Robustness of topological corner modes in photonic crystals

We analyze the robustness of corner modes in topological photonic crystals, taking a C-6-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry and Wilson loop calculations to demonstrate that the topological properties of the bulk crystal stem from an obstructed atomic limit phase. We then characterize the topological corner modes emerging within the gapped edge modes employing a semianalytical model, determining the appropriate real-space topological invariants. We provide a detailed account of the effect of long-range interactions on the topological modes in photonic crystals, and we quantify their robustness to perturbations. We conclude that, while photonic long-range interactions inevitably break chiral symmetry, the system is reducible to a chirally symmetric limit and the corner modes are protected by this together with lattice symmetries.