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

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