Abrikosov vortex

In superconductivity, an Abrikosov vortex is a vortex of supercurrent in a type-II superconductor theoretically predicted by Alexei Abrikosov in 1957.[2] 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 \( {\displaystyle \lambda >\xi /{\sqrt {2}}} \). 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
\( B(r)={\frac {\Phi _{0}}{2\pi \lambda ^{2}}}K_{0}\left({\frac {r}{\lambda }}\right)\approx {\sqrt {{\frac {\lambda }{r}}}}\exp \left(-{\frac {r}{\lambda }}\right), \)

where \( K_{0}(z) \) is a zeroth-order Bessel function. Note that, according to the above formula, at r → 0 {\displaystyle r\to 0} 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 {\displaystyle H} 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, with the average vortex density (flux density) approximately equal to the externally applied magnetic field. As with other lattices, defects may form as dislocations.

Vortices in a 200-nm-thick YBCO film imaged by scanning SQUID microscopy[1]

See also

Alexei Alexeyevich Abrikosov
Flux pinning
Ginzburg-Landau theory
Macroscopic quantum phenomena
Pinning force
Type-II superconductor

References

Wells, Frederick S.; Pan, Alexey V.; Wang, X. Renshaw; Fedoseev, Sergey A.; Hilgenkamp, Hans (2015). "Analysis of low-field isotropic vortex glass containing vortex groups in YBa2Cu3O7−x thin films visualized by scanning SQUID microscopy". Scientific Reports. 5: 8677. Bibcode:2015NatSR...5E8677W. PMC 4345321 Freely accessible. PMID 25728772. doi:10.1038/srep08677.
Abrikosov, A. A. (1957). "The magnetic properties of superconducting alloys". Journal of Physics and Chemistry of Solids. 2(3): 199–208. Bibcode:1957JPCS....2..199A.