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

Juan Zurita1,2, Charles Creffield2, and Gloria Platero1

1Instituto de Ciencia de Materiales de Madrid (CSIC), Cantoblanco, E-28049 Madrid, Spain
2Universidad Complutense de Madrid, E-28040 Madrid, Spain

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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.

Topological insulators are materials with an insulating bulk but a gapless surface spectrum. In ladder models, formed by two connected chains of sites, these states are located at the right and left of the system, and are pinned at zero energy if the relevant symmetries of the Hamiltonian are preserved. We explore the interplay between this protection and the effects of magnetically-induced localization in a family of models we have termed “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 topological edge states.

Some of these states can be tuned by changing the parameters of the model and remain protected even in very small systems, making them promising for quantum information purposes. Another kind of edge states is related to the Chern number of the 2D system created by changing the parameters of the model in a closed loop. Additionally, one of the ladders can belong to three different symmetry classes, one of which is unusual for a non-superconducting model. We propose some experimental setups to implement the CSSH ladders with current technology, focusing on the photonic lattice case.

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[1] R. G. Dias and A. M. Marques, "Long-range hopping and indexation assumption in 1D topological insulators", arXiv:2109.09201.

[2] Amrita Mukherjee, Atanu Nandy, Shreekantha Sil, and Arunava Chakrabarti, "Tailoring flat bands and topological phases in a multi-strand Creutz network", arXiv:2111.06347.

[3] Marco Di Liberto and Nathan Goldman, "Orbital order and chiral currents of interacting bosons with $\pi$-flux", arXiv:2111.13572.

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