ИСТИНА

We study above-barrier scattering of Dirac electrons by a smooth electrostatic potential combined with a coordinate-dependent mass in graphene. We consider sufficiently smooth potential and mass, so that semiclassical approximation can be used. This electronic optics setup naturally leads to focusing and the formation of caustics. We use Maslov canonical operator approach to construct a semiclassical asymptotics and study them near caustics. Because of the matrix character of the Dirac equation, wavefunction contains a nontrivial semiclassical phase, which influences the focusing. We consider several numerical examples and show that our semiclassical results are in very good agreement with the results of tight-binding calculations. Results are obtained together with K.J.A. Reijnders, M.I. Katsnelson, S.Yu. Dobrokhotov, and are published in [K.J.A. Reijnders et al. / Annals of Physics 397 (2018) 65.135]. Report is supported by Ministry of Education and Science of the Russian Federation, Russia, State Project AAAA-A17-117021310377-1.