Multiband topological states in the Penrose-triangle photonic crystals.

The topological edge state (TES) and topological corner state (TCS) in photonic crystals (PCs) provide effective ways to manipulate the propagation of light. To improve the performance and integration of topological photonic devices, the realization of multiband topological states by PCs combined with quasi-periodic structure needs to be urgently explored. In this Letter, a Penrose-triangle (P-T) PC, which arranges the basic structural unit of a 12-fold Penrose-type photonic quasi-crystal (PQC) in a triangular lattice, is proposed. The TES and TCS at low- and high-frequency bands can be generated in the same structure, accompanied by the realization of three groups of TCSs. This will provide a new structure for the generation of TESs and TCSs in PCs, and will provide a new way to improve the performance and integration of topological photonic devices.