Superconducting Coherence Length
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In
superconductivity Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
, the superconducting coherence length, usually denoted as \xi (Greek lowercase ''xi''), is the characteristic exponent of the variations of the density of superconducting component. The superconducting coherence length is one of two parameters in the
Ginzburg–Landau theory In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenol ...
of superconductivity. It is given by: : \xi = \sqrt where \alpha is a constant in the Ginzburg–Landau equation for \psi with the form \alpha_0 (T-T_c). In Landau mean-field theory, at temperatures ''T'' near the superconducting critical temperature ''Tc'' , ''ξ(T) ∝ (1-T/Tc)−1/2''. Up to a factor of \sqrt, it is equivalent characteristic exponent describing a recovery of the order parameter away from a perturbation in the theory of the second order phase transitions. In some special limiting cases, for example in the weak-coupling
BCS theory BCS theory or Bardeen–Cooper–Schrieffer theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes sup ...
of isotropic s-wave superconductor it is related to characteristic Cooper pair size: : \xi_ = \frac where \hbar is the
reduced Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivale ...
, m is the mass of a Cooper pair (twice the
electron mass The electron mass (symbol: ''m''e) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of a ...
), v_f is the Fermi velocity, and \Delta is the
superconducting energy gap In solid-state physics, an energy gap is an energy range in a solid where no electron states exist, i.e. an energy range where the density of states vanishes. Especially in condensed-matter physics, an energy gap is often known more abstractly as ...
. The superconducting coherence length is a measure of the size of a Cooper pair (distance between the two electrons) and is of the order of 10^ cm. The electron near or at the Fermi surface moving through the lattice of a metal produces behind itself an attractive potential of range of the order of 3\times 10^ cm, the lattice distance being of order 10^ cm. For a very authoritative explanation based on physical intuition see the CERN article by V.F. Weisskopf. The ratio \kappa = \lambda/\xi , where \lambda is the
London penetration depth In superconductors, the London penetration depth (usually denoted as \lambda or \lambda_L) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to e^ times that of the magnetic field at the surface ...
, is known as the Ginzburg–Landau parameter.
Type-I superconductor The interior of a bulk superconductor cannot be penetrated by a weak magnetic field, a phenomenon known as the Meissner effect. When the applied magnetic field becomes too large, superconductivity breaks down. Superconductors can be divided int ...
s are those with 0<\kappa<1/\sqrt, and
type-II superconductor In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the ...
s are those with \kappa>1/\sqrt. In strong-coupling, anisotropic and multi-component theories these expressions are modified.


See also

*
Ginzburg–Landau theory In physics, Ginzburg–Landau theory, often called Landau–Ginzburg theory, named after Vitaly Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenol ...
of superconductivity *
BCS theory BCS theory or Bardeen–Cooper–Schrieffer theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes sup ...
of superconductivity *
London penetration depth In superconductors, the London penetration depth (usually denoted as \lambda or \lambda_L) characterizes the distance to which a magnetic field penetrates into a superconductor and becomes equal to e^ times that of the magnetic field at the surface ...


References

{{DEFAULTSORT:Superconducting Coherence Length Superconductivity