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Fractional vorticesAdditional recommended knowledge
DefinitionThe term Fractional vortex is used for various quantum vortices or topological defects in different physical systems and in different contexts when these vortices have either phase winding different from or carry nonquantized or fractionally quantized magnetic field. Vortices on grain boundaries in dwave superconductors and Josephson JunctionsIn context of dwave superconductivity, a Fractional vortex known also as splinter vortex is a vortex of supercurrent carrying unquantized magnetic flux, in oppose to conventional Josephson vortex and semifluxons. Fractional vortices exist in the socalled 0π long Josephson junctions dense chains. Fractional vortices are solitons which are able to move and preserve their shape much like conventional Josephson vortices and in opposed to semifluxons which are attached to the boundary between 0 and π regions. Theoretically one can obtain an effective double sinGordon equation for the phase difference between the two superconducting banks of the 0π long Josephson junctions dense chains. This is done by taking the asymptotic expansion of the phase difference equation of motion to the second order which results in
where γ is a dimensionless constant defined by the junction's properties. The detailed mathematical procedure is similar to the one done for a parametrically driven pendulum, see for example^{[1]} and ^{[2]} , and can be extended to time dependent phenomena^{[3]}. For γ > 1 he above equation for the phase, ψ, has two stable equilibrium values ψ_{γ} = cos(1 / γ) and − ψ_{γ}. There are two fractional vortices which correspond to these two values one carries Φ_{1}= ψ_{γ}Φ_{0}/π flux and the other carries Φ_{2}= Φ_{0}Φ_{1} flux where Φ_{0} is the fundamental unit of magnetic flux quantum. For the first time fractional vortices were observed using dwave superconductors at asymmetric 45° grain boundaries YBa_{2}Cu_{3}O_{7δ} . In these systems the phase shift of π takes place inside the dwave superconductor and not at the barrier. Due to the advent of controlled coupling by proper chosen ferromagnetic thicknesses, 0–π JJs have also recently been realized in lowT_{c} SFSlike systems ^{[4]} and underdamped SIFStype ^{[5]}. SuperfluidityIn certain states of spin1 superfluids or Bose condensates condensate's wavefunction is invariant if to change a superfluid phase by π, along with a π rotation of spin angle. This is in contrast to 2π invariance of condensate wavefunction in a spin0 superfluid. A vortex resulting from such phase windings is called fractional or halfquantum vortex, in contrast to onequantum vortex where a phase changes by 2π ^{[6]}. Multicomponent superconductivity and metallic superfluidityThe term "Fractional vortex" appears also in context of multicomponent superconductivity of e.g. in the theories of the projected quantum states of liquid metallic hydrogen, where two order parameters originate from theoretically anticipated coexistence of electronic and protonic superconductivity. There a topological defects with an 2π (i.e. "integer") phase winding only in electronic or only in protonic condensate carries fractionally quantized magnetic flux and superfluid momentum and is called "fractional flux vortex" ^{[7]}. See alsoReferences
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Fractional_vortices". A list of authors is available in Wikipedia. 