Weak and Strong Localization in Low-Dimensional Semiconductor Structures

TL;DR

This paper investigates how localization length varies with the number of subbands in low-dimensional semiconductors, developing a weak localization theory that aligns with experimental temperature-dependent conductivity data.

Contribution

It introduces a weak localization framework for large N in low-dimensional structures, revealing proportional and exponential growth of localization length in different geometries.

Findings

Localization length proportional to N in quasi-1D systems

Localization length grows exponentially with N in quasi-2D systems

The developed theory matches experimental temperature dependence of conductivity

Abstract

The dependence of the localization length on the number of occupied subbands $N$ in low-dimensional semiconductors is investigated. The localization length is shown to be proportional to the number of occupied subbands in quasi-one-dimensional quantum wires while it grows exponentially with $N$ in quasi-two-dimensional systems. Also a weak localization theory is developed for large N with a well-defined small expansion parameter $1/N$. The temperature dependence of the conductivity deduced using this perturbation theory agrees with the experimentally observed dependence.