Braiding statistics and classification of two-dimensional charge-$2m$ superconductors

Abstract

We study braiding statistics between quasiparticles and vortices in two-dimensional charge-$2m$ (in units of $e$) superconductors that are coupled to a ${\mathbb{Z}}_{2m}$ dynamical gauge field, where $m$ is any positive integer. We show that there exist $16m$ types of braiding statistics when $m$ is odd, but only $4m$ types when $m$ is even. Based on the braiding statistics, we obtain a classification of topological phases of charge-$2m$ superconductors---or formally speaking, a classification of symmetry-protected topological phases, as well as invertible topological phases, of two-dimensional gapped fermions with ${\mathbb{Z}}_{2m}^f$ symmetry. Interestingly, we find that there is no nontrivial fermionic symmetry-protected topological phase with ${\mathbb{Z}}_4^f$ symmetry.

11 pages, 1 figure, 1 table. rewritten introduction. published version

References in corpus (3)

• Classification of topological insulators and superconductors in three spatial dimensions
• Charge $4e$ superconductivity from pair density wave order in certain high temperature superconductors
• Topological invariants for gauge theories and symmetry-protected topological phases

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