Localization-delocalization transition in one-dimensional electron systems with long-range correlated disorder

TL;DR

This paper studies how long-range correlated disorder affects electron localization in one-dimensional systems, revealing a transition between localized and delocalized states and challenging existing theoretical criteria.

Contribution

It provides numerical evidence of a localization-delocalization transition in 1d systems with correlated disorder and analyzes the critical behavior of the localization length.

Findings

Existence of a localization-delocalization transition in 1d systems

Critical exponent $ u$ disobeys the Harris criterion

Non-trivial dependence of localization length on disorder strength

Abstract

We investigate localization properties of electron eigenstates in one-dimensional (1d) systems with long-range correlated diagonal disorder. Numerical studies on the localization length $\xi$ of eigenstates demonstrate the existence of the localization-delocalization transition in 1d systems and elucidate non-trivial behavior of $\xi$ as a function of the disorder strength. The critical exponent $\nu$ for localization length is extracted for various values of parameters characterizing the disorder, revealing that every $\nu$ disobeys the Harris criterion $\nu > 2/d$.