Space group constraints on weak indices in topological insulators

TL;DR

This paper investigates how space group symmetries impose constraints on weak topological insulators, affecting their surface states and quantized conductivities, thereby guiding the search for topological materials.

Contribution

It reveals new symmetry-based constraints on weak topological indices, including quantization conditions and forbidden phases, extending understanding of topological phases in crystalline materials.

Findings

Screw rotation symmetry enforces Hall conductivity quantization along the screw axis.

Certain weak indices related to quantum spin Hall effects are forbidden by specific space group symmetries.

Results restrict the possible weak topological insulator phases based on crystal symmetry considerations.

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.