Design of pure and hybrid corner states in all-dielectric second-order photonic topological insulators

The groundbreaking discovery of high-order topological insulators has opened the avenues for exploring complex topological states, especially the corner states. Typically, corner states undergo hybridization because of point-group symmetry, leading to degeneracy that has yet to be thoroughly investigated in the realm of higher-order topological states. In this study, we introduce a straightforward yet effective photonic crystal design that facilitates the realization of robust photonic corner states and their intricate hybridization. We reveal that, in addition to the conventional point-group symmetry, the local sublattice symmetry also plays a pivotal role in protecting the corner states. By strategically disrupting the sublattice symmetry, we introduce a tunable mechanism for controlling the hybridization of corner states within our proposed photonic structure. This research sheds light on the symmetrical protection mechanisms of topological corner states in photonic crystals, paving the way for innovative designs of photonic devices leveraging the unique properties of zero-dimensional corner states.