Chemistry Reference
In-Depth Information
then equals 2
π
n
=
hn
, where
n
is an integer, while the right-hand side
equals
is the magnetic flux linking the loop (eq. (8.9)).
Re-arranging eq. (8.63) we find that the magnetic flux
−
2
e
, where
linking a closed
superconducting ring is quantised, with
hn
2
e
=
(8.64)
where the factor of 2
e
arises because the electrons are bound together in
Cooper pairs. Flux quantisation has been well confirmed experimentally
for conventional superconductors.
8.12 Josephson tunnelling
We saw in Section 8.8 that when two superconductors are separated by
an insulating layer, then electrons can tunnel through the layer, allowing
current to flow for a sufficiently large applied voltage. Even more striking
effects are observed if the insulating layer is very thin, so that the super-
conducting order parameters,
from both sides of the layer become
weakly coupled. This effect was first predicted in a short paper by Brian
Josephson, based on a theoretical analysis he carried out while still a stu-
dent at Cambridge (Josephson 1962), and for which he was awarded the
Nobel prize in 1973.
If we place an insulating layer next to a superconductor, the supercon-
ducting order parameter,
ψ(
r
)
will decay exponentially into the insulating
layer, analogous to the exponential decay of a bound state wavefunction
outside a square quantumwell (Chapter 1). If two superconducting regions
are separated by a thick insulating layer there will be no overlap between
their order parameters in the insulating layer; the two superconducting
regions will be decoupled, and act independently of each other. However,
for a sufficiently thin insulating layer
ψ(
r
)
the superconducting elec-
tron density will never drop fully to zero in the insulating layer, and so
the two regions will be weakly coupled, as illustrated in fig. 8.15(a), where
the weak link is formed by oxidising a small cross-section of what would
otherwise be a superconducting ring. Because both sides of the link are
at the same temperature, the superconducting electron density, and hence
the magnitude of the superconducting order parameter should be equal
on each side of the link, with magnitude say
(
∼
10Å
)
ψ
0
. We define the insulating
layer in the region
−
b
/
2
≤
x
≤
b
/
2, and allow for a difference in the phase,
θ
, of the order parameter on either side of the link, with
θ
=
θ
L
on the
left-hand side and
R
on the right-hand side. The superconducting
order parameter then varies in the insulating layer as (fig. 8.15(b))
θ
=
θ
e
i
θ
L
−
κ(
x
+
d
/
2
)
+
e
i
θ
R
+
κ(
x
−
d
/
2
)
)
ψ(
r
)
=
ψ
(
(8.65)
0
