Abrikosov vortex

The solution is a combination of fluxon solution by Fritz London, combined with a concept of core of quantum vortex by Lars Onsager.{{Cite journal|last=Onsager|first=L.|date=March 1949|title=Statistical hydrodynamics|url=http://link.springer.com/10.1007/BF02780991|journal=Il Nuovo Cimento|language=en|volume=6|issue=S2|pages=279–287|doi=10.1007/BF02780991|bibcode=1949NCim....6S.279O |s2cid=186224016 |issn=0029-6341|url-access=subscription}}{{Citation|last=Feynman|first=R.P.|title=Chapter II Application of Quantum Mechanics to Liquid Helium|date=1955|url=https://linkinghub.elsevier.com/retrieve/pii/S0079641708600773|series=Progress in Low Temperature Physics|volume=1|pages=17–53|publisher=Elsevier|language=en|doi=10.1016/s0079-6417(08)60077-3|isbn=978-0-444-53307-4|access-date=2021-04-11|url-access=subscription}}

In the quantum vortex_, supercurrent circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size $\backslash sim\backslash xi$ — the superconducting coherence length (parameter of a Ginzburg–Landau theory). The supercurrents decay on the distance about $\backslash lambda$ (London penetration depth) from the core. Note that in type-II superconductors $\backslash lambda>\backslash xi/\backslash sqrt\{2\}$. The circulating supercurrents induce magnetic fields with the total flux equal to a single flux quantum $\backslash Phi\_0$. 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 {{Cite journal|last=London|first=F.|date=1948-09-01|title=On the Problem of the Molecular Theory of Superconductivity |journal=Physical Review|volume=74|issue=5|pages=562–573|doi=10.1103/PhysRev.74.562|bibcode=1948PhRv...74..562L }}{{Cite book|last=London|first=Fritz |title=Superfluids|date=1961|publisher=Dover|edition=2nd |location=New York, NY}}

{{center|$$

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),

{{Cite book|last=de Gennes|first=Pierre-Gilles|title=Superconductivity of Metals and Alloys|publisher=Addison Wesley Publishing Company, Inc|year=2018|isbn=978-0-7382-0101-6|page=59|orig-year=1965}}}}

where $K\_0(z)$ is a zeroth-order Bessel function. Note that, according to the above formula, at $r\; \backslash to\; 0$ the magnetic field $B(r)\backslash propto\backslash ln(\backslash lambda/r)$, i.e. logarithmically diverges. In reality, for $r\backslash lesssim\backslash xi$ the field is simply given by

{{center|$$

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 $\backslash kappa>1/\backslash sqrt\{2\}$ 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 obeys London's magnetic flux quantization and carries one quantum of magnetic flux $\backslash Phi\_0$. 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.

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• Macroscopic quantum phenomena
• Nielsen–Olesen vortex

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Category:Superconductivity

Category:Vortices