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

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 localisation.

Keywords:

• Electrical conductivity
• disordered materials
• quantum transport
• electronic localisation

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by a grant of the Julian Schwinger Foundation for Physical Research.