宽带强局域拓扑边界态的优化设计

Optimal Design of Topological Boundary States with Large Bandwidth and Intense Localization

为了解决产生光量子霍尔效应的模型存在的边界态局域较弱和带宽较窄问题,构建了三角复式晶格光子晶体,并利用简约布里渊区中心点的能带简并得到奇宇称的p轨道和偶宇称的d轨道。首先,通过晶胞缩放反转两个轨道的位置,使拓扑相位发生变化。然后,分析了影响拓扑平庸结构带隙和非平庸结构带隙的主要因素。最后,对两种结构的介质柱半径和缩放距离进行了优化计算,找到实现两种结构最大公共带隙的最优参数,可实现的最大相对带宽为24.59%。在最优结构参数的基础上构建边界结构并计算出边界态色散曲线,结果表明,该边界态在有效带宽为0.0435时具有较强的自旋方向锁定和边界电磁场局域效应。

To solve the problem of weak local boundary states and narrow bandwidth in the model that produces the photon quantum Hall effect,in this paper,a triangular compound lattice photonic crystal is constructed,and the energy band degeneracy of the reduced Brillouin zone is used to obtain the odd parity p orbital and the even-parity d orbital.First,the position of the two orbitals is reversed by the unit cell scaling to change the topological phase.Then,the main factors affecting the band gap of topologically trivial structure and non-trivial structure are analyzed.Finally,the radii and scaling distances of dielectric cylinders of the two structures are optimized.The optimal parameters for achieving the maximum common band gap of the two structures are obtained.The maximum achievable relative bandwidth is 24.59%.Based on the optimal structure parameters,the boundary structure is constructed,and the boundary states dispersion curve is calculated.The results showed that the boundary states have strong spin direction locking and boundary electromagnetic field local effects when the effective bandwidth is 0.0435.