Conductivity low-energy asymptotics for monolayer graphene

TL;DR

This paper investigates how local band asymmetry caused by defects affects electron scattering and conductivity in monolayer graphene, providing explicit formulas and asymptotic analysis that align well with experimental observations.

Contribution

It introduces a model incorporating defect-induced band asymmetry in the Dirac equation and derives exact formulas for scattering parameters affecting electronic transport.

Findings

Explicit S-matrix formula for delta-shell potential

Asymptotic behavior of scattering phases and conductivity

Model results agree with experimental data

Abstract

Electron scattering problem in the monolayer graphene with short-range impurities is considered. The main novel element in the suggested model is the band asymmetry of the defect potential in the 2+1-dimensional Dirac equation. This asymmetry appears naturally if the defect violates the symmetry between sublattices. Our goal in the present paper is to take into account a local band asymmetry violation arising due to the defect presence. We analyze the effect of the electron scattering on the electronic transport parameters in the monolayer graphene. The explicit exact formula obtained for S-matrix for the suggested delta-shell potential model allowed us to study the asymptotic behavior of such characteristics as scattering phases, transport cross section, the transport relaxation time and the conductivity for small values of the Fermi energy. The obtained results are in a good agreement with the experimental data which shows that the considered model is reasonable.