Conductance distribution in quasi-one-dimensional disordered quantum wires

TL;DR

This paper introduces a systematic analytical method to determine the full conductance distribution in quasi-one-dimensional disordered quantum wires across all disorder regimes, revealing key features and transitions.

Contribution

It provides a comprehensive analytical framework for conductance distribution in disordered wires, capturing behavior from metallic to insulating regimes, including non-analyticities and distribution shape changes.

Findings

P(g) is Gaussian for g >> 1 in metals

P(g) has a log-normal tail for g << 1

Method aligns well with existing exact results

Abstract

We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically the full distribution of conductances P(g) for a quasi one dimensional wire within the model of non-interacting fermions. The method has been used in [1-3] to predict sharp features in P(g) near g=1 and the existence of non-analyticity in the conductance distribution in the insulating and crossover regimes, as well as to show how P(g) changes from Gaussian to log-normal behavior as the disorder strength is increased. Here we provide many details of the method, including intermediate results that offer much insight into the nature of the solutions. In addition, we show within the same framework that while for metals P(g) is a Gaussian around g >>1, there exists a log-normal tail for g << 1, consistent with earlier field theory calculations. We also obtain several other results that compare very well with available exact results in the metallic and insulating regimes.