## Abstract

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 language | English (US) |
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Article number | 054502 |

Pages (from-to) | 054502-1-054502-9 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 70 |

Issue number | 5 |

DOIs | |

State | Published - Aug 2004 |

## ASJC Scopus subject areas

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics