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File:YBCO vortices.jpg|thumb|Vortices in a 200-nm-thick YBCO film imaged by scanning SQUID microscopyscanning SQUID microscopyIn superconductivity, a fluxon (also called an Abrikosov vortex or quantum vortex) is a vortex of supercurrent in a type-II superconductor, used by Alexei Abrikosov to explain magnetic behavior of type-II superconductors.JOURNAL, 10.1016/0022-3697(57)90083-5, The magnetic properties of superconducting alloys, Journal of Physics and Chemistry of Solids, 2, 3, 199–208, 1957, Abrikosov, A. A., 1957JPCS....2..199A, Abrikosov vortices occur generically in the Ginzburg–Landau theory of superconductivity.

Overview

The solution is a combination of fluxon solution by Fritz London, combined with a concept of core of quantum vortex by Lars Onsager.JOURNAL, Onsager, L., March 1949, Statistical hydrodynamics,link.springer.com/10.1007/BF02780991, Il Nuovo Cimento, en, 6, S2, 279–287, 10.1007/BF02780991, 1949NCim....6S.279O, 186224016, 0029-6341, {{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}}In the quantum vortex, supercurrent circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size simxi — 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/sqrt{2}. 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 the same equation as in the London’s fluxoid JOURNAL, London, F., 1948-09-01, On the Problem of the Molecular Theory of Superconductivity, Physical Review, 74, 5, 562–573, 10.1103/PhysRev.74.562, 1948PhRv...74..562L, BOOK, London, Fritz, Superfluids, 1961, Dover, 2nd, New York, NY, {hide}center| BOOK, de Gennes, Pierre-Gilles, Superconductivity of Metals and Alloys, Addison Wesley Publishing Company, Inc, 2018, 978-0-7382-0101-6, 59, 1965, }}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)proptoln(lambda/r), i.e. logarithmically diverges. In reality, for rlesssimxi the field is simply given by{hide}center| {edih}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 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.

See also

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• Macroscopic quantum phenomena
• Nielsen–Olesen vortex

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References

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