论文标题
异常的浮雕高阶拓扑理论：分类，表征和散装对应关系
Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
论文作者
论文摘要
定期驱动的或浮雕系统可以实现在任何物质平衡状态中都不存在的异常拓扑现象，它们的分类和表征需要新的理论思想，这些思想超出了静态拓扑阶段的良好范围。在这项工作中，我们提供了一个通用框架，以了解异常的浮雕高级拓扑绝缘子（AFHOTIS），其分类仍然是一个具有挑战性的空缺问题。在两个维度（2D）中，这种Afhotis的定义是通过其坚固的对称性保护的角模式固定在特殊的准烯耐加工上，即使它们的所有浮雕频带都具有微不足道的乐队拓扑结构。发现AFHOTI的角模式物理学通常由生活在大量时间进化运算符相光谱中的3D Dirac/Weyl样拓扑奇异性表示。从物理上讲，这种相波段的奇异性本质上是拓扑量子临界的“足迹”，它将Afhoti与琐碎的绝热相关的静态相位到静态极限。引人注目的是，这些奇异性具有非常规性的分散关系，在3D中的任何静态晶格上都无法实现，但是，它们类似于4D拓扑结晶绝缘子的表面物理学。我们通过维数还原技术建立了上述高阶散装对应关系，该技术还允许对由点组对称保护的2D AFHOTI进行系统分类。我们演示了我们的理论应用于两个由$ C_2 $和$ D_4 $ symmetries保护的混凝土，实验可行的Afhotis模型。我们的作品为统一理论铺平了道路，用于分类和表征Floquet拓扑问题。
Periodically-driven or Floquet systems can realize anomalous topological phenomena that do not exist in any equilibrium states of matter, whose classification and characterization require new theoretical ideas that are beyond the well-established paradigm of static topological phases. In this work, we provide a general framework to understand anomalous Floquet higher-order topological insulators (AFHOTIs), the classification of which has remained a challenging open question. In two dimensions (2D), such AFHOTIs are defined by their robust, symmetry-protected corner modes pinned at special quasienergies, even though all their Floquet bands feature trivial band topology. The corner-mode physics of an AFHOTI is found to be generically indicated by 3D Dirac/Weyl-like topological singularities living in the phase spectrum of the bulk time-evolution operator. Physically, such a phase-band singularity is essentially a "footprint" of the topological quantum criticality, which separates an AFHOTI from a trivial phase adiabatically connected to a static limit. Strikingly, these singularities feature unconventional dispersion relations that cannot be achieved on any static lattice in 3D, which, nevertheless, resemble the surface physics of 4D topological crystalline insulators. We establish the above higher-order bulk-boundary correspondence through a dimensional reduction technique, which also allows for a systematic classification of 2D AFHOTIs protected by point group symmetries. We demonstrate applications of our theory to two concrete, experimentally feasible models of AFHOTIs protected by $C_2$ and $D_4$ symmetries, respectively. Our work paves the way for a unified theory for classifying and characterizing Floquet topological matters.
