Topological robust corner states of a two-dimensional square lattice with C4 symmetry in fully coupled dipolar arrays

Abstract

A profound insight into topological photonic systems will empower us to harness their maximum potential and discover uncharted topological phenomena. For the square quadripartite lattice with only nearest-neighbor reciprocal couplings, in the out-of-plane mode, sublattice symmetry makes the eigenvalues of the Hamiltonian symmetric around zero energy, while C 4 symmetry closes the gap between the central bands. Meanwhile, topological corner states (CSs) are fixed at zero energy due to chiral symmetry. Thereby, the CSs cannot appear in a gap, but are embedded in the bulk. In this paper, the full coupling between dipoles is considered in the Hamiltonian, i.e., not only the near-field of nearest-neighbor, but also the far-field dipole-dipole interactions are taken into account to investigate the new potential topological properties. The results show that the sublattice symmetry of the system will be broken, leading to the appearance of a zero-energy band gap. Nevertheless, the generalized chiral symmetry ensures that the CSs are still pinned to zero energy. That is, in-gap CSs are provided. Additionally, the silicon carbide materials used in this paper can confine light to the deep subwavelength scale, which has great potential in enhancing light-matter interactions in the terahertz range.