Ono Seishiro, Po Hoi Chun, Watanabe Haruki
Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan.
Department of Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
Sci Adv. 2020 May 1;6(18):eaaz8367. doi: 10.1126/sciadv.aaz8367. eCollection 2020 May.
Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the topological invariants with the behavior of the pairing order parameter on the normal-state Fermi surfaces. The existing formulas, however, become inadequate for the prediction of the recently proposed classes of topological crystalline superconductors. In this work, we advance the theory of symmetry indicators for topological (crystalline) superconductors to cover all space groups. Our main result is the exhaustive computation of the indicator groups for superconductors under a variety of symmetry settings. We further illustrate the power of this approach by analyzing fourfold symmetric superconductors with or without inversion symmetry and show that the indicators can diagnose topological superconductors with surface states of different dimensionalities or dictate gaplessness in the bulk excitation spectrum.
拓扑超导体是一类奇特的物质相，其具有稳健的表面态，可用于拓扑量子计算。寻找拓扑超导体的一个有用指导原则是将拓扑不变量与正常态费米面上配对序参量的行为联系起来。然而，现有的公式对于预测最近提出的几类拓扑晶体超导体已变得不够充分。在这项工作中，我们推进了拓扑（晶体）超导体的对称指标理论，以涵盖所有空间群。我们的主要结果是对各种对称设置下超导体的指标群进行了详尽计算。我们通过分析具有或不具有反演对称性的四重对称超导体进一步说明了这种方法的强大之处，并表明这些指标可以诊断具有不同维度表面态的拓扑超导体，或者确定体激发谱中的无隙性。
