Electronic optics in graphene in the semiclassical approximationстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
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Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 6 декабря 2018 г.
Аннотация:We study above-barrier scattering of Dirac electrons by a smooth
electrostatic potential combined with a coordinate-dependent mass
in graphene.Weassume that the potential and mass are sufficiently
smooth, so that we can define a small dimensionless semiclassical
parameter h ≪ 1. This electronic optics setup naturally leads to focusing
and the formation of caustics, which are singularities in the
density of trajectories. We construct a semiclassical approximation
for the wavefunction in all points, placing particular emphasis on
the region near the caustic, where the maximum of the intensity
lies. Because of the matrix character of the Dirac equation, this
wavefunction contains a nontrivial semiclassical phase, which is
absent for a scalar wave equation and which influences the focusing.
We carefully discuss the three steps in our semiclassical
approach: the adiabatic reduction of the matrix equation to an
effective scalar equation, the construction of the wavefunction
using the Maslov canonical operator and the application of the
uniform approximation to the integral expression for the wavefunction
in the vicinity of a caustic. We consider several numerical
examples and show that our semiclassical results are in very good
agreement with the results of tight-binding calculations. In particular,
we show that the semiclassical phase can have a pronounced
effect on the position of the focus and its intensity.