Delocalisation phenomena in one-dimensional models with long-range correlated disorder: a perturbative approach

TL;DR

This paper investigates how long-range correlated disorder affects electron localization in one-dimensional models, revealing a transition characterized by a change in the Lyapunov exponent's dependence on disorder strength.

Contribution

It introduces a fourth-order perturbative method to analyze the delocalization transition and distinguishes localization properties between Gaussian and non-Gaussian potentials.

Findings

Delocalization transition marked by a change from quadratic to quartic dependence of Lyapunov exponent on disorder.

Fourth-order perturbation enables detailed analysis of localization properties.

Differences in localization between Gaussian and non-Gaussian disorder potentials.

Abstract

We study the nature of electronic states in one-dimensional continuous models with weak correlated disorder. Using a perturbative approach, we compute the inverse localisation length (Lyapunov exponent) up to terms proportional to the fourth power of the potential; this makes possible to analyse the delocalisation transition which takes place when the disorder exhibits specific long-range correlations. We find that the transition consists in a change of the Lyapunov exponent, which switches from a quadratic to a quartic dependence on the strength of the disorder. Within the framework of the fourth-order approximation, we also discuss the different localisation properties which distinguish Gaussian from non-Gaussian random potentials.