`One-sided' log-normal distribution of conductances of a disordered quantum wire

TL;DR

This paper develops an analytical method to derive the full conductance distribution in disordered quantum wires, revealing a 'one-sided' log-normal distribution in the crossover regime and a Gaussian cutoff at higher disorder levels.

Contribution

It introduces a systematic analytical approach applicable across all disorder strengths to determine conductance distributions in non-interacting quantum wires.

Findings

Conductance distribution is highly asymmetric in the crossover regime.

Distribution follows a 'one-sided' log-normal form.

At high disorder, the distribution's tail is Gaussian-cut off.

Abstract

We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically for the first time the full distribution of conductance P(g) for a quasi one dimensional wire in the absence of electron-electron interaction. We show that in the crossover region between the metallic and insulating regimes, P(g) is highly asymmetric, given by an essentially `one sided' log-normal distribution. For larger disorder, the tail of the log-normal distribution for g > 1 is cut off by a Gaussian.