Chemistry Reference
In-Depth Information
critical temperature,
T
c
for aluminium and for niobium.
(
T
c
(
Al
)
=
1.2 K;
T
c
(
Nb
)
=
9.2 K; B
c
(
Al
)
=
10.5mT; B
c
(
Nb
)
=
206mT
)
.
8.5 A magnetic field
B
0
is applied parallel to the surface of a thin super-
conducting plate of thickness
d
which lies in the
x
-
y
plane. Taking
z
0 at the centre of the plate, show that the magnetic field varies
inside the plate as
=
B
(
z
)
=
B
0
cosh
(
z
/λ
)/
cosh
(
d
/
2
λ
)
L
L
Hence show that if
d
L
, the magnitude of the mean magnetisation
M
av
will be reduced from
B
0
λ
0
to
d
2
2
L
/µ
/(
λ
)(
/µ
)
. It can be shown
that this reduction in the average magnetisation leads to an enhance-
ment of the critical field
H
c
in a thin film, with
H
c
being proportional
to
12
B
0
0
(λ
/
)
H
c0
in a thin film, where
H
c0
is the critical field for a bulk
film of the same material.
d
L
8.6 Consider the superconducting circuit shown in fig. 8.20, with two
identical Josephson junctions in parallel. In the absence of a mag-
netic field, the phase difference
is the same for the two links,
so that the DC Josephson current is given by
I
θ
=
2
I
0
sin
θ
. When
a magnetic field is applied, this is no longer the case, so
B
.
Show by separately integrating around the two sides of the junction
that the total difference in phase difference between junction A and
junction B equals
q
θ
A
=
θ
/
, where
is the total magnetic flux linking
the loop, and
q
=
2
e
is the charge of a Cooper pair. Show if we set
θ
=
π/
2 at junction A, then the total DC Josephson current will vary
2
I
0
cos
2
=
(
+
(
/
))
=
(
/
)
as
I
. This is the superconducting
analogue of Young's fringes, with constructive and destructive inter-
ference leading to a sinusoidal variation of the DC Josephson current.
Show that the period of the oscillations is
I
0
1
cos
q
e
δ
=
/
=
0
.How
will the DC Josephson current vary if the two junctions are not iden-
tical, but instead link a high-
T
c
and a conventional superconductor,
as shown in fig. 8.19?
h
2
e
