Abrikosov vortex explained

In superconductivity, a fluxon (also called an Abrikosov vortex or quantum vortex) is a vortex of supercurrent in a type-II superconductor, used by Alexei Abrikosov to explain magnetic behavior of type-II superconductors.^[1] 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.^[2]

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 λ (London penetration depth) from the core. Note that in type-II superconductors λ >\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 ^{[3] [4]} 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 ( λ /r) , i.e. logarithmically diverges. In reality, for r\lesssim\xi the field is simply given by

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, 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

• Macroscopic quantum phenomena
• Nielsen–Olesen vortex

Notes and References

1. 10.1016/0022-3697(57)90083-5 . The magnetic properties of superconducting alloys . . 2 . 3 . 199–208. 1957. Abrikosov. A. A.. 1957JPCS....2..199A .
2. Onsager. L.. March 1949. Statistical hydrodynamics. Il Nuovo Cimento. en. 6. S2. 279–287. 10.1007/BF02780991. 1949NCim....6S.279O . 186224016 . 0029-6341.
3. London. F.. 1948-09-01. On the Problem of the Molecular Theory of Superconductivity . Physical Review. 74. 5. 562–573. 10.1103/PhysRev.74.562. 1948PhRv...74..562L .
4. Book: London, Fritz . Superfluids. 1961. Dover. 2nd . New York, NY.