Abrikosov vortex
In superconductivity, fluxon (also called a Abrikosov vortex and quantum vortex) is a vortex of supercurrent in a type-II superconductor, used by Alexei Abrikosov to explain magnetic behavior of type-II superconductors. Abrikosov vortices occur generically in the Ginzburg–Landau theory of superconductivity. Overview. The solution is a combination of fluxon solution by Fritz London, combined with a concept of core of quantum vortex by Lars Onsager. In the quantum vortex supercurrent circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size formula_1 — the superconducting coherence length (parameter of a Ginzburg –Landau theory). The supercurrents decay on the distance about formula_2 (London penetration depth) from the core. Note that in type-II superconductors formula_3. The circulating supercurrents induce magnetic fields with the total flux equal to a single flux quantum formula_4. 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 formula_5 where formula_6 is a zeroth-order Bessel function. Note that, according to the above formula, at formula_7 the magnetic field formula_8, i.e. logarithmically diverges. In  reality, for formula_9 the field is simply given by formula_10 where "κ" = "λ/ξ" is known as the Ginzburg–Landau parameter, which must be formula_11 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 formula_12 larger than the lower critical field formula_13 (but smaller than the upper critical field formula_14), 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 formula_4. 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.