From Wikipedia, the free encyclopedia
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
∼
ξ
{\displaystyle \sim \xi }
— the
superconducting coherence length (parameter of a
Ginzburg–Landau theory ). The supercurrents decay on the distance about
λ
{\displaystyle \lambda }
(
London penetration depth ) from the core. Note that in
type-II superconductors
λ
>
ξ
/
2
{\displaystyle \lambda >\xi /{\sqrt {2}}}
. The circulating
supercurrents induce magnetic fields with the total flux equal to a single
flux quantum
Φ
0
{\displaystyle \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
[3]
[4]
B
(
r
)
=
Φ
0
2
π
λ
2
K
0
(
r
λ
)
≈
λ
r
exp
(
−
r
λ
)
,
{\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),}
[7]
where
K
0
(
z
)
{\displaystyle K_{0}(z)}
is a zeroth-order
Bessel function . Note that, according to the above formula, at
r
→
0
{\displaystyle r\to 0}
the magnetic field
B
(
r
)
∝
ln
(
λ
/
r
)
{\displaystyle B(r)\propto \ln(\lambda /r)}
, i.e. logarithmically diverges. In reality, for
r
≲
ξ
{\displaystyle r\lesssim \xi }
the field is simply given by
B
(
0
)
≈
Φ
0
2
π
λ
2
ln
κ
,
{\displaystyle 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
κ
>
1
/
2
{\displaystyle \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
{\displaystyle H}
larger than the
lower critical field
H
c
1
{\displaystyle H_{c1}}
(but smaller than the
upper critical field
H
c
2
{\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
Φ
0
{\displaystyle \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.
See also
References
^ 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 YBa2 Cu3 O7−x thin films visualized by scanning SQUID microscopy" . Scientific Reports . 5 : 8677.
arXiv :
1807.06746 .
Bibcode :
2015NatSR...5E8677W .
doi :
10.1038/srep08677 .
PMC
4345321 .
PMID
25728772 .
^ Abrikosov, A. A. (1957). "The magnetic properties of superconducting alloys".
Journal of Physics and Chemistry of Solids . 2 (3): 199–208.
Bibcode :
1957JPCS....2..199A .
doi :
10.1016/0022-3697(57)90083-5 .
^
a
b
c London, F. (1948-09-01). "On the Problem of the Molecular Theory of Superconductivity". Physical Review . 74 (5): 562–573.
Bibcode :
1948PhRv...74..562L .
doi :
10.1103/PhysRev.74.562 .
^
a
b
c London, Fritz (1961). Superfluids (2nd ed.). New York, NY: Dover.
^ Onsager, L. (March 1949).
"Statistical hydrodynamics" . Il Nuovo Cimento . 6 (S2): 279–287.
Bibcode :
1949NCim....6S.279O .
doi :
10.1007/BF02780991 .
ISSN
0029-6341 .
S2CID
186224016 .
^ Feynman, R.P. (1955),
Chapter II Application of Quantum Mechanics to Liquid Helium , Progress in Low Temperature Physics, vol. 1, Elsevier, pp. 17–53,
doi :
10.1016/s0079-6417(08)60077-3 ,
ISBN
978-0-444-53307-4 , retrieved 2021-04-11
^ de Gennes, Pierre-Gilles (2018) [1965]. Superconductivity of Metals and Alloys . Addison Wesley Publishing Company, Inc. p. 59.
ISBN
978-0-7382-0101-6 .