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Superconductivity
and
Superfluidity
PHYS3430
Professor
Bob Cywinski
“Superconductivity is perhaps the
most remarkable physical property
in the Universe”
David Pines
Superconductivity
and
Superfluidity
PHYS3430
Professor
Bob Cywinski
“Superconductivity is perhaps the
most remarkable physical property
in the Universe”
David Pines
Superconductivity
and
Superfluidity
PHYS3430
Professor
Bob Cywinski
“Superconductivity is perhaps the
most remarkable physical property
in the Universe”
David Pines
Superconductivity
and
Superfluidity
PHYS3430
Professor
Bob Cywinski
“Superconductivity is perhaps the
most remarkable physical property
in the Universe”
David Pines
Text Books
Introduction to Superconductivity
A C Rose-Innes and E H Rhoderick
Pergamon Press
Superfluidity and Superconductivity
Dr Tilley and J Tilley
Institute of Physics Publishing
Introduction to Superconductivity
and High-Tc Materials
Good introduction to
phenomenology, without too much
maths - now quite out of date
Both topics covered well, but it flips
between the two topics too much
and tries to draw too many analogies
A good introduction, and cheap, but
now hard to get
M Cyrot and D Pavuna
World Scientific
plus appropriate chapters in Solid State Physics books
Lecture 1
Superconductivity and Superfluidity
Syllabus
Lectures will focus primarily on superconductivity but the salient features of the
phenomenon of superfluidity in liquid helium will be discussed towards the end of
the course
We shall cover the history of superconductivity and the early phenomenological
theories leading to a description of the superconducting state
The microscopic quantum mechanical basis of superconductivity will be
described, introducing the concepts of electron pairing, leading to the BCS theory
Superconductivity as a manifestation of macroscopic quantum mechanics will be
presented, together with the implication for superconducting devices, such as
SQUIDS
An overview of the principal groups of superconducting materials, and their
scientific and industrial interest will be given
Lecture 1
Superconductivity and Superfluidity
Discovery of Superconductivity
Discovered by Kamerlingh Onnes
in 1911 during first low temperature
measurements to liquefy helium
Whilst measuring the resistivity of
“pure” Hg he noticed that the electrical
resistance dropped to zero at 4.2K
In 1912 he found that the resistive
state is restored in a magnetic field or
1913
at high transport currents
Lecture 1
Superconductivity and Superfluidity
The superconducting elements
Li
Be
0.026
Na
K
Transition temperatures (K)
Critical magnetic fields at absolute zero (mT)
Mg
Ca
Sc
Ti
0.39
10
Rb
Cs
Sr
Ba
Y
La
6.0
110
Zr
V
Cr
Mn
Fe
Fe Co
C
N
O
F
Ne
Al
Si
P
S
Cl
Ar
Ge
As
Se
Br
Kr
I
Xe
At
Rn
1.14
10
Ni
Cu
Zn
Ga
0.875 1.091
(iron)
5.3
5.1
Tc=1K
Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te
(at 20GPa)
9.5
0.92 7.77
0.51 0.03
0.56
3.4
3.72
5.38
142
Nb
0.546
(Niobium)
4.7
198
9.5
141
HfTc=9K
Ta W
Re
Os
Ir
1.4
20
0.655
16.5
0.14
1.9
0.12
B
4.483 0.012
0.1
c 83
H =0.2T
7
5
3
Pt
Au
29.3
30
Hg
Tl
Pb
4.153
41
2.39
17
7.19
80
Bi
Po
Transition temperatures (K) and critical fields are generally low
Metals with the highest conductivities are not superconductors
The magnetic 3d elements are not superconducting
...or so we thought until 2001
Lecture 1
Superconductivity and Superfluidity
Superconducting transition temperature (K)
Superconductivity in alloys and oxides
160
HgBa2Ca2Cu3O9
(under pressure)
140
HgBa2Ca2Cu3O9
120
TlBaCaCuO
BiCaSrCuO
100
YBa2Cu3O7
Liquid Nitrogen
temperature (77K)
80
60
(LaBa)CuO
40
20
Hg Pb Nb
1910
Lecture 1
NbC
1930
NbN
Nb3Sn
Nb3Ge
V3Si
1950
1970
1990
Superconductivity and Superfluidity
In a metal a current is carried by free
conduction electrons - ie by plane waves
Plane waves can travel through a perfectly
periodic structure without scattering…..
….but at finite temperatures phonons destroy
the periodicity and cause resistance
resistivity
Zero resistance?
“impure metal”
T
Take, eg, pure copper with a resistivity at
room temperature of 2cm, and a
residual resistivity at 4.2K of 210-5 cm
………….a typical Cu sample would thus
have a resistance of only 210-11  at 4.2K
Lecture 1
Residual
resistivity
Even at T=0, defects such as grain
boundaries, vacancies, even surfaces give
rise to residual resistivity
T5
“ideal metal”
temperature
Superconductivity and Superfluidity
Zero resistance?
In a metal a current is carried by free
conduction electrons - ie by plane waves
Plane waves can travel through a perfectly
periodic structure without scattering…..
….but at finite temperatures phonons destroy
the periodicity and cause resistance
Even at T=0, defects such as grain
boundaries, vacancies, even surfaces give
rise to residual resistivity
Take, eg, pure copper with a resistivity at
room temperature of 2cm, and a
residual resistivity at 4.2K of 210-5 cm
………….a Cu typical sample would thus
have a resistance of only 210-11  at 4.2K
Lecture 1
Superconductivity and Superfluidity
Zero resistance?
The resistance of pure copper is so small is there really much
difference between it and that of a superconductor?
Take an electromagnet consisting of a 20cm diameter coil with
10000 turns of 0.3mmx0.3mm pure copper wire
R300K = 1 k
R4.2K= 0.01 
Pass a typical current of 20 Amps through the coil
P300K = 0.4MW
P4.2K= 4 Watts
At 4.2K this is more than enough to boil off the liquid
helium coolant!
Lecture 1
Superconductivity and Superfluidity
Measuring zero resistance
Can we determine an upper limit for the
resistivity of a superconductor?
This is done by injecting current into a
loop of superconductor
The current generates a magnetic field,
and the magnitude of this field is
measured as a function of time
i
This enables the decay constant of the
effective R-L circuit to be measured:
B( t )  i( t )  i(0)e(R / L )t
Using this technique, no discernable
change in current was observed over
two years:
sc  10-24.cm !!
Lecture 1
B
Superconductivity and Superfluidity
Measuring zero resistance
In practice the superconducting ring is cooled in a
uniform magnetic field of flux density BA to below TC
If the area of the ring is A, the flux threading the loop
is
  AB A
Now change BA: by Lenz’s law a current will flow
to oppose the change, hence
BA
Cool the ring in an applied
magnetic field - then
decrease the field to zero
Lecture 2
Superconductivity and Superfluidity
Measuring zero resistance
In practice the superconducting ring is cooled in a
uniform magnetic field of flux density BA to below TC
If the area of the ring is A, the flux threading the loop
is
  AB A
Now change BA: by Lenz’s law a current will flow
to oppose the change, hence
dB
di
emf  A A  Ri  L
dt
dt
In a “normal” loop, the Ri term quickly kills the
current, but if R=0
dB
di
A A L
dt
dt
Therefore Li+ABA = constant (=total flux in loop)
i
Currents will flow to
maintain the field in the
loop…. forever
So if R=0 the current will persist forever !!
Superconductivity and Superfluidity
…..and the corollary
If
A
dBA
di
 Ri  L
dt
dt
and Ri = 0 such that
Li+ABA = constant (=total flux in loop)
The flux in the superconducting loop must remain constant
however the field changes
Therefore if a loop is cooled into the superconducting state in zero
field and then the magnetic field is applied supercurrents must
circulate to maintain the total flux threading the loop at zero.
A superconducting cylinder can therefore provide perfect
magnetic shielding
A Meissner Shield
Lecture 2
Superconductivity and Superfluidity