Abstract

The band structure of graphene near the Fermi surface is often well described by the effective mass approximation. In this approach electron wave function obeys the Dirac-type equation. To describe a number of effects it is necessary to supplement the equation with boundary conditions. Using the Hermiticity and the time reversal symmetry we derive the phenomenological boundary conditions for a multicomponent effective wave function. The boundary conditions in the case of smooth crystalline potential near the edge are parameterized in terms of a real phenomenological constant that describes a general type edge. The edge states spectra (i.e. Tamm states spectra) for semi-infinite graphene are analyzed.

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