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

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    We establish the existence of topologically stable knot in two-gap superconductor whose topology π3(S2)\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 MgB2\rm MgB_2 superconductor.Comment: 4 pages, 3 figure

    Monopoles and Knots in Skyrme Theory

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    We show that the Skyrme theory actually is a theory of monopoles which allows a new type of solitons, the topological knots made of monopole-anti-monopole pair,which is different from the well-known skyrmions. Furthermore, we derive a generalized Skyrme action from the Yang-Mills action of QCD, which we propose to be an effective action of QCD in the infra-red limit. We discuss the physical implications of our results.Comment: 4 pages. Phys. Rev. Lett. in pres
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