Superconductivity and Abelian Chiral Anomalies

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.

An example with a figure and discussions are supplemented

References in corpus (2)

• Time-Reversal Symmetry-Breaking Superconductivity in Heavy Fermion PrOs4Sb12 detected by Muon Spin Relaxation
• Multiple Superconducting Phases in New Heavy Fermion Superconductor PrOs4Sb12

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