10 Ë 1 Fundamentals of superconductivity
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
휉 0 =ℏ휐F
휋훥 0
= 0. 18 ℏ휐F
kBTc, (1.26)
whereℏis the Planck constant,h, divided by 2휋,vFis the Fermi velocity, and
2 훥 0 = 3. 528 kBTcis the value of the superconducting energy gapEgat zero tempe-
rature in the superconducting state,kBis the Boltzmann constant, and휉 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 pathl
and the coherence length휉 0 , Pippard [17] gives an empirical formula for the effective
coherence length,휉l, for an impure conductor,
1
휉l=1
휉 0 +
1
훼l, (1.27)where훼is a constant and is about 0.8. In this case, the effective penetration
depth [18]휆eis
휆e=휆L 1 +휉 0
l1 / 2. (1.28)
The HTSC materials differ remarkably from conventional superconductors in which
they have much smaller coherence lengths. In the LTSC materials,휉is the order
of a few thousand angstroms, but in the HTSC materials, it is in the order of 1
to 10 Å. The small size of휉affects the HTSC thermodynamic and electromagnetic
properties.
The coherence length휉 0 is related to the GL coherence length,휉GL, through the
expression
휉GL(T)= 훼휉^0
1 −TT
c
2
¡, (1.29)
where훼is a constant.
The ratio of the penetration depths휆Land the coherence lengths휉is called as the
GL parameter휅:
휅=휆L/휉. (1.30)휅is an important parameter that characterizes the superconducting material and
distinguishes type I from type II superconductors.