Conductivity of disordered 2d binodal Dirac electron gas: Effect of the internode scattering

TL;DR

This paper investigates how internode scattering influences the dc conductivity of a disordered 2D Dirac electron gas, revealing that internode scattering does not necessarily lead to localization and identifying two distinct conductivity regimes.

Contribution

It compares two theoretical approaches and demonstrates that internode scattering does not always induce Anderson localization in disordered 2D Dirac systems.

Findings

Two conductivity scenarios are identified regardless of internode scattering.

Both theoretical methods used are shown to be equivalent.

Internode scattering does not necessarily cause localization.

Abstract

We study the dc conductivity of a weakly disordered 2d Dirac electron gas with two bands and two spectral nodes, employing a field theoretical version of the Kubo--Greenwood conductivity formula. In this paper we are concerned with the question how the internode scattering affects the conductivity. We use and compare two established techniques for treating the disorder scattering: The perturbation theory, there ladder and maximally crossed diagrams are summed up, and the functional integral approach. Both turn out to be entirely equivalent. For a large number of random potential configurations we have found only two different conductivity scenarios. Both scenarios appear independently of whether the disorder does or does not create the internode scattering. In particular we do not confirm the conjecture that the internode scattering tends to Anderson localization.