Non-Abrikosov Vortex and Topological Knot in Two-gap Superconductor

TL;DR

This paper demonstrates the existence of a topologically stable knot in two-gap superconductors, specifically in MgB2, by identifying a twisted magnetic vortex ring with non-trivial topology.

Contribution

It introduces a novel topological knot solution in two-gap superconductors and links it to physical realizations like MgB2.

Findings

Existence of topologically stable knots in two-gap superconductors

Construction of a helical magnetic vortex solution with non-vanishing core condensate

Proposal for realizing knots in MgB2 superconductor

Abstract

We establish the existence of topologically stable knot in two-gap superconductor whose topology $\pi_3(S^2)$ is fixed by the Chern-Simon index of the electromagnetic potential. We present a helical magnetic vortex solution in Ginzburg-Landau theory of two-gap superconductor which has a non-vanishing condensate at the core, and identify the knot as a twisted magnetic vortex ring made of the helical vortex. We discuss how the knot can be constructed in the recent two-gap $\rm MgB_2$ superconductor.