Effect of Disorder on Transport in Graphene

Abstract

Quenched disorder in graphene is characterized by 5 constants and experiences the logarithmic renormalization even from the spatial scales smaller than the Fermi wavelength. We derive and solve renormalization group equations (RGEs) describing the system at such scales. At larger scales, we derive a nonlinear supermatrix $\sigma$ model completely describing localization and crossovers between different ensembles. The parameters of this $\sigma$ model are determined by the solutions of the RGEs.