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The purity of a superconductor is characterized by the ratio
.
is the coherence length of the pure material, and is given by
Eq. (2.4). l is the electron mean free path, defined as:

(9) 
where
is the time interval between collisions of
conduction electrons with
impurities in the sample. The magnitude of
is determined in the
normal state. A sample is clean if
,
and dirty
if
[20]. The actual coherence length when
impurities are considered, is dependent upon the mean free path l.
Intuitively, one can define an effective coherence length
such that [13,17]:

(10) 
According to Eq. (2.10), the coherence length
becomes
shorter with decreasing l, so that in the dirty limit:

(11) 
and in the clean limit:

(12) 
Eq. (2.11) and Eq. (2.12) are valid only for T=0K.
In the clean limit (
)
at T=0K, the magnetic penetration
depth is
the London penetration depth given in
Eq. (2.1). The actual
coherence length
and the observed penetration depth
as determined by microscopic theory are given in the clean limit
(
)
as [21]:

(13) 

(14) 
and in the dirty limit (
):

(15) 

(16) 
where Equations (2.13) through (2.16)
are valid only in the neighborhood of T_{c},
such that
[22].
The important result is that according to Eqs.(2.15) and
(2.16), as l decreases (i.e. the superconductor becomes
more impure),
increases, while
decreases. Thus
at all temperatures in an impure material. The
hightemperature superconductors have short coherence lengths on the
order of
to 15Å. Since the electron mean free path
l is typically Å in these materials, then they are well
within the clean limit [23].
Next: BCS Theory for Conventional Superconductors
Up: Magnetic Properties of Conventional Superconductors
Previous: GinzburgLandau Theory
Jess H. Brewer
20010928