Renormalized transport properties of randomly gapped 2D Dirac fermions

TL;DR

This paper studies the transport behavior of 2D Dirac fermions with random gaps, revealing a scale-invariant diffusion process described by a new renormalizable nonlocal field theory, consistent with numerical findings.

Contribution

It introduces a novel renormalizable nonlocal field theory to describe transport in disordered 2D Dirac systems beyond charge neutrality, highlighting scale invariance and matching numerical results.

Findings

Absence of dynamic gap generation at zero mean random gap

Scale-invariant diffusion coefficient on large scales

Beta function of DC conductivity agrees with previous numerical results

Abstract

We investigate the scaling properties of the recently acquired fermionic non--linear $\sigma$--model which controls gapless diffusive modes in a two--dimensional disordered system of Dirac electrons beyond charge neutrality. The transport on large scales is governed by a novel renormalizable nonlocal field theory. For zero mean random gap, it is characterized by the absence of a dynamic gap generation and a scale invariant diffusion coefficient. The $\beta$ function of the DC conductivity, computed for this model, is in perfect agreement with numerical results obtained previously.