Distribution of conductance for Anderson Insulators: A theory with a single parameter

TL;DR

This paper derives an analytic distribution of conductance in 3D Anderson insulators, revealing non-trivial behavior near the metal-insulator transition and proposing a single-parameter description.

Contribution

It provides a novel analytic expression for conductance distribution in disordered conductors, emphasizing a single-parameter framework for the Anderson transition.

Findings

Distribution deviates from log-normal even in deep insulators

Variance scales as a fractional power of the mean conductance

Skewness changes sign near the transition

Abstract

We obtain an analytic expression for the full distribution of conductance for a strongly disordered three dimensional conductor within a perturbative approach based on the transfer-matrix formulation. Our results confirm numerical evidence that the log-normal limit of the distribution is not reached even in the deeply insulating regime. We show that the variance of the logarithm of the conductance scales as a fractional power of the mean, while the skewness changes sign as one approaches the Anderson metal-insulator transition from the deeply insulating limit, all described as a function of a single parameter. The approach suggests a possible single parameter description of the Anderson transition that takes into account the full nontrivial distribution of conductance.