Conductance distribution of disordered quasi one-dimensional wires

TL;DR

This paper analytically derives the conductance distribution in disordered quasi-one-dimensional wires across all disorder regimes, revealing a highly asymmetric distribution near the metal-insulator transition and a Gaussian cutoff at high conductance.

Contribution

It provides a comprehensive analytical description of conductance distribution for all disorder strengths in quasi-1D wires, including crossover behaviors.

Findings

Distribution is highly asymmetric near the crossover region.

Increased disorder leads to a Gaussian cutoff in the distribution.

Distribution transitions from log-normal to truncated forms with disorder.

Abstract

We determine analytically the distribution of conductances of quasi one-dimensional disordered electron systems, neglecting electron-electron interaction, for all strengths of disorder. We find that in the crossover region between the metallic and insulating regimes, P(g) is highly asymmetric, given by ``one-sided'' log-normal distribution. For larger disorder, the tail of the log-normal distribution is cut-off for g > 1 by a Gaussian.