Localization in one-dimensional incommensurate lattices beyond the Aubry-Andr\'e model

TL;DR

This paper explores localization phenomena in one-dimensional incommensurate lattices beyond the Aubry-Andre9 model, revealing the emergence of mobility edges through extended models and direct Schrf6dinger equation analysis.

Contribution

It introduces a generalized model with next-nearest-neighbor hopping and directly studies the Schrf6dinger equation, showing new localization behaviors and mobility edges beyond the traditional AA model.

Findings

Mobility edges appear in extended models.

Localization properties depend on incommensuration.

Differences from the Aubry-Andre9 model are demonstrated.

Abstract

Localization properties of particles in one-dimensional incommensurate lattices without interaction are investigated with models beyond the tight-binding Aubry-Andr\'e (AA) model. Based on a tight-binding t_1 - t_2 model with finite next-nearest-neighbor hopping t_2, we find the localization properties qualitatively different from those of the AA model, signaled by the appearance of mobility edges. We then further go beyond the tight-binding assumption and directly study the system based on the more fundamental single-particle Schr\"odinger equation. With this approach, we also observe the presence of mobility edges and localization properties dependent on incommensuration.