Localization Length in Quasi One Dimensional Disordered System Revised

TL;DR

This paper derives analytical formulas for electron localization lengths in weakly disordered quasi-one-dimensional quantum wires, validated by numerical analysis, and clarifies relationships among different length scales in such systems.

Contribution

It provides the first exact analytical expressions for localization lengths in Q1D disordered wires up to second order in disorder strength, for arbitrary channel numbers.

Findings

Analytical localization length formulas match numerical results.

Established relationships between different length scales in Q1D systems.

Validated theoretical predictions with numerical conductivity calculations.

Abstract

In the weak disordered regime we provide analytical expressions for the electron localization lengths in quasi-one dimensional (Q1D) disordered quantum wire with hard wall and periodic boundary conditions. They are exact up to order $W^2$ ($W$ being the disorder strength) for an arbitrary number of channels. Detailed numerical analysis of the Anderson localization, based on Kubo's formula for conductivity, show excellent agreement with analytical calculations. We establish relationship between various lengths in Q1D systems.