SciPost Phys. Core 8, 088 (2025) ·
published 28 November 2025
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We present a method for computing the classification groups of topological insulators and superconductors in the presence of $\mathbb{Z}_2^{× n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is characterized by four possible additional symmetry types for each generator of $\mathbb{Z}_2^{× n}$, 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 $\mathbb{Z}_2^{× 2}$ point group symmetry.
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