Non-Abrikosov Vortex and Topological Knot in Two-gap 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 $\mathrm{Mg}{\mathrm{B}}_2$ superconductor.

4 pages, 3 figures

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• New Interpretation of Skyrme Theory
• Knotted Solitons in a Charged Two-Condensate Bose System
• Superconductors that do not expel magnetic flux
• Knots in Physics
• Visualization of defect-induced interband proximity effect at the nanoscale