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Abrikosov vortices : ウィキペディア英語版
Abrikosov vortex
In superconductivity, an Abrikosov vortex is a vortex of supercurrent in a type-II superconductor theoretically predicted by Alexei Abrikosov in 1957.〔Abrikosov, A. A. (1957). (The magnetic properties of superconducting alloys ). Journal of Physics and Chemistry of Solids, 2(3), 199-208.〕 The supercurrent circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size \sim\xi — the superconducting coherence length (parameter of a Ginzburg-Landau theory). The supercurrents decay on the distance about \lambda (London penetration depth) from the core. Note that in type-II superconductors \lambda>\xi. The circulating supercurrents induce magnetic fields with the total flux equal to a single flux quantum \Phi_0. Therefore, an Abrikosov vortex is often called a fluxon.
The magnetic field distribution of a single vortex far from its core can be described by

B(r) = \fracK_0\left(\frac\right)
\approx \sqrt} \exp\left(-\frac\right),

where K_0(z) is a zeroth-order Bessel function. Note that, according to the above formula, at r \to 0 the magnetic field B(r)\propto\ln(\lambda/r), i.e. logarithmically diverges. In reality, for r\lesssim\xi the field is simply given by

B(0)\approx \frac\ln\kappa,

where ''κ'' = ''λ/ξ'' is known as the Ginzburg-Landau parameter, which must be \kappa>1/\sqrt in type-II superconductors.
Abrikosov vortices can be trapped in a type-II superconductor by chance, on defects, etc. Even if initially type-II superconductor contains no vortices, and one applies a magnetic field H larger than the lower critical field H_ (but smaller than the upper critical field H_), the field penetrates into superconductor in terms of Abrikosov vortices. Each vortex carries one thread of magnetic field with the flux \Phi_0. Abrikosov vortices form a lattice, usually triangular, with the average vortex density (flux density) approximately equal to the externally applied magnetic field. As with other lattices, defects may form as dislocations.
==See also==

* Alexei Alexeyevich Abrikosov
* Flux pinning
* Ginzburg-Landau theory
* Macroscopic quantum phenomena
* Pinning force
* Type-II superconductor

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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