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Topological order, symmetry, and Hall response of two-dimensional spin-singlet superconductors
University Colorado, USA ;Technical University of Munich, DEU ; University Calif Santa Barbara, USA.ORCID iD: 0000-0002-4615-2507
University Colorado, USA.
University Colorado, USA.
University Colorado, USA ; Calif Santa Barbara, USA.
2017 (English)In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 1, article id 014508Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
American Physical Society, 2017. Vol. 95, no 1, article id 014508
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-87170DOI: 10.1103/PhysRevB.95.014508ISI: 000391850800002OAI: oai:DiVA.org:kau-87170DiVA, id: diva2:1613017
Available from: 2021-11-20 Created: 2021-11-20 Last updated: 2023-06-20Bibliographically approved

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Moroz, Sergej

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