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Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors
112:028 (Nordita South) ()
112:028 (Nordita South)
Fully gapped two-dimensional superconductors coupled to dynamical electromagnetism are known to exhibit topological order. Although for an s-wave paired state its topological properties can be well captured by the toric code model, I will demonstrate that in the presence of global symmetries this picture is incomplete. In this talk I will present a unified low-energy description for spin-singlet paired states by deriving topological Chern-Simons field theories for s-wave, d + id, and higher even-wave chiral superconductors. These theories encode the quantum statistics and fusion rules of Bogoliubov quasiparticles and vortices and incorporate global continuous symmetries - specifically, spin rotation and conservation of magnetic flux - present in all singlet superconductors, which firmly establishes superconductors as symmetry enriched topological phases. I will discuss Hall responses for these symmetries and the physics at the edge.