Nonlocally-Correlated Disorder and Delocalization in One Dimension: Density of States

TL;DR

This paper investigates how nonlocal correlations in disorder affect electron delocalization in one-dimensional systems, revealing that such correlations stabilize delocalization and enhance states near the band center.

Contribution

It introduces a supersymmetric approach to analyze the impact of nonlocal disorder correlations on delocalization in 1D electron systems, extending prior white noise disorder models.

Findings

Delocalization transition remains stable with nonlocal short-range disorder.

States near the band center are amplified by disorder correlations.

Disorder correlation suppresses random fluctuations, affecting localization.

Abstract

We study delocalization transition in a one-dimensional electron system with quenched disorder by using supersymmetric (SUSY) methods. Especially we focus on effects of nonlocal correlation of disorder, for most of studies given so far considered $\delta$-function type white noise disorder. We obtain wave function of the "lowest-energy" state which dominates partition function in the limit of large system size. Density of states is calculated in the scaling region. The result shows that delocalization transition is stable against nonlocal short-ranged correlation of disorder. Especially states near the band center are enhanced by the correlation of disorder which partially suppresses random fluctuation of disorder. Physical picture of the localization and the delocalization transition is discussed.