Topological Vortex Lines in Two-Gap Superconductor

TL;DR

This paper investigates vortex lines in two-gap superconductors using topological methods, revealing conditions for fractional magnetic flux and linking topological invariants like the Chern-Simons action.

Contribution

It introduces a topological framework for understanding vortex lines in two-gap superconductors, including fractional flux conditions and linking invariants.

Findings

Vortex lines can carry arbitrary fractional magnetic flux.

The Chern-Simons action is a topological invariant related to vortex linking.

Topological properties determine vortex configurations in two-gap superconductors.

Abstract

Based on the U(1) gauge potential decomposition theory and the $\phi$-mapping method, we study the vortex lines in two-gap superconductor and obtain the condition, under which the vortices can carry an arbitrary fraction of magnetic flux. It has been pointed out that the Chern-Simon action is a topological invariant, which is just the total sum of all the self-linking numbers and all the linking numbers of the knot family.