Superconducting coherence length

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:^[1]

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

while in BCS theory:^[2]

$\xi = \frac{\hbar v_f}{\pi \Delta}$

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 $\kappa = \lambda/\xi$, where $\lambda$ is the London penetration depth, is known as the Ginzburg–Landau parameter. Type-I superconductors are those with $0<\kappa<1/\sqrt{2}$, and type-II superconductors are those with $\kappa>1/\sqrt{2}$.

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

1. Tinkham, M. (1996). Introduction to Superconductivity, Second Edition. New York, NY: McGraw-Hill. ISBN 0486435032.
2. Annett, James (2004). Superconductivity, Superfluids and Condensates. New York: Oxford university press. p. 62. ISBN 978-0-19-850756-7.