1.7 Coherence length Ë 9For the special case of a semi-infinite superconductor with a flat boundary within
free space, if the magnetic field outside the superconductor is constant and parallel
to the superconducting boundary plane, the differential equation (1.19) becomes
one-dimensional with a solution
B(x)=B( 0 )exp −x¾ m
휇 0 nse^2
1 / 2
¡=B( 0 )exp(−x/휆L), (1.22)whereB(0) is the magnetic field at the surface of the superconductor. Here we see that
when a magnetic field is present, superconducting currents are induced to shield the
magnetic field in the interior of a superconductor. The physical meaning of the London
penetration depth휆Lcan easily be understood.
Thus, the London equations imply a characteristic length scale휆Lover which
external magnetic field is exponentially suppressed.
휆L( 0 )={ m
휇 0 e^2 ns, (1.23)
where휆L( 0 )is the penetration depth at the absolute zero and is one of the in-
herent characteristic parameters of a superconductor. According to the temperature
dependence of the density of superconducting electrons in the two-fluid model, the
penetration depth depends on temperature (BCS calculation also gives a similar
relationship) as shown below,
휆L(T)={ m
휇 0 e^2 ns(T)= 휆L(^0 )
[ 1 −t^4 ]^1 /^2, (1.24)
wheret=T/Tc. Close toTc,휆Ltends to infinity, and at a temperature very close toTc,
Eq. (1.24) can be expressed as
휆L(T)=^1
2
휆L( 0 )( 1 −t)−(^12)
. (1.25)
It should be noted that for superconductors in the superconducting state, the field
can only penetrate into the superconductor by a penetration depth휆Lfor both DC and
AC magnetic fields. For superconductors in the normal state, there is no penetration
depth, namely the magnetic field cannot be shielded.
1.7 Coherence length
The coherence length휉is one of the most important parameters describing supercon-
ductivity. It can be intuitively understood as the mutual correlation length between