Superconducting coherence length

In superconductivity, the superconducting coherence length, usually denoted as ξ {displaystyle xi } (Greek lowercase xi), is the characteristic exponent of the variations of the density of superconducting component. In superconductivity, the superconducting coherence length, usually denoted as ξ {displaystyle xi } (Greek lowercase xi), 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 α {displaystyle alpha } is a constant in the Ginzburg-Landau equation for ψ {displaystyle psi } with the form α 0 ( T − T c ) {displaystyle alpha _{0}(T-T_{c})} . In Landau mean-field theory, at temperatures T near the superconducting critical temperature Tc , ξ(T) ∝ (1-T/Tc)−1. Up to a factor of 2 {displaystyle {sqrt {2}}} , 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 ℏ {displaystyle hbar } is the reduced Planck constant, m {displaystyle m} is the mass of a Cooper pair (twice the electron mass), v f {displaystyle v_{f}} is the Fermi velocity, and Δ {displaystyle Delta } is the superconducting energy gap. The ratio κ = λ / ξ {displaystyle kappa =lambda /xi } , where λ {displaystyle lambda } is the London penetration depth, is known as the Ginzburg–Landau parameter. Type-I superconductors are those with 0 < κ < 1 / 2 {displaystyle 0<kappa <1/{sqrt {2}}} , and type-II superconductors are those with κ > 1 / 2 {displaystyle kappa >1/{sqrt {2}}} . In strong-coupling, anisotropic and multi-component theories these expressions are modified .