具有反常Floquet高阶拓扑的超导体
Superconductors with anomalous Floquet higher-order topology
摘要：
我们开发了一个二维（2D）反常Floquet高阶拓扑超导体（AFHOTSC），这是动态的马约拉纳携带相位的物质，没有静态对应的一般理论。尽管它的散装Floquet带的平凡，AFHOTSC一般功能的同时存在的角落本地化马约拉纳模式在零和$π/T$准能量，超出任何静态拓扑能带理论的范围内的现象。我们表明，AFHOTSC的关键是它不可避免的奇异行为的相位谱的散装时间演化算子。通过将这种演化相位奇异性映射到频闪边界签名，我们将所有受对称类D中的旋转群对称性保护的2D AFHOTSC分类。我们进一步提取了一个高阶拓扑指数，明确预测Floquet角Majorana模式的存在下，我们确认数值。我们的理论是Floquet超导系统动力学拓扑理论的一个里程碑。
英文摘要：
We develop a general theory for two-dimensional (2D) anomalous Floquet higher-order topological superconductors (AFHOTSC), which are dynamical Majorana-carrying phases of matter with no static counterpart. Despite the triviality of its bulk Floquet bands, an AFHOTSC generically features the simultaneous presence of corner-localized Majorana modes at both zero and $π/T$ quasi-energies, a phenomenon beyond the scope of any static topological band theory. We show that the key to AFHOTSC is its unavoidable singular behavior in the phase spectrum of the bulk time-evolution operator. By mapping such evolution-phase singularities to the stroboscopic boundary signatures, we classify all 2D AFHOTSCs that are protected by a rotation group symmetry in symmetry class D. We further extract a higher-order topological index for unambiguously predicting the presence of Floquet corner Majorana modes, which we confirm numerically. Our theory serves as a milestone towards a dynamical topological theory for Floquet superconducting systems.
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