Finite-size scaling in a 2D disordered electron gas with spectral nodes

TL;DR

This paper investigates the DC conductivity of a 2D disordered electron gas with spectral nodes, revealing finite conductivity and logarithmic finite-size scaling consistent with experimental graphene data.

Contribution

It introduces a field theoretical approach to analyze conductivity in disordered 2D electron gases with spectral nodes, showing finite conductivity without weak localization divergence.

Findings

Finite conductivity with logarithmic finite-size scaling

No logarithmic divergence as in weak localization

Results align with experimental graphene conductivity behavior

Abstract

We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo--Greenwood conductivity formula. Disorder scattering is treated within the standard perturbation theory by summing up ladder and maximally crossed diagrams. The emergent gapless (diffusion) modes determine the behavior of the conductivity on large scales. We find a finite conductivity with an intermediate logarithmic finite-size scaling towards smaller conductivities but do not obtain the logarithmically divergence of the weak-localization approach. Our results agree with the experimentally observed logarithmic scaling of the conductivity in graphene with the formation of a plateau near $e^2/\pi h$.