Conductance distribution in 3D Anderson insulators: deviation from log-normal form

TL;DR

This paper develops a numerical method to derive the conductance distribution in 3D Anderson insulators across all disorder strengths, revealing deviations from the log-normal distribution typical of quasi-1D systems.

Contribution

It introduces a novel numerical approach to compute the 3D conductance distribution and provides the first analytical characterization of its form in the insulating regime.

Findings

Conductance distribution in 3D insulators differs from log-normal.

Method applies to all disorder strengths.

Analytical form obtained for the insulating regime.

Abstract

We show how a recent proposal to obtain the distribution of conductances in three dimensions (3D) from a generalized Fokker-Planck equation for the joint probability distribution of the transmission eigenvalues can be implemented for all strengths of disorder by numerically evaluating certain correlations of transfer matrices. We then use this method to obtain analytically, for the first time, the 3D conductance distribution in the insulating regime and provide a simple understanding of why it differs qualitatively from the log-normal distribution of a quasi one-dimensional wire.