In a standard superconductor, described by a complex field fermionic condensate wave function (denoted
Contents
- Fractional vortices at phase discontinuities
- Splintered vortices double sine Gordon solitons
- Spin triplet Superfluidity
- ii Vortices with integer phase winding and fractional flux in multicomponent superconductivity
- References
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
(ii) A different situation occurs in uniform multicomponent superconductors which allow stable vortex solutions with integer phase winding
Fractional vortices at phase discontinuities
Josephson phase discontinuities may appear in specially designed long Josephson junctions (LJJ). For example, so-called 0-π LJJ have a
An LJJ reacts to the phase discontinuity by bending the Josephson phase
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, that depends on the value of κ.
Splintered vortices (double sine-Gordon solitons)
In the context of d-wave superconductivity, a fractional vortex (also known as splintered vortex) is a vortex of supercurrent carrying unquantized magnetic flux Φ1<Φ0, which depends on parameters of the system. 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. These splintered vortices are solitons. They are able to move and preserve their shape similar to conventional integer Josephson vortices (fluxons). This is opposite to the fractional vortices pinned at phase discontinuity, e.g. semifluxons, which are pinned at the discontinuity and cannot move far from it.
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. Large scale means that the scale is much larger than the facet size. This equation is double sin-Gordon equation, which in normalized units reads
where g<0 is a dimensionless constant resulting from averaging over tiny facets. The detailed mathematical procedure of averaging is similar to the one done for a parametrically driven pendulum, and can be extended to time-dependent phenomena. In essence, (EqDSG) described extended φ Josephson junction.
For g<-1 (EqDSG) has two stable equilibrium values (in each 2π interval): ψ=±φ, where φ=cos(-1/g). They corresponding to two energy minima. Correspondingly, there are two fractional vortices (topological solitons): one with the phase ψ(x) going from -φ to +φ, while the other has the phase ψ(x) changing from +φ to -φ+2π. The first vortex has a topological change of 2φ and carries the magnetic flux Φ1=(φ/π)Φ0. The second vortex has a topological change of 2π-2φ and carries the flux Φ2=Φ0-Φ1.
Splintered vortices were first observed at the asymmetric 45° grain boundaries between two d-wave superconductors YBa2Cu3O7−δ.
Spin-triplet Superfluidity
In certain states of spin-1 superfluids or Bose condensates, the condensate wavefunction is invariant if the superfluid phase changes by
(ii) Vortices with integer phase winding and fractional flux in multicomponent superconductivity
Different kinds of "Fractional vortices" appear in a different context in multi-component superconductivity where several independent charged condensates or superconducting components interact with each other electromagnetically. Such a situation occurs for example in the