Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder

TL;DR

This paper demonstrates that one-dimensional random potentials with specific long-range correlations can exhibit a mobility edge, and provides algorithms to construct such potentials with controllable localization properties.

Contribution

It introduces a method to generate 1D correlated potentials with mobility edges using binary correlators and chaotic trajectories, advancing understanding of localization in disordered systems.

Findings

Mobility edges exist in 1D correlated disordered potentials.

Constructed potentials show mobility edges at specific energies.

Numerical simulations confirm the theoretical predictions.

Abstract

We show that a mobility edge exists in 1D random potentials provided specific long-range correlations. Our approach is based on the relation between binary correlator of a site potential and the localization length. We give the algorithm to construct numerically potentials with mobility edge at any given energy inside allowed zone. Another natural way to generate such potentials is to use chaotic trajectories of non-linear maps. Our numerical calculations for few particular potentials demonstrate the presence of mobility edges in 1D geometry.