Corner States in 2D Square Lattice Second‐Order Photonic Topological Insulators Composed of L‐Shaped Sublattices

Abstract

Higher‐order photonic topological states have recently attracted great attention due to the realizability of photonic nanocavities with high robustness against structural disorder. Herein, it is revealed that square‐lattice photonic crystals with L‐shaped sublattices exhibit second‐order photonic topological phases. In the approximation considering only the nearest‐neighbor interactions, the photonic system with an expanded sublattice exhibits topologically nontrivial phase represented by the nonzero polarization, approaching in the extreme case, whereas it is trivial for the cases of the shrunken one. Unlike the conventional square lattices with four dielectric rods, the proposed photonic systems have a single corner state for squared topological boundaries, while they exhibit three corner states when they have triangular boundaries. Although the weakly anisotropic systems with the expanded L‐shaped sublattices exhibit different corner states, they disappear for a substantial increase of anisotropy. The results obtained in this work enrich the diversity and understanding of higher‐order photonic topological systems and pave the way for wide applications of higher‐order topological phases in photonics, including coherent nanosources based on nanolasing and nonlinear frequency conversion.