Chemistry Reference
In-Depth Information
120
80
S
40
N
0
1
2
3
T
(K)
4
5
6
Figure 8.12
The variation in the heat capacity,
c
v
, of a superconducting (S) and normal
metal (N), at and below the superconducting tranisition temperature,
T
c
(after Corak
et al
. 1956).
Further evidence for
the superconducting energy gap,
and its
temperature dependence, comes from a variety of sources.
1 A normal metal absorbs microwaves and far infra-red radiation, by
exciting electrons from just below to just above the Fermi energy. In
a superconductor at zero temperature, there is an absorption edge at
h
below which the superconductor is perfectly reflecting to
incident photons.
ν
=
2
(
0
)
2
The low-temperature electron specific heat,
c
v
, varies exponentially
with temperature, as
c
v
∼
exp
(
−
/
kT
)
in a superconductor, compared
T
, in a normal metal (fig. 8.12). The differ-
ence arises because energy can only be added to the electrons in the
superconductor by exciting electrons across the energy gap, breaking
Cooper pairs to create single electron states above the Fermi energy,
E
F
.
3 Consider two normal metals separated at low temperature by a very
thin insulating layer (fig. 8.13a(i)). For a sufficiently thin insulator,
the two metals will share the same Fermi energy,
E
F
(fig.8.13a(i)). If
a voltage,
V
, is now applied across the structure, most of the potential
drop will occur across the insulating layer (fig.8.13a(ii)), giving rise to
a current due to electrons tunnelling from one metal to the other. The
current is predicted, and observed, to increase linearly with applied
field,
V
, due to the linear shift in the the relative positions of the Fermi
energies (fig. 8.13a(iii)). By contrast, when two superconductors are
separated by a thin insulator (fig. 8.13b(i)), little current is observed at
a very low applied voltage
V
(fig. 8.13b(iii)), because electrons cannot
to a linear variation,
c
v
∼
