Superconductivity and Abelian chiral anomalies

Y. Hatsugai, S. Ryu, M. Kohmoto

Research output: Contribution to journalArticlepeer-review


Motivated by the geometric character of spin Hall conductance, the topological invariants of generic superconductivity are discussed based on the Bogoliuvov-de Gennes equation on lattices. They are given by the Chern numbers of degenerate condensate bands for unitary order, which are realizations of Abelian chiral anomalies for non-Abelian connections. The three types of Chern numbers for the x, y, and z directions are given by covering degrees of some doubled surfaces around the Dirac monopoles. For nonunitary states, several topological invariants are defined by analyzing the so-called q helicity. Topological origins of the nodal structures of superconducting gaps are also discussed.

Original languageEnglish (US)
Article number054502
Pages (from-to)054502-1-054502-9
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number5
StatePublished - Aug 2004
Externally publishedYes

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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