Realization of hierarchical topological transitions and high-Q-response corner states in second-order topological photonic crystals

Topological photonic crystals (PCs) provide a convenient method of electromagnetic wave processing. Recently, higher-order photonic topological insulators have been investigated as an intriguing topological phase beyond the usual bulk-edge correspondence. Previous studies of corner states in higher-order topological insulators mainly focus on topological multipole systems realized by introducing a negative coupling between constituent units or based on the two-dimensional Su-Schrieffer-Heeger model. In this work, we study a second-order topological insulator of square lattice that can host one-dimensional edge states and zero-dimensional corner states by means of breaking the symmetry of the structure. A corner mode with a high quality factor over 22 000 is formed by combining two types of such PCs with different topological phases. The significant topological phase transitions in the bulk and at the edges can be realized by simply changing the diameter of the constituent cylinders. Our results provide a topological way to guide and trap electromagnetic waves.