论文标题
双曲线晶格中的高阶拓扑绝缘子
Higher-order topological insulators in hyperbolic lattices
论文作者
论文摘要
为了探索高阶拓扑现象的非欧亚人概括，我们通过打破量子旋转厅绝缘子的时间反向对称性（TRS）来构建双曲线晶格中的高阶拓扑绝缘体模型。我们研究了三种双曲线晶格，即分别分别分别分别是双曲线$ \ {4,5 \} $，$ \ {8,3 \} $和$ \ {12,3 \} $ lattices。非欧酸核粉高阶拓扑行为的特征是零能量有效的角状态出现在双曲线晶格中。通过调整TRS断裂项的变化周期，我们分别在这三种不同的双曲线晶格中获得4、8和12零能量的有效角状态。发现双曲线晶格的零能量有效角状态的数量取决于TRS断裂项的变化周期。实时空间四极力矩用于表征具有四个零能量有效角状态的双曲线晶格的高阶拓扑。通过对称分析，可以证实双曲零能量有效的角状态受颗粒 - 孔对称$ p $的保护，有效的手性对称$ sm_ {z {z {z {z} $以及组合的对称性$ c_ {p} t $和$ c_ {p} m_ {z {z} $。除非这四个对称性同时损坏，否则双曲线零能量有效角状态保持稳定。在存在障碍存在下，双曲线零能量的稳健性，通过检查零能量模式的稳健性，进一步证实了双曲线零能量有效角状态的拓扑性质。我们的论文提供了一条研究非欧几里得几何系统中双曲线高阶拓扑绝缘子的途径。
To explore the non-Euclidean generalization of higher-order topological phenomena, we construct a higher-order topological insulator model in hyperbolic lattices by breaking the time-reversal symmetry (TRS) of quantum spin Hall insulators. We investigate three kinds of hyperbolic lattices, i.e., hyperbolic $\{4,5\}$, $\{8,3\}$ and $\{12,3\}$ lattices, respectively. The non-Euclidean higher-order topological behavior is characterized by zero-energy effective corner states appearing in hyperbolic lattices. By adjusting the variation period of the TRS breaking term, we obtain 4, 8 and 12 zero-energy effective corner states in these three different hyperbolic lattices, respectively. It is found that the number of zero-energy effective corner states of a hyperbolic lattice depends on the variation period of the TRS breaking term. The real-space quadrupole moment is employed to characterize the higher-order topology of the hyperbolic lattice with four zero-energy effective corner states. Via symmetry analysis, it is confirmed that the hyperbolic zero-energy effective corner states are protected by the particle-hole symmetry $P$, the effective chiral symmetry $Sm_{z}$, and combined symmetries $C_{p}T$ and $C_{p}m_{z}$. The hyperbolic zero-energy effective corner states remain stable unless these four symmetries are broken simultaneously. The topological nature of hyperbolic zero-energy effective corner states is further confirmed by checking the robustness of the zero-energy modes in the hyperbolic lattices in the presence of disorder. Our paper provides a route for research on hyperbolic higher-order topological insulators in non-Euclidean geometric systems.
