In superconductivity, fluxon (also called a Abrikosov vortex and quantum vortex) is a vortex of

supercurrent A supercurrent is a superconducting current, that is, electric current which flows without dissipation in a superconductor. Under certain conditions, an electric current can also flow without dissipation in microscopically small non-superconductin ...

in a

type-II superconductor In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the ...

, used by Alexei Abrikosov to explain magnetic behavior of type-II superconductors. Abrikosov vortices occur generically in the

Ginzburg–Landau theory In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenol ...

of superconductivity.

Overview

The solution is a combination of fluxon solution by

Fritz London Fritz Wolfgang London (March 7, 1900 – March 30, 1954) was a German physicist and professor at Duke University. His fundamental contributions to the theories of chemical bonding and of intermolecular forces ( London dispersion forces) are today ...

, combined with a concept of core of quantum vortex by

Lars Onsager Lars Onsager (November 27, 1903 – October 5, 1976) was a Norwegian-born American physical chemist and theoretical physicist. He held the Gibbs Professorship of Theoretical Chemistry at Yale University. He was awarded the Nobel Prize in C ...

. In the quantum vortex_,

circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size

\sim\xi

— the

superconducting coherence length In superconductivity, the superconducting coherence length, usually denoted as \xi (Greek lowercase ''xi''), is the characteristic exponent of the variations of the density of superconducting component. The superconducting coherence length is one o ...

(parameter of a

). The supercurrents decay on the distance about

\lambda

(

London penetration depth In superconductors, the London penetration depth (usually denoted as \lambda or \lambda_L) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to e^ times that of the magnetic field at the surface ...

) from the core. Note that in

type-II superconductors In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the ...

\lambda>\xi/\sqrt

. The circulating

s 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 where

K_0(z)

is a zeroth-order

Bessel function Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary ...

. 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 where ''κ'' = ''λ/ξ'' is known as the Ginzburg–Landau parameter, which must be

\kappa>1/\sqrt

s. Abrikosov vortices can be trapped in a

by chance, on defects, etc. Even if initially

contains no vortices, and one applies a magnetic field

H

larger than the lower critical field

H_

(but smaller than the upper critical field

H_

), 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.

References

{{Reflist Superconductivity Vortices

Overview

See also

References