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 ˜ξ — 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 > ξ. The circulating supercurrents induce magnetic field with the total flux equal to a single flux quantum Φ₀. Therefore, an Abrikosov vortex is often called a fluxon.

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The magnetic field distribution of a single vortex far from its core can be described by

where K₀(z) is the so-called Bessel function. Note that, according to the above formula, at the magnetic field , i.e. logarithmically diverges. In reality, for the field is simply given by

where κ = λ/ξ is known as the Ginzburg-Landau parameter, which must be 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 first critical field H_c1 (but smaller than the second 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 Φ₀. 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

References