Superconducting coherence length

In superconductivity, the superconducting coherence length, usually denoted as ξ (Greek lowercase xi), is the characteristic exponent of the variations of the density of superconducting component.

In some special limiting cases, for example in the weak-coupling BCS theory it is related to characteristic Cooper pair size.

The superconducting coherence length is one of two parameters in the Ginzburg-Landau theory of superconductivity. It is given by:

while in BCS theory:

where ℏ is the reduced Planck constant, m is the mass of a Cooper pair (twice the electron mass), v f is the Fermi velocity, and Δ is the superconducting energy gap.

The ratio κ = λ / ξ , where λ is the London penetration depth, is known as the Ginzburg–Landau parameter. Type-I superconductors are those with 0 < κ < 1 / 2 , and type-II superconductors are those with κ > 1 / 2 .

For temperatures T near the superconducting critical temperature T_c , ξ(T) ∝ (1-T/T_c)⁻¹.