Localization in Semiconductor Quantum Wire Nanostructures

TL;DR

This paper investigates how disorder affects electron localization in semiconductor quantum wire nanostructures, revealing that localization length depends on mobility, disorder range, and subband crossing.

Contribution

It introduces a transfer matrix-Lyapunov exponent method to analyze localization length variations with disorder type and subband effects in quantum wires.

Findings

Localization length increases with effective mobility.

Finite-range disorder enhances localization length.

Crossing into the second subband sharply reduces localization length.

Abstract

Localization properties of quasi-one dimensional quantum wire nanostructures are investigated using the transfer matrix-Lyapunov exponent technique. We calculate the localization length as a function of the effective mean-field mobility assuming the random disorder potential to be arising from dopant-induced short-range $\delta$-function or finite-range Gaussian impurity scattering. The localization length increases approximately linearly with the effective mobility, and is also enhanced by finite-range disorder. There is a sharp reduction in the localization length when the chemical potential crosses into the second subband.