Abrikosov vortex

In superconductivity, an Abrikosov vortex is a vortex of supercurrent in a type-II superconductor. The supercurrent circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size $simxi$ — 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 field 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
$B(r)\; =\; frac\{Phi\_0\}\{2pilambda^2\}K\_0left(frac\{r\}\{lambda\}\; ight)\; approx\; sqrt\{frac\{lambda\}\{r\; expleft(-frac\{r\}\{lambda\}\; ight),$
where $K\_0(z)$ is the so-called Bessel function. Note that, according to the above formula, at $r\; o\; 0$ the magnetic field $B(r)proptoln(lambda/r)$, i.e. logarithmically diverges. In reality, for $rlesssimxi$ the field is simply given by

$B(0)approx\; frac\{Phi\_0\}\{2pilambda^2\}lnkappa,$
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 first critical field $H\_\{c1\}$ (but smaller than the second 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.

ee also

* Ginzburg-Landau theory
* type-II superconductor
* Alexei Alexeyevich Abrikosov

References