Single-Particle Mobility Edge without Disorder

TL;DR

This paper demonstrates that a disorder-free one-dimensional lattice with an electric field can exhibit a true mobility edge, challenging the belief that disorder is necessary for localization and revealing new localization phenomena.

Contribution

The study analytically shows the existence of an exact mobility edge in a disorder-free lattice under an electric field, expanding understanding of localization mechanisms.

Findings

Presence of an exact mobility edge without disorder

Localization extends to weak electric fields

Number of localized states inversely proportional to field strength

Abstract

The existence of localization and mobility edges in one-dimensional lattices is commonly thought to depend on disorder (or quasidisorder). We investigate localization properties of a disorder-free lattice subject to an equally spaced electric field. We analytically show that, even though the model has no quenched disorder, this system manifests an exact mobility edge and the localization regime extends to weak fields, in contrast to gigantic field for the localization of a usual Stark lattice. For strong fields, the Wannier-Stark ladder is recovered and the number of localized eigenstates is inversely proportional to the spacing. Moreover, we study the time dependence of an initially localized excitation and dynamically probe the existence of mobility edge.