The conuctivity low energy asymptotics for monolayer graphene

The 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 monolayer graphene. The explicit exact formulae obtained for S-matrix for $\delta$-shell potential allowed us to study the asymptotic behavior of such scattering data 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 good agreement with experimental curves which show that the considered model is reasonable.