次维度拓扑、指示符和高阶相位
Subdimensional topologies, indicators and higher order phases
摘要：
拓扑能带结构的研究在过去的十年中引发了突出的研究兴趣，最终在最近制定的相当多产的分类方案，封装了很大一部分的阶段和功能。在这方面，我们最近报道了一类未探索的拓扑结构，蓬勃发展的概念{ \it子维拓扑}。虽然这样的相位在完整的布里渊区上进行评估时具有平凡的指标和频带表示，但它们在子维空间（例如平面或线）内具有稳定或脆弱的拓扑结构。这种观点不仅细化分类追求，但可以导致在全维意义上的可观察的特征。例如，在三个空间维度（3D）中，子维度拓扑可以由具有一般拓扑不变量的非平凡平面来表征，这些平面由远离这些平面的Weyl节点来补偿。因此，这些相具有三维稳定的特征，如Weyl节点，费米弧和边缘状态，可以通过子维分析系统地预测。在本工作中，我们进一步阐述了这些概念。我们提出了改进的表示计数方案，并解决独特的体积边界效应，包括动量依赖（高阶）的边缘状态，有一个签名依赖于垂直动量。因此，我们希望这些见解可以刺激新的活动，以进一步加深对这些未探索阶段的理解。
英文摘要：
The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features. Within this context we recently reported on a class of unexplored topological structures that thrive on the concept of {\it sub-dimensional topology}. Although such phases have trivial indicators and band representations when evaluated over the complete Brillouin zone, they have stable or fragile topologies within sub-dimensional spaces, such as planes or lines. This perspective does not just refine classification pursuits, but can result in observable features in the full dimensional sense. In three spatial dimensions (3D), for example, sub-dimensional topologies can be characterized by non-trivial planes, having general topological invariants, that are compensated by Weyl nodes away from these planes. As a result, such phases have 3D stable characteristics such as Weyl nodes, Fermi arcs and edge states that can be systematically predicted by sub-dimensional analysis. Within this work we further elaborate on these concepts. We present refined representation counting schemes and address distinctive bulk-boundary effects, that include momentum depended (higher order) edge states that have a signature dependence on the perpendicular momentum. As such, we hope that these insights might spur on new activities to further deepen the understanding of these unexplored phases.
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