Anderson transition in one-dimensional systems with spatial disorder

TL;DR

This paper investigates how spatial disorder affects conductance and eigenstates in a 1D Kronig-Penney model, revealing an Anderson transition and characterizing conductance distributions across regimes.

Contribution

It demonstrates the occurrence of an Anderson transition in 1D systems with spatial disorder, a phenomenon previously thought unlikely in such low dimensions.

Findings

Anderson transition can occur in 1D systems with disorder.

Conductance distribution becomes system-size independent at transition.

Metallic phase exhibits Gaussian conductance distribution.

Abstract

A simple Kronig-Penney model for one-dimensional (1D) mesoscopic systems with $\delta $ peak potentials is used to study numerically the influence of a spatial disorder on the conductance fluctuations and distribution at different regimes. We use the Levy laws to investigate the statistical properties of the eigenstates. We found the possibility of an Anderson transition even in 1D meaning that the disorder can also provide constructive quantum interferences. We found at this transition that the conductance probability distribution has a system-size independent shape with large fluctuations in good agreement with previous works. In these 1D systems, the metallic phase is well characterized by a Gaussian conductance distribution. Indeed, the results for the conductance distribution are in good agreement with the previous works in 2D and 3D systems for other models.