Elcoro Luis, Wieder Benjamin J, Song Zhida, Xu Yuanfeng, Bradlyn Barry, Bernevig B Andrei
Department of Condensed Matter Physics, University of the Basque Country UPV/EHU, Bilbao, Spain.
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA.
Nat Commun. 2021 Oct 13;12(1):5965. doi: 10.1038/s41467-021-26241-8.
For over 100 years, the group-theoretic characterization of crystalline solids has provided the foundational language for diverse problems in physics and chemistry. However, the group theory of crystals with commensurate magnetic order has remained incomplete for the past 70 years, due to the complicated symmetries of magnetic crystals. In this work, we complete the 100-year-old problem of crystalline group theory by deriving the small corepresentations, momentum stars, compatibility relations, and magnetic elementary band corepresentations of the 1,421 magnetic space groups (MSGs), which we have made freely accessible through tools on the Bilbao Crystallographic Server. We extend Topological Quantum Chemistry to the MSGs to form a complete, real-space theory of band topology in magnetic and nonmagnetic crystalline solids - Magnetic Topological Quantum Chemistry (MTQC). Using MTQC, we derive the complete set of symmetry-based indicators of electronic band topology, for which we identify symmetry-respecting bulk and anomalous surface and hinge states.
100多年来，晶体固体的群论表征为物理和化学中的各种问题提供了基础语言。然而，由于磁性晶体的对称性复杂，在过去70年里，具有相称磁序的晶体群论仍不完整。在这项工作中，我们通过推导1421个磁性空间群（MSG）的小共表示、动量星、相容性关系和磁性基本带共表示，完成了晶体群论这个有100年历史的问题，我们已通过毕尔巴鄂晶体学服务器上的工具将这些内容免费提供。我们将拓扑量子化学扩展到磁性空间群，以形成磁性和非磁性晶体固体中能带拓扑的完整实空间理论——磁性拓扑量子化学（MTQC）。使用MTQC，我们推导出了基于对称性的电子能带拓扑指标的完整集合，据此我们确定了尊重对称性的体相以及反常表面和铰链态。
