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| In [[superconductivity]], the '''superconducting coherence length''', usually denoted as <math>\xi</math> (Greek lowercase ''xi''), is the characteristic exponent of the variations of the density of superconducting component.
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| In some special [[limiting case]]s, for example in the weak-coupling [[BCS theory]] it is related to characteristic Cooper pair size.
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| The superconducting coherence length is one of two parameters in the [[Ginzburg-Landau theory]] of superconductivity. It is given by:<ref name=Tinkham>{{cite book|last=Tinkham|first=M.|title=Introduction to Superconductivity, Second Edition|publisher=McGraw-Hill|location=New York, NY|year=1996|isbn=0486435032}}</ref>
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| :<math> \xi = \sqrt{\frac{\hbar^2}{2 m |\alpha|}}</math>
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| while in BCS theory
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| :<math> \xi = \frac{2\hbar v_f}{\pi \Delta}</math>
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| where <math>\hbar</math> is the [[reduced Planck constant]], <math>m</math> is the mass of a Cooper pair (twice the [[electron mass]]), <math>v_f</math> is the Fermi velocity, and <math>\Delta</math> is the superconducting energy gap.
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| The ratio ''κ'' = ''λ/ξ'', where λ is the [[London penetration depth]], is known as the Ginzburg–Landau parameter. [[Type-I superconductor]]s are those with 0 < ''κ'' < 1/√2, and [[type-II superconductor]]s are those with ''κ'' > 1/√2.
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| For temperatures ''T'' near the superconducting critical temperature ''T<sub>c</sub>'', ''ξ(T) ∝ (1-T/T<sub>c</sub>)<sup>-1</sup>''.
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| ==See also== | |
| * [[Ginzburg-Landau theory]] of superconductivity
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| * [[BCS theory]] of superconductivity
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| ==References==
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| {{reflist}}
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| {{DEFAULTSORT:Superconducting Coherence Length}}
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| [[Category:Superconductivity]]
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