In 1950, Ginzburg and Landau introduced the so-called *superconducting
order parameter*
to describe the nonlocality of the
superconducting properties.
can be thought of as a
measure of the order in the superconducting state at position below *T*_{c}. It has the properties that
as
,
and
(i.e. the local density of superconducting electrons). At the time
Ginzburg-Landau (GL) theory was developed, the nature of the superconducting
carriers was yet to be determined. Interpreting *m*^{*} as the
effective mass and *q* as the charge of the
fundamental superconducting particles (whatever they
may be), they derived the penetration depth as:

where is the value of deep inside the superconductor (i.e. its equilibrium value). The coherence length defined in the GL-formalism is:

where is a temperature-dependent coefficient in the series expansion of the free energy (see [19]). As written, (2.6) and (2.7) suggest that the penetration depth and the coherence length are temperature dependent quantities. Eq. (2.7) is closely related to the Pippard coherence length defined in Eq. (2.4). In GL-theory, the coherence length is the characteristic length for variations in . One noteable difference is that Pippard's coherence length is independent of temperature. In fact in the dirty limit reduces to Eq. (2.4). Near the transition temperature

The variation of and with temperture near

2001-09-28