

Seminar of the Department of Mathematical Physics, Steklov Mathematical Institute of RAS
April 10, 2014 11:00, Moscow, Steklov Mathematical Institute of RAS, Room 430 (8 Gubkina)






Semiclassical theory of potential scattering for massless Dirac fermions
K. Reijnders^{} 
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Abstract:
Massless Dirac fermions, the charge carriers in graphene and topological
insulators, have very unusual properties. One of the most striking
phenomena they exhibit is Klein tunneling: an electron normally incident
on an electrostatic potential barrier will always be transmitted. This
is in stark contrast to conventional Schrödinger particles, for which
the transmission is exponentially small. In this talk, I will discuss
scattering of twodimensional massless Dirac fermions by a
onedimensional potential in detail. In particular, I will show that
there are three different regimes of scattering. For each of these
regimes, I will show how the transmission for a generic potential
barrier can be obtained by using the semiclassical
(WentzelKramersBrillouin) approximation. The predictions provided by
our analytic expressions show good agreement with numerical calculations
for all considered cases. This talk is based on work that was done
together with Mikhail Katsnelson and Timur Tudorovskiy.

