Low Temperature Physics: 44, 1245 (2018); https://doi.org/10.1063/1.5078521
Fizika Nizkikh Temperatur: Volume 44, Number 12 (December 2018), p. 1598-1605 ( to contents , go back )
Scattering problems and boundary conditions for 2D electron gas and graphene
Theoretische Physik III, Ruhr-Universitaet Bochum, D-44801 Bochum, Germany
Received July 3, 2018, published online October 26, 2018
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's function technique. In particular, the reflection wave function contains terms inversely proportional to the distance to the graphene lattice edge. The Dirac equation and the momentum dependence of the wave functions of the quasi-particles near the conical points are also found by the perturbation theory with degeneracy in terms of the Bloch functions taken at the degeneracy points. The developed approach allows to formulated the validity criteria for the Dirac equation in a rather simple way.
Key words: graphene, 2D electron gas, Dirac equation, boundary conditions, validity criteria, Green functions.