Factorial moment generating function

In superconductivity, the superconducting coherence length, usually denoted as $\xi$ (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:

$\xi ={\sqrt {\frac {\hbar ^{2}}{2m|\alpha |}}}$

while in BCS theory

$\xi ={\frac {2\hbar v_{f}}{\pi \Delta }}$

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

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

See also

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

References

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