Topological Zero-Energy Modes in Gapless Commensurate Aubry-Andr\'e-Harper Models

TL;DR

This paper demonstrates that the commensurate off-diagonal Aubry-Andre9-Harper model exhibits topologically nontrivial zero-energy edge modes in the gapless regime, linking it to Majorana chain properties and suggesting experimental observability.

Contribution

It reveals the topological nature of the commensurate off-diagonal AAH model in the gapless regime, a novel finding contrasting with the incommensurate case.

Findings

Supports zero-energy edge modes in the gapless regime

Links topological properties to Majorana chains

Discusses potential for experimental detection

Abstract

The Aubry-Andr\'e or Harper (AAH) model has been the subject of extensive theoretical research in the context of quantum localization. Recently, it was shown that one-dimensional quasicrystals described by the incommensurate AAH model has a nontrivial topology. In this Letter, we show that the commensurate off-diagonal AAH model is topologically nontrivial in the gapless regime and supports zero-energy edge modes. Unlike the incommensurate case, the nontrivial topology in the off-diagonal AAH model is attributed to the topological properties of the one-dimensional Majorana chain. We discuss the feasibility of experimental observability of our predicted topological phase in the commensurate AAH model.