Insuperconductivity, afluxon (also called anAbrikosov vortex orquantum vortex) is a vortex ofsupercurrent in atype-II superconductor, used by Soviet physicistAlexei Abrikosov to explain magnetic behavior of type-II superconductors.^[2] Abrikosov vortices occur generically in theGinzburg–Landau theory of superconductivity.

The solution is a combination of fluxon solution byFritz London,^[3][4] combined with a concept of core of quantum vortex byLars Onsager.^[5][6]

In the quantum vortex_,supercurrent circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size${\displaystyle \sim \xi }$ — thesuperconducting coherence length (parameter of aGinzburg–Landau theory). The supercurrents decay on the distance about${\displaystyle \lambda }$ (London penetration depth) from the core. Note that intype-II superconductors${\displaystyle \lambda >\xi /\sqrt{2}}$. The circulatingsupercurrents induce magnetic fields with the total flux equal to a singleflux quantum${\displaystyle {\mathrm{\Phi }}_0}$. Therefore, an Abrikosov vortex is often called afluxon.

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^[3][4]

${\displaystyle B(r)=\frac{{\mathrm{\Phi }}_0}{2\pi {\lambda }^2}{K}_0\left(\frac{r}{\lambda }\right)\approx \sqrt{\frac{\lambda }{r}}\exp \left(-\frac{r}{\lambda }\right),}$^[7]

where${\displaystyle K_0(z)}$ is a zeroth-orderBessel function. Note that, according to the above formula, at${\displaystyle r\to 0}$ the magnetic field${\displaystyle B(r)\propto \ln (\lambda /r)}$, i.e. logarithmically diverges. In reality, for${\displaystyle r\lesssim \xi }$ the field is simply given by

${\displaystyle B(0)\approx \frac{{\mathrm{\Phi }}_0}{2\pi {\lambda }^2}\ln \kappa ,}$

whereκ =λ/ξ is known as the Ginzburg–Landau parameter, which must be${\displaystyle \kappa >1/\sqrt{2}}$ intype-II superconductors.

Abrikosov vortices can be trapped in atype-II superconductor by chance, on defects, etc. Even if initiallytype-II superconductor contains no vortices, and one applies a magnetic field${\displaystyle H}$ larger than thelower critical field${\displaystyle H_{c1}}$ (but smaller than theupper critical field${\displaystyle H_{c2}}$), 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${\displaystyle {\mathrm{\Phi }}_0}$.^[3][4] 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.

• Superconductivity
• Vortices

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