非本原晶格中的滑移对称拓扑晶体绝缘体相
Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice
摘要：
我们研究了由滑移对称性保护的拓扑晶体绝缘体相，该滑移对称性由Z2拓扑数表征。本文从本原格中的Z2拓扑不变量出发，导出了非本原格中由滑移对称性保护的Z2拓扑不变量的一个公式。通过将Brillouin区折叠到基心晶格的Brillouin区中，建立了基心晶格中具有滑移对称性的空间群No.9的滑移-Z2不变量公式。该公式是写在k空间中的Berry曲率和Berry相位的积分。当空间群为No.15时，我们还导出了一个滑移-Z ~ 2不变量的公式。这将公式简化为Fu-Kane式，用$k$空间中高对称点的不可约表示来表示。我们还构造了这些拓扑不变量的层构造方法，并从k-空间方法的结果完全一致。
英文摘要：
We study the topological crystalline insulator phase protected by the glide symmetry, which is characterized by the Z2 topological number. In the present paper, we derive a formula for the Z2 topological invariant protected by glide symmetry in a nonprimitive lattice, from that in a primitive lattice. We establish a formula for the glide-Z2 invariant for the space group No. 9 with glide symmetry in the base-centered lattice, by folding the Brillouin zone into that of the primitive lattice where the formula for the glide-Z2 invariant is known. The formula is written in terms of integrals of the Berry curvatures and Berry phases in the k-space. We also derive a formula of the glide-Z2 invariantwhen the inversion symmetry is added, and the space group becomes No. 15. This reduces the formula into the Fu-Kane-like formula, expressed in terms of the irreducible representations at high-symmetry points in $k$ space. We also construct these topological invariants by the layer-construction approach, and the results completely agree with those from the k-space approach.
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