Space group constraints on weak indices in topological insulators

Abstract

Lattice translation symmetry gives rise to a large class of "weak" topological insulators (TIs), characterized by translation-protected gapless surface states and dislocation bound states. In this work we show that space group symmetries lead to constraints on the weak topological indices that define these phases. In particular we show that screw rotation symmetry enforces the Hall conductivity along the screw axis to be quantized in multiples of the screw rank, which generally applies to interacting systems. We further show that certain 3D weak indices associated with quantum spin Hall effects (class AII) are forbidden by the Bravais-lattice and by glide or even-fold screw symmetries. These results put a strong constraints on candidates of weak TIs in the experimental and numerical search for topological materials, based on the crystal structure alone.

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• Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb
• Topological Insulators from Group Cohomology
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Interplay of non-symmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na${}_4$Ir${}_3$O${}_8$
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Crystalline finite-size topology
• Chern insulators in two and three dimensions: A global perspective
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems