Semiclassical theory of potential scattering for massless Dirac fermions

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.