![YBCO vortices](https://upload.wikimedia.org/wikipedia/commons/7/7d/YBCO_vortices.jpg)
In superconductivity,
fluxon
In physics, a fluxon is a quantum of electromagnetic flux. The term may have any of several related meanings.
Superconductivity
In the context of superconductivity, in type II superconductors fluxons (also known as Abrikosov vortices) can form ...
(also called a Abrikosov vortex and quantum vortex) is a vortex of
supercurrent in a
type-II superconductor
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases.
It also features the ...
, used by
Alexei Abrikosov to explain magnetic behavior of type-II superconductors. Abrikosov vortices occur generically in the
Ginzburg–Landau theory
In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenol ...
of superconductivity.
Overview
The solution is a combination of fluxon solution by
Fritz London
Fritz Wolfgang London (March 7, 1900 – March 30, 1954) was a German physicist and professor at Duke University. His fundamental contributions to the theories of chemical bonding and of intermolecular forces (London dispersion forces) are today c ...
,
combined with a concept of core of quantum vortex by
Lars Onsager
Lars Onsager (November 27, 1903 – October 5, 1976) was a Norwegian-born American physical chemist and theoretical physicist. He held the Gibbs Professorship of Theoretical Chemistry at Yale University. He was awarded the Nobel Prize in Che ...
.
In the quantum vortex
, supercurrent circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size
— the
superconducting coherence length In superconductivity, the superconducting coherence length, usually denoted as \xi (Greek lowercase ''xi''), is the characteristic exponent of the variations of the density of superconducting component.
The superconducting coherence length is one o ...
(parameter of a
Ginzburg–Landau theory
In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenol ...
). The supercurrents decay on the distance about
(
London penetration depth
In superconductors, the London penetration depth (usually denoted as \lambda or \lambda_L) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to e^ times that of the magnetic field at the surface ...
) from the core. Note that in
type-II superconductors
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases.
It also features the ...
. The circulating
supercurrents induce magnetic fields with the total flux equal to a single
flux quantum . Therefore, an Abrikosov vortex is often called a
fluxon
In physics, a fluxon is a quantum of electromagnetic flux. The term may have any of several related meanings.
Superconductivity
In the context of superconductivity, in type II superconductors fluxons (also known as Abrikosov vortices) can form ...
.
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
where
is a zeroth-order
Bessel function
Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation
x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0
for an arbitrary ...
. Note that, according to the above formula, at
the magnetic field
, i.e. logarithmically diverges. In reality, for
the field is simply given by
where ''κ'' = ''λ/ξ'' is known as the Ginzburg–Landau parameter, which must be
in
type-II superconductor
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases.
It also features the ...
s.
Abrikosov vortices can be trapped in a
type-II superconductor
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases.
It also features the ...
by chance, on defects, etc. Even if initially
type-II superconductor
In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases.
It also features the ...
contains no vortices, and one applies a magnetic field
larger than the
lower critical field (but smaller than the
upper critical field
For a given temperature, the critical field refers to the maximum magnetic field strength below which a material remains superconducting. Superconductivity is characterized both by perfect conductivity (zero resistance) and by the complete expulsio ...
), 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
.
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
*
Flux pinning
Flux pinning is a phenomenon that occurs when flux vortices in a type-II superconductor are prevented from moving within the bulk of the superconductor, so that the magnetic field lines are "pinned" to those locations. The superconductor must be a ...
*
Ginzburg–Landau theory
In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenol ...
*
Macroscopic quantum phenomena
Macroscopic quantum phenomena are processes showing quantum behavior at the macroscopic scale, rather than at the atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and sup ...
*
Pinning force Pinning force is a force acting on a pinned object from a pinning center. In solid state physics, this most often refers to the vortex pinning, the pinning of the magnetic vortices ( magnetic flux quanta, Abrikosov vortices) by different kinds of ...
*
Andreev reflection
Andreev reflection (AR), named after the Russian physicist Alexander F. Andreev, is a type of particle scattering which
occurs at interfaces between a superconductor (S) and a normal state material (N). It is a charge-transfer process by which ...
*
Josephson effect
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mech ...
*
Nielsen–Olesen vortex
In theoretical physics, a Nielsen–Olesen vortex is a point-like object localized in two spatial dimensions or, equivalently, a classical solution of field theory with the same property. This particular solution occurs if the configuration space ...
References
{{Reflist
Superconductivity
Vortices