of turning points. We compare our results to numerical calculations and find good agreement.
The talk is based on our recent work: K. J. A. Reijnders, T. Tudorovskiy, M. I. Katsnelson,
arXiv:1206.2869v2 [cond-mat.mes-hall].

Abstract: http://www.raumzeitmaterie.de/docs/tudorovskiy.2013-1-16.16-00.pdf

Related to:

• Timur Tudorovskiy
• [C7] Differential Operators of Mathematical Physics - Spectral Theory and Dynamics