In a standard superconductor, described by a complex field (condensates wave function), vortices carry quantized magnetic field: a consequence of -invariance of the phase of the condensate wave function . There a winding of the phase by creates a vortex which carries one flux quantum. See Quantum vortex.
The term Fractional vortex is used for various very different quantum vortices or topological defects in very different contexts when:
(i) A physical system allows phase windings different from . 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 by a weak link (Josephson Junction), such a situation also occurs in some cases in polycrystalline samples on grain boundaries etc. It results in vortices having fractional phase windings and thus fractional flux). Similar situation occurs in Spin-1 Bose condensates for a vortex with phase winding combined with a domain of overturned spins.
(ii) Different situation occurs in uniform multicomponent superconductors which allow stable vortex solution with a phase winding which however carry arbitrarily fractionally quantized magnetic flux [ [http://link.aps.org/abstract/PRL/v89/e067001] . Egor Babaev, Phys.Rev.Lett. 89 (2002) 067001.] .
(i) Vortices with non-integer phase winding
Fractional Josephson vortices at phase discontinuities
(not yet finished)
Josephson phase discontinuities may appear in specially designed long Josephson junctions (LJJ). For example, so-called 0- LJJ have a discontinuity of the Josephson phase at a point where 0 and parts join. Josephson phase discontinuities can also be introduces using artificial tricks, e.g. a pair of tiny current injectors attached to one of the superconducting electrodes of the LJJ
author = A. Ustinov
year = 2002
title = Fluxon insertion into annular Josephson junctions
journal = Appl. Phys. Lett.
volume = 80
pages = 3153--3155
doi = 10.1063/1.1474617]
author = B. A. Malomed and A. V. Ustinov
year = 2004
title = Creation of classical and quantum fluxons by a current dipole n a long Josephson junction
journal = Phys. Rev. B
volume = 69
pages = 064502
doi = 10.1103/PhysRevB.69.064502] .
author = E. Goldobin, A. Sterck, T. Gaber, D. Koelle, R. Kleiner
year = 2004
title = Dynamics of semifluxons in Nb long Josephson 0- junctions
journal = Phys. Rev. Lett.
volume = 92
pages = 057005
doi = 10.1103/PhysRevLett.92.057005] .We will denote the value of the phase discontinuity by and, without losing generality, assume that