Asymptotic behavior of the conductance in disordered wires with perfectly conducting channels

TL;DR

This paper analyzes the asymptotic conductance behavior in disordered wires with perfectly conducting channels, using exact solutions of the DMPK equation and supersymmetry methods, revealing consistent results across models.

Contribution

It provides the first exact calculation of conductance moments in disordered wires with perfectly conducting channels, confirming the universality with the Chalker-Coddington model.

Findings

Average conductance approaches a finite value for large wire length

Second moment of conductance indicates reduced fluctuations due to perfect channels

Results are consistent between DMPK and supersymmetry approaches

Abstract

We study the conductance of disordered wires with unitary symmetry focusing on the case in which $m$ perfectly conducting channels are present due to the channel-number imbalance between two-propagating directions. Using the exact solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation for transmission eigenvalues, we obtain the average and second moment of the conductance in the long-wire regime. For comparison, we employ the three-edge Chalker-Coddington model as the simplest example of channel-number-imbalanced systems with $m = 1$, and obtain the average and second moment of the conductance by using a supersymmetry approach. We show that the result for the Chalker-Coddington model is identical to that obtained from the DMPK equation.