Chemistry Reference
In-Depth Information
0.01
T
c
N
SC
0
1
2
T
(K)
3
4
Figure 8.8
Variation of the entropy,
S
, with temperature in the normal (N) and
superconducting (SC) states of a metal (after Keesom and van Laer 1938).
which are of order 10
−
4
eV, indicating it is most unlikely that all of the
electrons gain energy in the superconducting transition.
We can instead apply an argument analogous to that usedwhen estimat-
ing the paramagnetic susceptibility of a metal in Chapter 6, where we saw
that electrons within an energy
µ
B
B
of the Fermi energy gained energy of
order
B
B
by flipping their spin direction. We presume here that the super-
conducting transition is due to those electrons within an energy
µ
2
of the
Fermi energy,
E
F
, and that each of these electrons gains energy of order
ε
ε
2
through the superconducting interaction. We estimate the number of such
electrons per unit volume,
n
sc
,as
n
sc
≈
g
(
E
F
)ε
(8.44)
2
(
)
where
g
is the density of states at the Fermi energy in the normal metal.
It can be shown from eq. (5.15) that
g
E
F
2
3
for a free-electron
metal. Substituting this into eq. (8.44), we can estimate that
(
E
F
)
=
(
N
/
E
F
)
n
sc
N
∼
ε
2
E
F
(8.45)
where we drop the factor of
3
, because we are just making an order of
magnitude estimate. The total energy gained per unit volume by these
n
sc
superconducting electrons equals
N
1
2
0
B
2
ε
(
=
µ
)
,
n
sc
ε
=
N
ε
1
,sothat
1
2
E
F
ε
1
ε
∼
(8.46)
2
ε
2
