Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice

• Published in: arXiv.org
• Main Authors: Kim, Heejae, Murakami, Shuichi
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 14.11.2020
• Subjects: Brillouin zones; Crystal structure; Crystallinity; Invariants; Physics - Mesoscale and Nanoscale Physics; Physics - Strongly Correlated Electrons; Symmetry; Topology
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2006.03607

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.