Abstract
We show that in two-gap superconductors there exist vortices which carry an arbitrary fraction of magnetic flux quantum and in two dimensions under certain conditions these vortices undergo a BKT transition which marks onset of quasi-long-range order only in a difference of phases of the two order parameters. In the second part of the talk we show that an U(1)× U(1) Ginzburg–Landau model or a GL model where U(1)× U(1) symmetry is weakly broken to U(1) is exactly equivalent to a version of the Faddeev's the nonlinear O(3) sigma model. This implies in particular that such a system possesses a hidden O(3) symmetry and besides that allows for the formation of knotted solitons. The second part of the talk is based on a joint work with L.D. Faddeev and A. Niem: Phys. Rev. B 65 (2002) 100512.
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