论文标题
具有嵌套带反演表面的高阶拓扑阶段的拓扑分类
Topological classification of Higher-order topological phases with nested band inversion surfaces
论文作者
论文摘要
高阶拓扑阶段（HOTP）保持着宽大的散装带和拓扑边界状态，该状态位于边界，编成较高的边界高于一个。在本文中，我们基于一种称为嵌套带反转表面（BISS）的方法，为完整的Altland-Zirnbauer十倍对称类别提供热热的统一结构和拓扑表征。具体而言，基于此方法构建的HOTP被分解为一系列子系统，高阶拓扑边界状态来自其一阶拓扑的相互作用。我们的分析始于每个对称类别中连续哈密顿量的热门人士的一般讨论，然后转到几个晶格示例，这些晶格示例说明了基于嵌套双轴法的拓扑表征。尽管有一个最小的模型具有多个空间对称性，但我们的方法不依赖于任何空间对称性，并且可以轻松地将其扩展为任意拓扑阶的拓扑阶。此外，我们将讨论扩展到具有两种不同机制引起的不对称边界状态的系统，即打破$ \ MATHCAL {C} _4 $旋转对称性的交叉BISS，以及破坏了某些Chiral Mirror Mirror Symmeties Minimal Models的旋转对称者。
Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this paper, we provide a unified construction and topological characterization of HOTPs for the full Altland-Zirnbauer tenfold symmetry classes, based on a method known as nested band inversion surfaces (BISs). Specifically, HOTPs built on this method are decomposed into a series of subsystems, and higher-order topological boundary states emerges from the interplay of their first-order topology. Our analysis begins with a general discussion of HOTPs in continuous Hamiltonians for each symmetry class, then moves on to several lattice examples illustrating the topological characterization based on the nested-BIS method. Despite the example minimal models possessing several spatial symmetries, our method does not rely on any spatial symmetry, and can be easily extended into arbitrary orders of topology in dimensions. Furthermore, we extend our discussion to systems with asymmetric boundary states induced by two different mechanisms, namely, crossed BISs that break a $\mathcal{C}_4$ rotation symmetry, and non-Clifford operators that break certain chiral-mirror symmetries of the minimal models.
