Superconducting coherence length

In superconductivity, the superconducting coherence length, usually denoted as $\xi$ (Greek lowercase xi), can be interpreted as:

• the approximate size of the Cooper pair, or
• the length scale over which the superconducting order parameter changes considerably.

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

$\xi ={\sqrt {\frac {\hbar ^{2}}{2m|\alpha |}}}={\frac {2\hbar v_{f}}{\pi \Delta }}$

where $\hbar$ is the reduced Planck constant, $m$ is the mass of a Cooper pair (twice the electron mass), $v_{f}$ is the velocity of Cooper pairs, and $\Delta$ 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 those with κ > 1/√2.

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

See also

• Phenomenological Ginzburg-Landau theory of superconductivity
• Microscopic BCS theory of superconductivity