Chemistry Reference
In-Depth Information
Φ
0
External flux,
Φ
Figure 8.16
Schematic illustration of variation of screening current with external mag-
netic flux linking a superconducting loop with one weak (Josephson)
link.
circulating in the ring, therefore, varies with applied field as indicated
schematically in fig. 8.16. A more detailed analysis of the principles of the
SQUID magnetometer is provided in several text books (e.g. Myers 1997;
Hook and Hall 1991; Tanner 1995). By appropriate design of the magne-
tometer, it is possible to measure magnetic field to very high sensitivity, of
order 10
−
11
G or less. Such devices are now available commercially. Mag-
netometers can also be designed to measure very small changes in field
gradient, achieved by having an external double coil, where the two coils
are wound in opposite directions. A constant field then gives rise to equal
and opposite flux in each half of the coil, with the double coil then only
sensitive to changes in the field, that is, the field gradient (Tanner).
8.13 AC Josephson effect
We write the superconducting order parameter as
because of its
similarity to the quantum mechanical wavefunctions found by solving
Schrödinger's equation. We saw in Chapter 1 that if
ψ(
r
)
is a solution of
the steady-state Schrödinger equationwith energy
E
n
thenwe can describe
the time dependence of this state by
φ
(
r
)
n
(
)
=
φ
(
)
(
/
)
r
,
t
r
exp
i
E
n
t
(8.67)
n
n
Likewise the superconducting order parameter of a state with energy
E
i
varies with time as
(
r
,
t
)
=|
ψ(
r
)
|
exp
(
i
θ(
t
))
(8.68)
where the phase factor
θ(
t
)
is given by
E
i
t
θ(
)
=
θ
+
t
(8.69)
0
When we apply a DC voltage,
V
, to a superconducting circuit containing a
Josephson junction, all of the voltage will be dropped across the weak link
