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

Abstract

Electron scattering in the monolayer graphene has been considered within the framework of our model of short-range defects proposed earlier. Electronic properties are determined by the Dirac equation for the two-component spinor wave function. Perturbation is modeled by the annular well with a band-asymmetric potential. Band-asymmetry of the potential stems from the local structure defect and leads to the mass (gap) perturbation in the Dirac equation. Transitions between the K and K’ critical points in the Brillouin zone are neglected, which is valid provided that the short-range perturbation has a finite radius. Exact explicit formulas for the scattering matrix have been derived. Results are presented in terms of the scattering phases and in the geometrical form of a relation between some 2-vectors. The characteristic equation for the bound and resonance states has been obtained in the form of an orthogonality condition. An approximate calculation of observables in terms of the scattering theory results is outlined.