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 C6v symmetry to C3v,C3,C2v and even C2 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.%拓扑绝缘体是当前凝聚态物理领域研究的热点问题.利用石墨烯材料的特殊能带特性来实现拓扑输运特性在设计下一代电子和能谷电子器件方面具有较广泛的应用前景.基于光子与电子的类比,利用光子拓扑材料实现了确定性界面态;构建了具有C6v对称性的类似石墨烯结构的的光子晶体复杂晶格;通过多种方式降低晶格对称性来获得具有C3v,C3,C2v和C2对称的晶体,从而打破能谷简并实现全光子带隙结构;将体拓扑性质不同的两种光子晶体摆放在一起,在此具有反转体能带性质的界面上,实现了具有单向传输特性的拓扑确定性界面态的传输.利用光子晶体结构的容易加工性,可以简便地调控拓扑界面态控制光的传播,可为未来光拓扑绝缘体的研究提供良好的平台.
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