Engineering topological phase transition and Aharonov-Bohm caging in a flux-staggered lattice

TL;DR

This paper demonstrates how a flux-staggered lattice can undergo a topological phase transition controlled by magnetic flux, enabling external tuning of topological properties and Aharonov-Bohm caging effects, with potential applications in quantum information transport.

Contribution

It introduces a method to induce topological phase transitions in a flux-staggered lattice via external magnetic flux tuning, mapped to an SSH model for easier analysis.

Findings

Topological phase transition controlled by magnetic flux.

Enhanced Aharonov-Bohm caging through flux tuning.

Exact analysis of topologically protected edge states.

Abstract

A tight binding network of diamond shaped unit cells trapping a staggered magnetic flux distribution is shown to exhibit a topological phase transition under a controlled variation of the flux trapped in a cell. A simple real space decimation technique maps a binary flux staggered network into an equivalent Su-Shrieffer-Heeger (SSH) model. In this way, dealing with a subspace of the full degrees of freedom, we show that a topological phase transition can be initiated by tuning the applied magnetic field that eventually simulates an engineering of the numerical values of the overlap integrals in the paradigmatic SSH model. Thus one can use an external agent, rather than monitoring the intrinsic property of a lattice to control the topological properties. This is advantageous from an experimental point of view. We also provide an in-depth description and analysis of the topologically protected edge states, and discuss how, by tuning the flux from outside one can enhance the spatial extent of the Aharonov-Bohm caging of single particle states for any arbitrary period of staggering. This feature can be useful for the study of transport of quantum information. Our results are exact.