Abrikosov vortex

In superconductivity, an Abrikosov vortex is a vortex of supercurrent in a type-II superconductor. 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

ko:아브리코소브 소용돌이