Compact Topological Edge States in Flux-Dressed Graphenelike Photonic Lattices.

Flat band lattice systems promote the appearance of perfectly compact bulk states, whereas topology favors edge localization. In this work, we report the existence of compact topological edge states on flux-dressed photonic graphene ribbons. We found that robust localization is achieved through a synergy of Aharonov-Bohm caging and topological protection mechanisms. The topological nontriviality of the compact edge states is characterized through both theoretical derivations and experimental observations of an integer Zak phase obtained from the mean chiral displacement. Experiments are performed using direct laser writing of a graphene ribbon photonic lattice having 0 or π effective magnetic fluxes. Mode stability is demonstrated by the exceptional localization of the edge compact mode and its resilience to fabrication tolerances and input phase deviations. Our findings demonstrate the existence of perfectly compact topological edge states, as a concrete and promising example of synergy in between flat band physics and topology.