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 two-dimensional massless Dirac
fermions by a one-dimensional 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
(Wentzel-Kramers-Brillouin) approximation. The predictions provided by
our analytic expressions show good agreement with numerical
calculations for all considered cases. The talk is based on my common
works with M. Katsnelson and T. Tudorovskii.
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