Modified London Equation, Abrikosov-Like Vortices and Knot Solitons in Two-Gap Superconductors

TL;DR

This paper derives a modified London equation for two-gap superconductors, revealing unique vortex structures, including Abrikosov-like vortices and knot solitons, which exhibit topological features distinct from single-gap superconductors.

Contribution

It introduces an exact modified London equation for two-gap superconductors and characterizes novel vortex and knot soliton structures with topological insights.

Findings

Vortices in two-gap superconductors are soft and continuous.

Finite energy vortices are topologically akin to baby skyrmions.

Knot solitons are twisted Abrikosov-like vortices with connected ends.

Abstract

We derive the exact modified London equation for the two-gap superconductor, compare it with its single-gap counterpart. We show that the vortices in the two-gap superconductor are soft (or continuous) core vortices. In particular, we discuss the topological structure of the finite energy vortices (Abrikosov-like vortices), and find that they can be viewed as the incarnation of the baby skyrmion stretched in the third direction. Besides, we point out that the knot soliton in the two-gap superconductor is the twisted Abrikosov-like vortex with its two periodic ends connected smoothly. The relation between the magnetic monopoles and the Abrikosov-like vortices is also discussed briefly.