Tunable zero modes and quantum interferences in flat-band topological insulators

TL;DR

This paper explores tunable zero-energy modes and quantum interference effects in flat-band topological insulators called CSSH ladders, revealing their rich topological phases, protected edge states, and potential for quantum information applications.

Contribution

It introduces CSSH ladders combining Creutz and SSH models, demonstrating their tunability, topological protection, and unconventional edge modes, including experimental proposals.

Findings

CSSH ladders exhibit flat bands and multiple topological phases.

Protected zero modes are robust even in small systems due to AB caging.

Some models show topological end modes related to Chern numbers.

Abstract

We investigate the interplay between Aharonov-Bohm (AB) caging and topological protection in a family of quasi-one-dimensional topological insulators, which we term CSSH ladders. Hybrids of the Creutz ladder and the SSH chain, they present a regime with completely flat bands, and a rich topological phase diagram, with several kinds of protected zero modes. These are reminiscent of the Creutz ladder edge states in some cases, and of the SSH chain edge states in others. Furthermore, their high degree of tunability, and the fact that they remain topologically protected even in small systems in the rungless case, due to AB caging, make them suitable for quantum information purposes. One of the ladders can belong to the BDI, AIII and D symmetry classes depending on its parameters, the latter being unusual in a non-superconducting model. Two of the models can also harbor topological end modes which do not follow the usual bulk-boundary correspondence, and are instead related to a Chern number. Finally, we propose some experimental setups to implement the CSSH ladders with current technology, focusing on the photonic lattice case.