Conductance Fluctuations in Disordered Wires with Perfectly Conducting Channels

TL;DR

This paper investigates how conductance fluctuations behave in disordered quantum wires with unequal numbers of left- and right-moving channels, revealing that universality breaks down unless the number of channels is very large.

Contribution

It introduces a study of conductance fluctuations in wires with perfectly conducting channels, highlighting the breakdown of universality for finite channel imbalances.

Findings

Conductance variance depends on the imbalance of channels.

Universality of conductance fluctuations breaks down for finite channel differences.

Perfectly conducting channels influence the long-wire conductance behavior.

Abstract

We study conductance fluctuations in disordered quantum wires with unitary symmetry focusing on the case in which the number of conducting channels in one propagating direction is not equal to that in the opposite direction. We consider disordered wires with $N+m$ left-moving channels and $N$ right-moving channels. In this case, $m$ left-moving channels become perfectly conducting, and the dimensionless conductance $g$ for the left-moving channels behaves as $g \to m$ in the long-wire limit. We obtain the variance of $g$ in the diffusive regime by using the Dorokhov-Mello-Pereyra-Kumar equation for transmission eigenvalues. It is shown that the universality of conductance fluctuations breaks down for $m \neq 0$ unless $N$ is very large.