Physics:Abrikosov vortex

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Vortices in a 200-nm-thick YBCO film imaged by scanning SQUID microscopy[1]

In 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.[2] Abrikosov vortices occur generically in the Ginzburg–Landau theory of superconductivity.

Overview

The solution is a combination of fluxon solution by Fritz London,[3][4] combined with a concept of core of quantum vortex by Lars 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 [math]\displaystyle{ \sim\xi }[/math] — the superconducting coherence length (parameter of a Ginzburg–Landau theory). The supercurrents decay on the distance about [math]\displaystyle{ \lambda }[/math] (London penetration depth) from the core. Note that in type-II superconductors [math]\displaystyle{ \lambda\gt \xi/\sqrt{2} }[/math]. The circulating supercurrents induce magnetic fields with the total flux equal to a single flux quantum [math]\displaystyle{ \Phi_0 }[/math]. 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 [3] [4]

[math]\displaystyle{ 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), }[/math][7]

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

[math]\displaystyle{ B(0)\approx \frac{\Phi_0}{2\pi\lambda^2}\ln\kappa, }[/math]

where κ = λ/ξ is known as the Ginzburg–Landau parameter, which must be [math]\displaystyle{ \kappa\gt 1/\sqrt{2} }[/math] 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 [math]\displaystyle{ H }[/math] larger than the lower critical field [math]\displaystyle{ H_{c1} }[/math] (but smaller than the upper critical field [math]\displaystyle{ H_{c2} }[/math]), 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 [math]\displaystyle{ \Phi_0 }[/math].[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.

See also


References

  1. ↑ Wells, Frederick S.; Pan, Alexey V.; Wang, X. Renshaw; Fedoseev, Sergey A.; Hilgenkamp, Hans (2015). "Analysis of low-field isotropic vortex glass containing vortex groups in YBa2Cu3O7−x thin films visualized by scanning SQUID microscopy". Scientific Reports 5: 8677. doi:10.1038/srep08677. PMID 25728772. Bibcode: 2015NatSR...5E8677W. 
  2. ↑ Abrikosov, A. A. (1957). "The magnetic properties of superconducting alloys". Journal of Physics and Chemistry of Solids 2 (3): 199–208. doi:10.1016/0022-3697(57)90083-5. Bibcode: 1957JPCS....2..199A. 
  3. ↑ 3.0 3.1 3.2 London, F. (1948-09-01). "On the Problem of the Molecular Theory of Superconductivity". Physical Review 74 (5): 562–573. doi:10.1103/PhysRev.74.562. Bibcode: 1948PhRv...74..562L. 
  4. ↑ 4.0 4.1 4.2 London, Fritz (1961). Superfluids (2nd ed.). New York, NY: Dover. 
  5. ↑ Onsager, L. (March 1949). "Statistical hydrodynamics" (in en). Il Nuovo Cimento 6 (S2): 279–287. doi:10.1007/BF02780991. ISSN 0029-6341. Bibcode: 1949NCim....6S.279O. http://link.springer.com/10.1007/BF02780991. 
  6. ↑ Feynman, R.P. (1955) (in en), Chapter II Application of Quantum Mechanics to Liquid Helium, Progress in Low Temperature Physics, 1, Elsevier, pp. 17–53, doi:10.1016/s0079-6417(08)60077-3, ISBN 978-0-444-53307-4, https://linkinghub.elsevier.com/retrieve/pii/S0079641708600773, retrieved 2021-04-11 
  7. ↑ de Gennes, Pierre-Gilles (2018). Superconductivity of Metals and Alloys. Addison Wesley Publishing Company, Inc. p. 59. ISBN 978-0-7382-0101-6. 



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