Effect of Disorder on Transport in Graphene

TL;DR

This paper investigates how quenched disorder affects electronic transport in graphene by deriving renormalization group equations and a supermatrix sigma-model to describe localization and ensemble crossovers.

Contribution

It introduces a comprehensive theoretical framework combining RGEs and a supermatrix sigma-model for disordered graphene at various scales.

Findings

Logarithmic renormalization of disorder constants at sub-Fermi scales

Derivation of RGEs governing disorder effects in graphene

Construction of a sigma-model describing localization phenomena

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 non-linear 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.