Semiclassical theory of potential scattering for massless Dirac fermions

Abstract

In this paper we study scattering of two-dimensional massless Dirac fermions by a potential that depends on a single Cartesian variable. Depending on the energy of the incoming particle and its angle of incidence, there are three different regimes of scattering. To find the reflection and transmission coefficients in these regimes, we apply the Wentzel-Kramers-Brillouin (WKB), also called semiclassical, approximation. We use the method of comparison equations to extend our prediction to nearly normal incidence, where the conventional WKB method should be modified due to the degeneracy of turning points. We compare our results to numerical calculations and find good agreement.

Minor revision; several references have been added

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• Guided modes and terahertz transitions for two-dimensional Dirac fermions in a smooth double-well potential
• Spin pumping into two-dimensional electron systems
• Weyl fermions in cylindrical wires
• Quantum Charged Spinning Massless Particles in 2+1 dimensions
• Semiclassical theory for plasmons in spatially inhomogeneous media
• Coupling of Klein-Andreev Resonant States in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$-graphene-Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+x}$ Devices