Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors

Abstract

Fully gapped two-dimensional superconductors coupled to dynamical electromagnetism are known to exhibit topological order. In this work, we develop a unified low-energy description for spin-singlet paired states by deriving topological Chern-Simons field theories for $s$-wave, $d+id$, and chiral higher even-wave superconductors. These theories capture 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. For all such systems, we compute the Hall response for these symmetries and investigate the physics at the edge. In particular, the weakly-coupled phase of a chiral $d+id$ chiral state has a spin Hall coefficient ${\nu }_s=2$ and a vanishing Hall response for the magnetic flux symmetry. We argue that the latter is a generic result for two-dimensional superconductors with gapped photons, thereby demonstrating the absence of a spontaneous magnetic field in the ground state of chiral superconductors. It is also shown that the Chern-Simons theories of chiral spin-singlet superconductors derived here fall into Kitaev's 16-fold classification of topological superconductors.

15 pages, 6 figures, published version

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Resonantly-paired fermionic superfluids
• Chiral Superconductors
• Chiral $d$-wave Superconductivity in SrPtAs
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Superconductivity in the Honeycomb-Lattice Pnictide SrPtAs
• Bulk-Edge Correspondence in 2+1-Dimensional Abelian Topological Phases
• Orbital Angular Momentum and Spectral Flow in Two Dimensional Chiral Superfluids
• Bridging Fermionic and Bosonic Short Range Entangled States
• Orbital momentum of chiral superfluids and spectral asymmetry of edge states
• Effective theory of vortices in two-dimensional spinless chiral $p$-wave superfluids
• Effective Field Theory for a p-wave Superconductor in the Subgap Regime

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• Proposed Spontaneous Generation of Magnetic Fields by Curved Layers of a Chiral Superconductor
• Anyon Superconductivity from Topological Criticality in a Hofstadter-Hubbard Model
• Non-diagonal anisotropic quantum Hall states
• Nonlocal effects of low-energy excitations in quantum-spin-liquid candidate Cu${}_3$Zn(OH)${}_6$FBr
• Screening and Topological Order in Thin Superconducting Films
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• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Rotational Symmetry Protected Edge and Corner States in Abelian topological phases
• Origin of Topological Order in a Cooper Pair Insulator
• Kondo enabled transmutation between spinons and superconducting vortices: origin of magnetic memory in 4Hb-$\mathrm{Ta}{\mathrm{S}}_2$
• Topological states in strongly correlated systems
• Electronic States and Anomalous Hall Effect in Strongly Correlated Topological Systems
• A Two-Gauge Field Model for Magnetoelectric Boundaries