Mean Free Path in Disordered Multichannel Tight-Binding Wires

TL;DR

This paper investigates the relationship between mean free paths and localization length in disordered multichannel tight-binding wires, introducing an average channel mean free path that generalizes Thouless' relation.

Contribution

It generalizes Thouless' relation to multichannel systems and defines an exact average mean free path in terms of the total reflection coefficient.

Findings

Derived an exact expression for the average mean free path.

Showed that the localization length scales with the number of channels and the average mean free path.

Compared the exact mean free path with the maximum entropy approach.

Abstract

Transport in a disordered tight-binding wire involves a collection of different mean free paths resulting from the distinct fermi points, which correspond to the various scattering channels of the wire. The generalization of Thouless' relation between the mean free path and the localization length $\xi$ permits to define an average channel mean free path,$\bar\ell$, such that $\xi\sim N\bar\ell$ in an $N$-channel system. The averaged mean free path $\bar\ell$ is expressed exactly in terms of the total reflection coefficient of the wire and compared with the mean free path defined in the maximum entropy approach.