论文标题
多个高阶拓扑阶段，具有均匀和奇数对的零能量角模式
Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a $C_3$ symmetry broken model
论文作者
论文摘要
最近设计了$ C_3 $对称性破碎的蜂窝状晶格的量子异常霍尔绝缘子的高阶角模式。在这里，我们考虑存在反转对称性破坏亚晶状体质量的扩展haldane模型，时间反转对称性破坏Zeeman场和自旋轨道耦合相互作用，在这里我们发现只有量子旋转霍尔绝缘子才能托管二极点二极化相，而其余两个一阶式拓扑酶则不属于Latter latter latter latter。值得注意的是，当已经存在旋转轨道耦合时，零能量偶极状态的四倍变性可以将零能量偶极状态的二极化态变为两倍（撤回）。另一方面，在不存在或存在自旋轨道耦合的情况下，亚晶格质量和Zeeman场项相互竞争，以零能量固定在零能量的情况下。有趣的是，只要保留反转对称性，大量极化就可以从拓扑表征偶极相表征偶极相。有效的差距标准可以定性地模仿SOT相的程度，该阶段的程度是有限的Zeeman交换场，亚物质质量和SOC相互作用之间的相互作用。
The higher-order corner modes for quantum anomalous Hall insulators in $C_3$ symmetry broken honeycomb lattice have been engineered recently. Here we consider an extended Haldane model in presence of inversion symmetry breaking sub-lattice mass, time-reversal symmetry breaking Zeeman field and spin-orbit coupling interaction where we find that only the quantum spin Hall insulator can host the second-order dipolar phase while the remaining two first-order topological phases do not morph into the latter. Remarkably, four-fold degeneracy of zero-energy dipolar states can be reduced to two-fold under the application (withdrawn) of sub-lattice mass (Zeeman field) term when the spin-orbit coupling is already present. On the other hand, the sub-lattice mass and Zeeman field terms compete with each other to pin down the two mid-gap states at zero-energy in the absence or presence of spin-orbit coupling. Interestingly, the bulk-polarization can topologically characterize the dipolar phase irrespective of the energy of the mid-gap states as long as inversion symmetry is preserved. The effective gap criterion can qualitatively mimic the extent of SOT phase originated by the interplay between finite Zeeman exchange field, sub-lattice mass, and SOC interaction.
