The solution is a combination of fluxon solution by
Fritz London, In the quantum vortex,
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/\sqrt{2}. 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 the same equation as in the London's fluxoid {{center| 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 {{center| 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 obeys London's magnetic flux quantization and carries one quantum of magnetic flux \Phi_0. Abrikosov vortices form a lattice, usually triangular (of
hexagonal symmetry), 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==