Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice

Abstract

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.

arXiv comment21 pages, 4 figures

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Cited by in corpus (8)

• Topological classification and diagnosis in magnetically ordered electronic materials
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• Anomalous Crystal Shapes of Topological Crystalline Insulators
• $Z_2$ Dirac points with topologically protected multihelicoid surface states
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Generalization of the Nested Wilson Loop Formalism in Topological Dirac Semimetals with Higher-order Fermi Arcs
• Parallel and anti-parallel helical surface states for topological semimetals
• Theoretical analysis of glide-Z_2 magnetic topological photonic crystals