归纳法和Smith分解在230空间群电子能带结构计算和拓扑分类中的应用
Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
摘要：
固体中的电子性质取决于表示布里渊区中电子态的波函数的具体形式。自拓扑绝缘体发现以来，对称性对电子能带结构的限制一直是人们关注的焦点。在这项工作中，我们采用两种不同的方法来表征所有类型的带在一个固体的对称性特征值的分析：归纳程序和史密斯分解方法。在给定的空间群中，任何电子能带的对称本征值或非代表可以表示为相对少量的建筑单元（\emph{basic}带）的本征值的叠加。所有空间群中的这些基本带都是从P1开始的群-子群链得到的。一旦知道了空间群中的基本带的全部集合，就可以很容易地导出所有其他类型的带（平凡的、强拓扑的或脆弱拓扑的）。特别是，我们证实了之前对所有空间群中脆弱根带的计算。此外，我们定义了一个自同构组的电子频带的等价物，它允许定义最小子集，例如，独立的基本或脆弱的根带。
英文摘要：
The electronic properties in a solid depend on the specific form of the wave-functions that represent the electronic states in the Brillouin zone. Since the discovery of topological insulators, much attention has been paid to the restrictions that the symmetry imposes on the electronic band structures. In this work we apply two different approaches to characterize all types of bands in a solid by the analysis of the symmetry eigenvalues: the induction procedure and the Smith Decomposition method. The symmetry eigenvalues or irreps of any electronic band in a given space group can be expressed as the superposition of the eigenvalues of a relatively small number of building units (the \emph{basic} bands). These basic bands in all the space groups are obtained following a group-subgroup chain starting from P1. Once the whole set of basic bands are known in a space group, all other types of bands (trivial, strong topological or fragile topological) can be easily derived. In particular, we confirm previous calculations of the fragile root bands in all the space groups. Furthermore, we define an automorphism group of equivalences of the electronic bands which allows to define minimum subsets of, for instance, independent basic or fragile root bands.
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