History of gravitational theory

In superconductivity, an Abrikosov vortex is a vortex of supercurrent in a type-II superconductor theoretically predicted by Alexei Abrikosov in 1957. 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 $\lambda >\xi$. 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 $r\to 0$ 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 $H$ 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, may be with defects/dislocations) with the average vortex density (flux density) approximately equal to the externally applied magnetic field.

See also

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

References

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