Superconductivity and Abelian Chiral Anomalies

Details Superconductivity and Abelian Chiral Anomalies Superconductivity and Abelian Chiral Anomalies

2003-08-17

arxiv.org/abs/cond-mat/0308332v2

Physics

Condensed Matter

Superconductivity

An example with a figure and discussions are supplemented

Scientific paper

10.1103/PhysRevB.70.054502

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.

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