Vertex corrections to the mean-field electrical conductivity in strongly disordered electron systems

TL;DR

This paper introduces an extended mean-field approach that non-perturbatively incorporates vertex corrections, improving the description of electrical conductivity in strongly disordered electron systems.

Contribution

It presents a novel approximate scheme that extends mean-field theory to include leading-order vertex corrections non-perturbatively for better transport property predictions.

Findings

Provides a formula for the two-particle vertex and conductivity including vertex corrections.

Ensures the conductivity remains non-negative across all disorder regimes.

Improves the theoretical understanding of quantum coherence effects in disordered systems.

Abstract

Mean-field theory of non-interacting disordered electron systems is widely and successfully used to describe equilibrium properties of alloys in the whole range of disorder strengths. It, however, fails to take into account effects of quantum coherence and localizing back-scattering effects when applied to transport phenomena. We present an approximate scheme extending the mean-field theory for one-electron properties in that it offers a formula for the two-particle vertex and the electrical conductivity non-perturbatively including the leading-order vertex corrections in a way that the approximation remains consistent and the conductivity non-negative in all disorder regimes.