Topological Properties of a Two-Dimensional Photonic Square Lattice without C4 and Mx(y) Symmetries

Rich topological phenomena, edge states, and two types of corner states are unveiled in a two-dimensional square-lattice all-dielectric photonic crystal without both C4 and Mx(y) symmetries. Specifically, nontrivial type-I corner states, which do not exist in systems with C4 and Mx(y) since the degeneracy, are protected by a nonzero quadrupole moment, no longer quantized to but less than 0.5. Excellent properties, for example, subwavelength localization and air-concentrated field distribution, are presented. Type-II corner states, induced by long-range interactions, are easier to be realized due to asymmetry. This work broadens the topological physics for the symmetries-broken systems and provides potential applications.