拓扑量子化学中的能带连接性：作为图论问题的能带结构
Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
摘要：
传统的固体理论非常适合于描述动量空间中孤立点附近的局部能带结构，但很难捕捉到理解拓扑现象所必需的完整的全局图像。在最近的一篇论文[B。Bradlyn等人，Nature 547，298（2017）]，我们已经介绍了克服这一困难的方法，即根据图论将跨越布里渊区的许多断开的局部“k-dot-p”能带结构缝合在一起的问题公式化。在目前的手稿中，我们给出了我们完整的理论结构的细节。我们表明，晶体对称性强烈约束允许的能带的连通性，我们采用图论技术，如图形连接枚举这些约束的所有解决方案。图论的工具使我们能够在这些溶液中识别不连通的能带群，从而识别拓扑上不同的绝缘相。
英文摘要：
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a recent paper [B. Bradlyn et al., Nature 547, 298 (2017)], we have introduced the way to overcome this difficulty by formulating the problem of sewing together many disconnected local "k-dot-p" band structures across the Brillouin zone in terms of graph theory. In the current manuscript we give the details of our full theoretical construction. We show that crystal symmetries strongly constrain the allowed connectivities of energy bands, and we employ graph-theoretic techniques such as graph connectivity to enumerate all the solutions to these constraints. The tools of graph theory allow us to identify disconnected groups of bands in these solutions, and so identify topologically distinct insulating phases.
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