Superconductors are topologically ordered

T. H. Hansson, Vadim Oganesyan, Shivaji Lal Sondhi

Research output: Contribution to journalArticlepeer-review

216 Scopus citations


We revisit a venerable question: what is the nature of the ordering in a superconductor? We find that the answer is properly that the superconducting state exhibits topological order in the sense of Wen, i.e., that while it lacks a local order parameter, it is sensitive to the global topology of the underlying manifold and exhibits an associated fractionalization of quantum numbers. We show that this perspective unifies a number of previous observations on superconductors and their low lying excitations and that this complex can be elegantly summarized in a purely topological action of the "BF" type and its elementary quantization. On manifolds with boundaries, the BF action correctly predicts non-chiral edge states, gapped in general, but crucial for fractionalization and establishing the ground state degeneracy. In all of this the role of the physical electromagnetic fields is central. We also observe that the BF action describes the topological order in several other physically distinct systems thus providing an example of topological universality.

Original languageEnglish (US)
Pages (from-to)497-538
Number of pages42
JournalAnnals of Physics
Issue number2
StatePublished - Oct 2004

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy


  • Fractional Hall effect
  • Gauge theories
  • Spin liquids
  • Superconductivity


Dive into the research topics of 'Superconductors are topologically ordered'. Together they form a unique fingerprint.

Cite this