Electrons scattering in the monolayer graphene with a band-asymmetric annular potential well

TL;DR

This paper investigates electron scattering in monolayer graphene with a band-asymmetric annular potential well, deriving explicit formulas for the scattering matrix and analyzing the effects of band asymmetry on scattering properties.

Contribution

It provides exact explicit formulas for the scattering matrix in graphene with band-asymmetric potentials, linking scattering phases to geometrical relations and deriving the characteristic equation.

Findings

Explicit formulas for the scattering matrix were derived.

Band asymmetry induces mass (gap) perturbation in the Dirac equation.

Relations between scattering phases and geometrical vectors were established.

Abstract

Electron scattering in the monolayer graphene with short-range impurities modelled by the annular well with a band-asymmetric potential has been considered. Band-asymmetry of the potential resulted in the mass (gap) perturbation in the Dirac equation. Exact explicit formulae for the scattering matrix have been derived. The results are presented in terms of the scattering phases and in the geometrical form of a relation between some 2-vectors. The characteristic equation is obtained. It has a form of the orthogonality condition. An approximate calculation of observables in terms the scattering theory results is outlined.