1.7　Coherence length

The coherence length ξ is one of the most important parameters describing su perconductivity.It can be intuitively understood as the mutual correlation length between which the two electrons that constitute the Cooper pair.It refers to the space scale of the electronic wave function.The BCS theory gives the coherence length as

where is the Planck constant, h，divided by 2π，vF is the Fermi velocity, and 2Δ0 =3.528kB Tc is the value of the superconducting energy gap Eg at zero temperature in the superconducting state, kB is the Boltzmann constant, and ξ 0 is the coherence length at zero temperature of a pure（without impurities）material.

When there is only a small size difference between the electron mean free path l and the coherence length ξ 0，Pippard17gives an empirical formula for the effective coherence length， ξ l ，for an impure conductor，

whereαis a constant and is about 0.8.In this case, the effective penetration depth18λe is

The HTSC materials differ remarkably from conventional superconductors in which they have much smaller coherence lengths.In the LTSC materials， ξ is the order of a few thousand angstroms, but in the HTSC materials it is in the order of 1 to 10 angstroms.The small size of ξ affects the HTSC thermodynamic and electromagnetic properties.

The coherence length ξ 0 is related to the Ginzburg-Landau coherence length， ξ GL ，through the expression

whereαis a constant.

The ratio of the penetration depths λL and the coherence lengths ξ is called as the Ginzburg-Landau（GL）parameterκ：

κis an important parameter that characterizes the superconducting material and distinguishes type I from type II superconductors.

The coherence lengths ξ of the HTSC materials have strong anisotropy.The conductivity along the chains（b-axis）is more than twice that in the a-axis direc tion which is perpendicular to the chains19.This results in large anisotropy of the coherence lengths and the values of the superconducting gap at the same critical temperature.