二维介电光子晶体中的赝自旋态与拓扑相变

基于背散射抑制且对缺陷免疫的传输性质,光子拓扑绝缘体为电磁传输调控提供了一种新颖的思路.类比电子体系中的量子自旋霍尔效应,本文设计出一种简单的二维介电光子晶体,以实现自旋依赖的光子拓扑边界态.该光子晶体是正三角环形硅柱子在空气中排列而成的蜂窝结构.将硅柱子绕各自中心旋转60°,可实现二重简并的偶极子态和四极子态之间的能带翻转.这两对二重简并态的平均能流密度围绕原胞中心的手性可充当赝自旋自由度,其点群对称性可用来构建赝时间反演对称.根据k·p微扰理论,给出了布里渊区中心附近的有效哈密顿量以及对应的自旋陈数,由此证实能带翻转的实质是拓扑相变.数值计算结果揭示,在拓扑非平庸和平庸的光子晶体分界面上可实现单向传输且对弯曲、空穴等缺陷免疫的拓扑边界态.本文中的光子晶体只由电介质材料组成并且晶格结构简单,实现拓扑相变时无需改变柱子的填充率或位置,只需转动一个角度.因此,这种结构在拓扑边界态的应用中更为有效.

Pseudospin states and topological phase transitions in twodimensional photonic crystals made of dielectric materials

Based on the transmission properties of against backscattering and robustness against defects, photonic topological insulators have opened up a novel way to steer the propagation of electromagnetic wave. In order to construct the photonic analogs of the quantum spin Hall effect in an electronic system, we propose a simple two-dimensional photonic crystal made of dielectric materials to realize topologically protected edge states associated with the photonic pseudospin. The photonic crystal comprises a honeycomb array of equilateraltriangle-ring-shaped silicon rods embedded in an air host. By simply rotating the silicon rods around their respective centers by 60°, the band inversion between a twofold degenerated dipolar mode and a twofold degenerated quadrupolar mode is clearly observed in the Brillouin zone center. For the double twofold degenerated states, the chirality of the time-averaged Poynting vector surrounding the unit cell center(i.e.,right-hand or left-hand circular polarizations) plays the role of the pseudospin degree of freedom in the present photonic system, and their point group symmetry can be utilized to construct a pseudo-time-reversal symmetry.perturbation theory, we develop an effective Hamiltonian for the associated dispersion relation around the Brillouin zone center and calculate the spin Chen number, which indicates that the band inversion leads to a topological phase transition from a trivial to a nontrivial state. With numerical simulations, we unambiguously demonstrate that the unidirectional propagation of pseudospin-dependent edge state along the interface between a topologically nontrivial photonic crystal and a trivial one, and robustness of the edge states against different defects including sharp bend and cavity, regardless of the type of interface. The photonic system proposed by us consists of dielectric materials and the corresponding lattice structure is simple. And without changing the fill ratio or changing the positions of the silicon rods, a simple rotation of the silicon rods can generate the topological phase transition. So the potential applications of the pseudospin-dependent edge states based on our design are expected in more efficient way.