Classification of topological insulators and superconductors with multiple order-two point group symmetries

Abstract

We present a method for computing the classification groups of topological insulators and superconductors in the presence of ${\mathbb{Z}}_2^{\times n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is characterized by four possible additional symmetry types for each generator of ${\mathbb{Z}}_2^{\times n}$, together with bit values encoding whether pairs of generators commute or anticommute. We show that the classification is fully determined by the number of momentum- and real-space variables flipped by each generator, as well as the number of variables simultaneously flipped by any pair of generators. As a concrete illustration, we provide the complete classification table for the case of ${\mathbb{Z}}_2^{\times 2}$ point group symmetry.

v2: Corrected errors in Eqs. (8, 9, 16, 23, 25, 42, 43) and Table 6

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