In superconductivity, an Abrikosov vortex is a vortex of supercurrent in a type-II superconductor theoretically predicted by Alexei Abrikosov in 1957. The supercurrent circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size
∼
ξ
— the superconducting coherence length (parameter of a Ginzburg-Landau theory). The supercurrents decay on the distance about
λ
(London penetration depth) from the core. Note that in type-II superconductors
λ
>
ξ
/
2
. The circulating supercurrents induce magnetic fields with the total flux equal to a single flux quantum
Φ
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
B
(
r
)
=
Φ
0
2
π
λ
2
K
0
(
r
λ
)
≈
λ
r
exp
(
−
r
λ
)
,
where
K
0
(
z
)
is a zeroth-order Bessel function. Note that, according to the above formula, at
r
→
0
the magnetic field
B
(
r
)
∝
ln
(
λ
/
r
)
, i.e. logarithmically diverges. In reality, for
r
≲
ξ
the field is simply given by
B
(
0
)
≈
Φ
0
2
π
λ
2
ln
κ
,
where κ = λ/ξ is known as the Ginzburg-Landau parameter, which must be
κ
>
1
/
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
c
1
(but smaller than the upper critical field
H
c
2
), the field penetrates into superconductor in terms of Abrikosov vortices. Each vortex carries one thread of magnetic field with the flux
Φ
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.
