Topological Objects in Two-gap Superconductor:I

TL;DR

This paper explores topological objects like non-Abrikosov vortices and magnetic knots in two-gap superconductors, revealing their types, stability, and potential realization in materials such as MgB2.

Contribution

It identifies two types of non-Abrikosov vortices and demonstrates the construction of stable magnetic knots with topological properties in two-gap superconductors.

Findings

Two types of non-Abrikosov vortices identified: D-type and N-type.

Stable magnetic knots constructed by twisting and connecting vortices.

Topological properties described by the Chern-Simon index.

Abstract

We discuss topological objects, in particular the non-Abrikosov vortex and the magnetic knot made of the twisted non-Abrikosov vortex, in two-gap superconductor. We show that there are two types of non-Abrikosov vortex in Ginzburg-Landau theory of two-gap superconductor, the D-type which has no concentration of the condensate at the core and the N-type which has a non-trivial profile of the condensate at the core, under a wide class of realistic interaction potential. Furthermore, we show that we can construct a stable magnetic knot by twisting the non-Abrikosov vortex and connecting two periodic ends together, whose knot topology $\pi_3(S^2)$ is described by the Chern-Simon index of the electromagnetic potential. We discuss how these topological objects can be constructed in $\rm MgB_2$ or in liquid metallic hydrogen.