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In a standard superconductor, described by a complex field fermionic condensate wave function , vortices carry quantized magnetic fields because the condensate wave function | Ψ | e i ϕ {\displaystyle |\Psi |e^{i\phi }} is invariant to increments of the phase ϕ {\displaystyle \phi } by 2 π {\displaystyle 2\pi }. There a winding of the phase ϕ {\displaystyle {\phi }} by 2 π {\displaystyle 2\pi } creates a vortex which carries one flux quantum. See quantum vortex.
The term Fractional vortex is used for two kinds of very different quantum vortices which occur when:
A physical system allows phase windings different from 2 π × i n t e g e r {\displaystyle 2\pi \times {\mathit {integer}}} , i.e. non-integer or fractional phase winding. Quantum mechanics prohibits it in a uniform ordinary superconductor, but it becomes possible in an inhomogeneous system, for example, if a vortex is placed on a boundary between two superconductors which are connected only by an extremely weak link ; such a situation also occurs in some cases in polycrystalline samples on grain boundaries etc. At such superconducting boundaries the phase can have a discontinuous jump. Correspondingly, a vortex placed onto such a boundary acquires a fractional phase winding hence the term fractional vortex. A similar situation occurs in Spin-1 Bose condensate, where a vortex with π {\displaystyle \pi } phase winding can exist if it is combined with a domain of overturned spins.
A different situation occurs in uniform multicomponent superconductors which allow stable vortex solutions with integer phase winding 2 π N {\displaystyle 2\pi N} , where N = ± 1 , ± 2 , . . . {\displaystyle N=\pm 1,\pm 2,...} , which however carry arbitrarily fractionally quantized magnetic flux.