论文标题
晶体的十倍拓扑：晶体拓扑绝缘子和超导体的统一分类
Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
论文作者
论文摘要
著名的Altland-Zirnbauer对称性类别的十倍，它通过其非空间对称性模式来辨别任何量子系统。它位于拓扑绝缘子和超导体的周期表的核心，该表提供了所有对称类别的弱相互交互电子的非晶体拓扑阶段的完整分类。近年来，在晶体材料中发现了许多具有不同表面状态的拓扑现象。在本文中，我们获得了拓扑不同的地面以及具有晶体拓扑绝缘子的异常表面状态的详尽分类，以及用于关键空间组，层组和杆组的超导体。这是针对阿尔特兰 - 齐尔鲍尔非空间对称性类的整个十倍的统一方式完成的。我们建立了一个利用现代数学框架的全面范式；它使我们能够获得适用于通用拓扑分类问题的结果。特别是，该范式提供了有效的计算工具，可实现对整个十倍的固有统一处理。
The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any quantum system by its pattern of non-spatial symmetries. It lays at the core of the periodic table of topological insulators and superconductors which provided a complete classification of weakly-interacting electrons' non-crystalline topological phases for all symmetry classes. Over recent years, a plethora of topological phenomena with diverse surface states has been discovered in crystalline materials. In this paper, we obtain an exhaustive classification of topologically distinct groundstates as well as topological phases with anomalous surface states of crystalline topological insulators and superconductors for key space-groups, layer-groups, and rod-groups. This is done in a unified manner for the full tenfold-way of Altland-Zirnbauer non-spatial symmetry classes. We establish a comprehensive paradigm that harnesses the modern mathematical framework of equivariant spectra; it allows us to obtain results applicable to generic topological classification problems. In particular, this paradigm provides efficient computational tools that enable an inherently unified treatment of the full tenfold-way.
