Abrikosov vortex

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In superconductivity, an Abrikosov vortex is a vortex of supercurrent in a type-II superconductor theoretically predicted by Alexei Abrikosov in 1957.[1] 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) = \frac{\Phi_0}{2\pi\lambda^2}K_0\left(\frac{r}{\lambda}\right)
  \approx \sqrt{\frac{\lambda}{r}} \exp\left(-\frac{r}{\lambda}\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{\Phi_0}{2\pi\lambda^2}\ln\kappa,

where κ = λ/ξ is known as the Ginzburg-Landau parameter, which must be \kappa>1/\sqrt{2} 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_{c1} (but smaller than the upper critical field H_{c2}), 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, may be with defects/dislocations) with the average vortex density (flux density) approximately equal to the externally applied magnetic field.

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