Symmetry-based indicators of band topology in the 230 space groups.,Nature Communications

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Symmetry-based indicators of band topology in the 230 space groups.
Nature Communications ( IF 14.7 ) Pub Date : 2017-06-30 , DOI: 10.1038/s41467-017-00133-2
Hoi Chun Po _{1,

2} , Ashvin Vishwanath _{1,

2} , Haruki Watanabe ₃

Affiliation

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for inversion-symmetric topological insulators, demonstrate that symmetry labels can sometimes unambiguously indicate underlying band topology. Here we develop a systematic approach to expose all such symmetry-based indicators of band topology in all the 230 space groups. This is achieved by first developing an efficient way to represent band structures in terms of elementary basis states, and then isolating the topological ones by removing the subset of atomic insulators, defined by the existence of localized symmetric Wannier functions. Aside from encompassing all earlier results on such indicators, including in particular the notion of filling-enforced quantum band insulators, our theory identifies symmetry settings with previously hidden forms of band topology, and can be applied to the search for topological materials.Understanding the role of topology in determining electronic structure can lead to the discovery, or appreciation, of materials with exotic properties such as protected surface states. Here, the authors present a framework for identifying topologically distinct band-structures for all 3D space groups.

中文翻译：

230 个空间群中基于对称性的能带拓扑指标。

对称性和拓扑之间的相互作用导致了丰富多样的电子拓扑相，保护状态，例如拓扑绝缘体和狄拉克半金属。先前的结果，例如反演对称拓扑绝缘体的 Fu-Kane 奇偶校验准则，表明对称标签有时可以明确地指示基础能带拓扑。在这里，我们开发了一种系统方法来揭示所有 230 个空间群中所有此类基于对称性的能带拓扑指标。这是通过首先开发一种有效的方法来用基本基态表示能带结构，然后通过删除原子绝缘体子集（由局部对称 Wannier 函数的存在定义）来隔离拓扑结构来实现的。除了涵盖这些指标的所有早期结果（特别包括填充强制量子带绝缘体的概念）之外，我们的理论还利用先前隐藏的能带拓扑形式识别了对称设置，并且可以应用于拓扑材料的搜索。确定电子结构中的拓扑结构可以导致发现或欣赏具有奇异特性（例如受保护的表面态）的材料。在这里，作者提出了一个框架，用于识别所有 3D 空间群的拓扑不同的能带结构。

更新日期：2017-07-01

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