Thursday, June 14, 2012

1206.2869 (K. J. A. Reijnders et al.)

Semiclassical theory of potential scattering for massless Dirac fermions    [PDF]

K. J. A. Reijnders, T. Tudorovskiy, M. I. Katsnelson
In this paper we study the scattering of massless Dirac fermions within a one-dimensional geometry. Depending on the energy of an incoming particle and its transversal momentum, there are three different regimes of scattering. To find the reflection and transmission coefficients for these regimes, we apply the Wentzel-Kramers-Brillouin (WKB) or semiclassical approximation. For a barrier supporting hole states, that is, the Klein tunneling regime, we use the method of comparison equations to extend our prediction for the transmission coefficient to the entire range of incidence angles. For above-barrier scattering, we find a simple semiclassical formula for the reflection coefficient, that shows total transmission at normal incidence. We compare our results with numerical calculations and an exact solution, and find good agreement. We observe that for a generic (asymmetric) n-p-n junction, the side resonances are suppressed.
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