Localization fom conductance in few-channel disordered wires

TL;DR

This paper analyzes localization phenomena in two- and three-channel quasi-one-dimensional disordered wires using tight-binding models, deriving exact expressions for localization lengths and examining the effects of interchain hopping.

Contribution

It provides new exact analytic formulas for localization lengths in multi-channel disordered wires, extending the Thouless expression to systems with interchain coupling.

Findings

Localization length decreases with weak interchain hopping compared to 1D

In three-channel systems, localization length can increase with larger interchain hopping

Exact expressions reduce to known 1D results in the limit of no interchain coupling

Abstract

We study localization in two- and three channel quasi-1D systems using multichain tight-binding Anderson models with nearest-neighbour interchain hopping. In the three chain case we discuss both the case of free- and that of periodic boundary conditions between the chains. The finite disordered wires are connected to ideal leads and the localization length is defined from the Landauer conductance in terms of the transmission coefficients matrix. The transmission- and reflection amplitudes in properly defined quantum channels are obtained from S-matrices constructed from transfer matrices in Bloch wave bases for the various quasi-1D systems. Our exact analytic expressions for localization lengths for weak disorder reduce to the Thouless expression for 1D systems in the limit of vanishing interchain hopping. For weak interchain hopping the localization length decreases with respect to the 1D value in all three cases. In the three-channel cases it increases with interchain hopping over restricted domains of large hopping.