Localization and adiabatic pumping in a generalized Aubry-Andr\'e-Harper model

TL;DR

This paper introduces a generalized Aubry-Andre9-Harper model with a tunable phase shift, revealing a localization transition, topological phase changes, and adiabatic pumping phenomena, expanding understanding of localization and topological effects in quasiperiodic systems.

Contribution

It develops a generalized AAH model with a tunable phase, demonstrating localization transitions, topological phase changes, and adiabatic pumping, which were not present in the original model.

Findings

Localization transition controlled by phase shift

Existence of topologically trivial and non-trivial phases

Adiabatic pumping of boundary states and breakdown phenomena

Abstract

A generalization of the Aubry-Andr\'e-Harper (AAH) model is developed, containing a tunable phase shift between on-site and off-diagonal modulations. A localization transition can be induced by varying just this phase, keeping all other model parameters constant. The complete localization phase diagram is obtained. Unlike the original AAH model, the generalized model can exhibit a transition between topologically trivial bandstructures and topologically non-trivial bandstructures containing protected boundary states. These boundary states can be pumped across the system by adiabatic variations in the phase shift parameter. The model can also be used to demonstrate the phenomenon of adiabatic pumping breakdown due to localization.