Superconducting coherence length
In superconductivity, the superconducting coherence length, usually denoted as , is the characteristic exponent of the variations of the density of superconducting component.
The superconducting coherence length is one of two parameters in the Ginzburg–Landau theory of superconductivity. It is given by:
where is a constant in the Ginzburg–Landau equation for with the form.
In Landau mean-field theory, at temperatures T near the superconducting critical temperature Tc, ξ ∝ −1/2. Up to a factor of, it is equivalent characteristic exponent describing a recovery of the order parameter away from a perturbation in the theory of the second order phase transitions.
In some special limiting cases, for example in the weak-coupling BCS theory of isotropic s-wave superconductor it is related to characteristic Cooper pair size:
where is the reduced Planck constant, is the mass of a Cooper pair, is the Fermi velocity, and is the superconducting energy gap.
The ratio, where is the London penetration depth, is known as the Ginzburg–Landau parameter. Type-I superconductors are those with, and type-II superconductors are those with.
In strong-coupling, anisotropic and multi-component theories these expressions are modified.
