Fate of topological states in incommensurate generalized Aubry-Andr\'e models

TL;DR

This paper investigates how topological edge states behave in one-dimensional optical lattices with incommensurate modulations, exploring the interplay between localization and topological properties.

Contribution

It analyzes the persistence of topological states in generalized Aubry-Andr models with both commensurate and incommensurate modulations, linking localization phenomena with topological features.

Findings

Topological edge states can survive in localized regimes.

Incommensurate modulations influence the stability of topological states.

The energy spectrum undergoes significant changes with system parameters.

Abstract

We study one-dimensional optical lattices described by generalized Aubry-Andr\'e models that include both commensurate and incommensurate modulations of the hopping amplitude. This brings together two interesting features of this class of systems: Anderson localization and the existence of topological edge states. We follow changes of the single-particle energy spectrum induced by variations of the system parameters, with focus on the survival of topological states in the localized regime.