论文标题
在230个空间组的电子带结构的计算和拓扑分类中，诱导程序和史密斯分解的应用
Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
论文作者
论文摘要
实体中的电子特性取决于代表布里鲁因地区电子状态的波函数的特定形式。自从发现拓扑绝缘子以来，对对称性对电子带结构施加的限制引起了很多关注。在这项工作中，我们采用两种不同的方法来通过分析对称特征值的分析来表征固体中所有类型的频段：诱导程序和史密斯分解方法。给定空间群中任何电子带的对称特征值或无元素可以表示为相对较少数量的建筑单元（\ emph {basic}频段）的特征值的叠加。所有空间组中的这些基本频段均在从P1开始的组 - 组链链中获得。一旦整个基本频带在空间群中都知道，所有其他类型的频段（琐碎，强拓扑或易碎拓扑）都可以很容易地得出。特别是，我们确认所有空间组中脆弱的根条带的先前计算。此外，我们定义了电子带的等价自动形态组，该组允许定义，例如独立的基本或脆弱的根条带的最小子集。
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.
