60
4 Fundamental Electromagnetic Properties of Superconductors
where ξ is the coherence length given by
ξ =
(2m ∗ |α|)
1/2
=
2
√
2eμ 0 H c λ
.
(4.29)
We can chose a real number for ψ. Since the magnetic field is not applied, ψ is close
to 1. Hence, if we put as ψ = 1 − f , f is much smaller than 1. Thus, (4.28) is reduced
to
ξ
2 d
2 f
dx 2 − 2f = 0.
(4.30)
The solution of this equation is given by
f = f 0 exp
−
√
2|x|
ξ
.
(4.31)
This shows that ξ is the characteristic length of the spatial variation in the order
parameter.
The spatial variation in the order parameter around the center of a quantized
magnetic flux packet is also given by ξ . The structure of the central region of the
quantized magnetic flux in type II superconductors is shown in Fig. 4.6. The region
of radius ξ around the center of the quantized magnetic flux is called the normal core.
The coherence length in the Ginzburg–Landau theory given by (4.29) increases with
increasing temperature, because |α| varies in proportion to 1−T /T c . This is different
from the coherence length ξ 0 in the Bardeen-Cooper-Schrieffer (BCS) theory, which
Fig. 4.6 Spatial structure of the order parameter and magnetic flux density in the central region of
an isolated quantized magnetic flux packet