We establish the existence of a topologically stable knot in a two-gap superconductor whose topology π₃(S²) is fixed by the Chern-Simon index of the electromagnetic potential. We present a helical magnetic vortex solution in a Ginzburg-Landau theory of a two-gap superconductor which has a nonvanishing 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 MgB₂ superconductor.
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Cho et al. (2006) studied this question.
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