In superconductivity, an
Abrikosov vortex is a vortex of
supercurrentA supercurrent is a superconducting current, that is, electric current which flows without dissipation....
in a
type-II superconductorA Type-II superconductor is a superconductor characterized by the formation of vortex lattices in magnetic field. It has a continuous second order phase transition from the superconducting to the normal state within an increasing magnetic field....
. The
supercurrentA supercurrent is a superconducting current, that is, electric current which flows without dissipation....
circulates around the normal (i.e. non-superconducting) core of the vortex. The core has a size
— the
superconducting coherence lengthA Superconducting coherence length, usually denoted as \xi, can be interpreted in two different ways:* It gives approximate spatial dimension of the Cooper pair,...
(parameter of a
Ginzburg-Landau theoryIn physics, Ginzburg–Landau theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity...
). The supercurrents decay on the distance about
(
London penetration depthIn superconductors, the London penetration depth characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to 1/e times that of the magnetic field at the surface of the superconductor...
) from the core. Note that in type-II superconductors
. The circulating
supercurrentA supercurrent is a superconducting current, that is, electric current which flows without dissipation....
s induce magnetic fields with the total flux equal to a single
flux quantumThe magnetic flux quantum Φ0 is the quantum of magnetic flux passing through a superconductor. The phenomenon of flux quantization was discovered B. S. Deaver and W. M. Fairbank and, independently, by R. Doll and M. Nabauer, in 1961...
. Therefore, an Abrikosov vortex is often called a
fluxonIn physics, a fluxon is a quantum of electromagnetic flux. The term may have any of several related meanings.- Superconductivity :In the context of superconductivity, a fluxon is a small whisker of normal phase surrounded by superconducting phase. Supercurrents circulate around its center...
.
The magnetic field distribution of a single vortex far from its core can be described by
where
is a zeroth-order
Bessel functionIn mathematics, Bessel functions, first defined by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel, are canonical solutions y of Bessel's differential equation:...
. 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 superconductorA Type-II superconductor is a superconductor characterized by the formation of vortex lattices in magnetic field. It has a continuous second order phase transition from the superconducting to the normal state within an increasing magnetic field....
s.
Abrikosov vortices can be trapped in a
type-II superconductorA Type-II superconductor is a superconductor characterized by the formation of vortex lattices in magnetic field. It has a continuous second order phase transition from the superconducting to the normal state within an increasing magnetic field....
by chance, on defects, etc. Even if initially
type-II superconductorA Type-II superconductor is a superconductor characterized by the formation of vortex lattices in magnetic field. It has a continuous second order phase transition from the superconducting to the normal state within an increasing magnetic field....
contains no vortices, and one applies a magnetic field
larger than the lower critical field
(but smaller than the
upper critical field-Upper critical field:The upper critical field is the magnetic field which completely suppresses superconductivity in a Type II superconductor at 0K ....
), the field penetrates into superconductor in terms of
Abrikosov vortices. Each vortex carries one thread of magnetic field with the flux
. Abrikosov vortices form a lattice (usually triangular, may be with defects/dislocations) with the average vortex density (flux density) approximately equal to the externally applied magnetic field.
See also
- Ginzburg-Landau theory
In physics, Ginzburg–Landau theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical theory used to model superconductivity. It does not purport to explain the microscopic mechanisms giving rise to superconductivity...
- Type-II superconductor
A Type-II superconductor is a superconductor characterized by the formation of vortex lattices in magnetic field. It has a continuous second order phase transition from the superconducting to the normal state within an increasing magnetic field....
- Alexei Alexeyevich Abrikosov
Alexei Alexeyevich Abrikosov is a Soviet and Russian theoretical physicist whose main contributions are in the field of condensed matter physics. He was awarded the Nobel Prize in Physics in 2003.- Biography :...
- 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 by different kinds of the defects in a type II superconductor...
- Flux pinning
Flux pinning is the phenomenon that magnetic flux lines do not move in spite of the Lorentz force acting on them inside a current-carrying...