Delocalization in coupled one-dimensional chains

TL;DR

This paper investigates how weak disorder affects electron transport in coupled one-dimensional chains, revealing an odd-even effect in conductance distribution linked to a delocalization transition at the band center.

Contribution

It provides an exact calculation of the conductance distribution at the band center and explains the odd-even effect through level repulsion of transmission eigenvalues.

Findings

Delocalization transition occurs only for odd number of chains.

Exact conductance distribution is obtained at the band center.

Odd-even effect is explained by level repulsion phenomena.

Abstract

A weakly disordered quasi-one-dimensional tight-binding hopping model with $N$ rows is considered. The probability distribution of the Landauer conductance is calculated exactly in the middle of the band, $\epsilon=0$, and it is shown that a delocalization transition at this energy takes place if and only if $N$ is odd. This even-odd effect is explained by level repulsion of the transmission eigenvalues.