In a standard superconductor, described by a complex field fermionic condensate wave function (denoted
), vortices carry quantized magnetic fields because the condensate wave function
The term Fractional vortex is used for two kinds of very different quantum vortices which occur when: (i) A physical system allows phase windings different from
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 (also called a Josephson junction); such a situation also occurs on grain boundaries etc.
A similar situation occurs in Spin-1 Bose condensate, where a vortex with
phase winding can exist if it is combined with a domain of overturned spins.
(ii) A different situation occurs in uniform multicomponent superconductors, which allow stable vortex solutions with integer phase winding
, which however carry arbitrarily fractionally quantized magnetic flux.
[1] Observation of fractional-flux vortices was reported in a multiband Iron-based superconductor.
LJJ can be fabricated using tailored ferromagnetic barrier[3][4] or using d-wave superconductors.
[5][6] The Josephson phase discontinuities can also be introduced using artificial tricks, e.g., a pair of tiny current injectors attached to one of the superconducting electrodes of the LJJ.
The bending of the Josephson phase inevitably results in appearance of a local magnetic field
This type of vortex is pinned at the phase discontinuity point, but may have two polarities, positive and negative, distinguished by the direction of the fractional flux and direction of the supercurrent (clockwise or counterclockwise) circulating around its center (discontinuity point).
[10] The semifluxon is a particular case of such a fractional vortex pinned at the phase discontinuity point.
Although, such fractional Josephson vortices are pinned, if perturbed they may perform a small oscillations around the phase discontinuity point with an eigenfrequency,[11][12] that depends on the value of κ.
Physically, such vortices may appear at the grain boundary between two d-wave superconductors, which often looks like a regular or irregular sequence of 0 and π facets.
One can also construct an artificial array of short 0 and π facets to achieve the same effect.
They are able to move and preserve their shape similar to conventional integer Josephson vortices (fluxons).
Theoretically, one can describe a grain boundary between d-wave superconductors (or an array of tiny 0 and π facets) by an effective equation for a large-scale phase ψ.
The detailed mathematical procedure of averaging is similar to the one done for a parametrically driven pendulum,[15][16] and can be extended to time-dependent phenomena.
[17] In essence, (EqDSG) described extended φ Josephson junction.
The first vortex has a topological change of 2φ and carries the magnetic flux Φ1=(φ/π)Φ0.
Splintered vortices were first observed at the asymmetric 45° grain boundaries between two d-wave superconductors[14] YBa2Cu3O7−δ.
theories of the projected quantum states of liquid metallic hydrogen, where two order parameters originate from theoretically anticipated coexistence of electronic and protonic Cooper pairs.
Also these fractional vortices carry a superfluid momentum which does not obey Onsager-Feynman quantization [19] [20] Despite the integer phase winding, the basic properties of these kinds of fractional vortices are very different from the Abrikosov vortex solutions.
For example, in contrast to the Abrikosov vortex, their magnetic field generically is not exponentially localized in space.
Also in some cases the magnetic flux inverts its direction at a certain distance from the vortex center [21]