▎ 摘　　要

Topological insulators have aroused much research interest in condensed matter physics in recent years. Topological protected edge states can propagate unidirectionally and backscattering free along the boundaries of the topological insulators' which will be important for future electronic devices for its immunity to defects. Topology is dependent only on the symmetry of lattice of the system rather than its specific wave form. Thus, based on the analogy between electronics and photons, photonic topological insulator has also been demonstrated both theoretically and experimentally. Graphene, composed of a monolayer of carbon atoms in honeycomb lattice, exhibits unusual properties due to its intriguing band diagram. Many types of graphene allotropes have been proposed theoretically. However, due to fabrication difficulties, most of graphene allotropes are unavailable. Here, we propose to study two dimensional (2D) photonic crystal (PC) with complex lattices, similar to that of graphene allotrope. The complex PC structure provides more degrees of freedom in manipulating its symmetry. Interface states can also exist in the interface region between two PCs, if they have different topological properties. Without any surface decoration, deterministic interface states can be created when bulk photonic band inversion can be induced and are demonstrated theoretically and experimentally in 2D PCs with square lattice. By controlling the parameters of PCs, their bulk photonic band properties are engineered and topological phase transition occurs. By inverting the bulk photonic band properties, interface states exist in the common band gaps for two PC systems in the gapped region. Similarly, we proceed to complex honeycomb lattice of PCs. By lowering its original C-6 v symmetry to C-3 v, C-3, C-2 v and even C-2 symmetry, the degeneracies of valley Dirac dispersion at the corners of Brillouin zone are lifted. Photonic band inversion occurs in all four symmetries and the deterministic interface states are numerically realized in the interface region between two PCs. Unidirectional propagation of interface state immune to backscattering along the interface channels is demonstrated if a source with proper optical vortex index is utilized. Due to its easy fabrication, PC is a perfect platform to explore the topological properties of complex lattice and these acquired topological optical states can be of benefit to the control the propagation of light in the photonic waveguide.