superconductivity and superfluidity phys3430 professor bob cywinski “superconductivity is perhaps...
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SuperconductivitySuperconductivityandandSuperfluiditySuperfluidity
PHYS3430PHYS3430
Professor Professor Bob CywinskiBob Cywinski “Superconductivity is perhaps the
most remarkable physical property in the Universe” David Pines
SuperconductivitySuperconductivityandandSuperfluiditySuperfluidity
PHYS3430PHYS3430
Professor Professor Bob CywinskiBob Cywinski “Superconductivity is perhaps the
most remarkable physical property in the Universe” David Pines
SuperconductivitySuperconductivityandandSuperfluiditySuperfluidity
PHYS3430PHYS3430
Professor Professor Bob CywinskiBob Cywinski “Superconductivity is perhaps the
most remarkable physical property in the Universe” David Pines
SuperconductivitySuperconductivityandandSuperfluiditySuperfluidity
PHYS3430PHYS3430
Professor Professor Bob CywinskiBob Cywinski “Superconductivity is perhaps the
most remarkable physical property in the Universe” David Pines
Superconductivity and Superfluidity
Text BooksText Books
Introduction to SuperconductivityA C Rose-Innes and E H RhoderickPergamon Press
Superfluidity and SuperconductivityDr Tilley and J TilleyInstitute of Physics Publishing
Introduction to Superconductivity and High-Tc MaterialsM Cyrot and D PavunaWorld Scientific
plus appropriate chapters in Solid State Physics books
Good introduction to phenomenology, without too much maths - now quite out of date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
Lecture 1
Superconductivity and Superfluidity
SyllabusSyllabus
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 SuperconductivityDiscovery of Superconductivity
Whilst measuring the resistivity of “pure” Hg he noticed that the electrical resistance dropped to zero at 4.2K
Discovered by Kamerlingh Onnes in 1911 during first low temperature measurements to liquefy helium
In 1912 he found that the resistive state is restored in a magnetic field or at high transport currents 19131913
Lecture 1
Superconductivity and Superfluidity
The superconducting elementsThe superconducting elements
Li Be0.026
B C N O F Ne
Na Mg Al1.1410
Si P S Cl Ar
K Ca Sc Ti0.3910
V5.38142
Cr Mn Fe Co Ni Cu Zn0.875
5.3
Ga1.091
5.1
Ge As Se Br Kr
Rb Sr Y Zr0.546
4.7
Nb9.5198
Mo0.929.5
Tc7.77141
Ru0.51
7
Rh0.03
5
Pd Ag Cd0.56
3
In3.429.3
Sn3.7230
Sb Te I Xe
Cs Ba La6.0110
Hf0.12
Ta4.483
83
W0.012
0.1
Re1.420
Os0.65516.5
Ir0.141.9
Pt Au Hg4.153
41
Tl2.3917
Pb7.1980
Bi Po At Rn
Transition temperatures (K)Critical magnetic fields at absolute zero (mT)
Transition temperatures (K) and critical fields are generally low
Metals with the highest conductivities are not superconductors
The magnetic 3d elements are not superconducting
Nb(Niobium)
Tc=9KHc=0.2T
Fe(iron)Tc=1K
(at 20GPa)
Fe(iron)Tc=1K
(at 20GPa)
...or so we thought until 2001
Lecture 1
Superconductivity and Superfluidity
1910 1930 1950 1970 1990
20
40
60
80
100
120
140
160
Su
per
con
du
ctin
g t
ran
siti
on
tem
per
atu
re (
K)
Superconductivity in alloys and oxidesSuperconductivity in alloys and oxides
Hg Pb NbNbCNbC NbNNbN
V3SiV3Si
Nb3SnNb3Sn Nb3GeNb3Ge
(LaBa)CuO(LaBa)CuO
YBa2Cu3O7YBa2Cu3O7
BiCaSrCuOBiCaSrCuO
TlBaCaCuOTlBaCaCuO
HgBa2Ca2Cu3O9HgBa2Ca2Cu3O9
HgBa2Ca2Cu3O9
(under pressure)
HgBa2Ca2Cu3O9
(under pressure)
Liquid Nitrogen temperature (77K)
Lecture 1
Superconductivity and Superfluidity
Zero resistance?Zero resistance?
In a metal a current is carried by free conduction electrons - ie by plane waves
temperature
resi
stiv
ity
Plane waves can travel through a perfectly periodic structure without scattering…..
….but at finite temperatures phonons destroy the periodicity and cause resistance
“ideal metal”T5
T
Take, eg, pure copper with a resistivity at room temperature of 2cm, and a residual resistivity at 4.2K of 210-5 cm
………….a typical Cu sample would thus have a resistance of only 210-11 at 4.2K
Even at T=0, defects such as grain boundaries, vacancies, even surfaces give rise to residual resistivity
Re
sid
ua
l re
sist
ivity
“impure metal”
Lecture 1
Superconductivity and Superfluidity
Zero resistance?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 2cm, and a residual resistivity at 4.2K of 210-5 cm
………….a Cu typical sample would thus have a resistance of only 210-11 at 4.2K
Lecture 1
Superconductivity and Superfluidity
Zero resistance? 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 resistanceMeasuring zero resistance
Can we determine an upper limit for the resistivity of a superconductor?
This enables the decay constant of the effective R-L circuit to be measured:
t)L/R(e)0(i)t(i)t(B
Using this technique, no discernable change in current was observed over two years:
sc 10-24.cm !!
This is done by injecting current into a loop of superconductor
iThe current generates a magnetic field, and the magnitude of this field is measured as a function of time
B
Lecture 1
Superconductivity and Superfluidity
Measuring zero resistanceMeasuring 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
AAB
BA
Cool the ring in an applied magnetic field -
Now change BA: by Lenz’s law a current will flow to oppose the change, hence
then decrease the field to zero
Lecture 2
Superconductivity and Superfluidity
Measuring zero resistanceMeasuring 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
AAB
Now change BA: by Lenz’s law a current will flow to oppose the change, hence
dtdi
LRidt
dBA A
In a “normal” loop, the Ri term quickly kills the current, but if R=0
dtdi
Ldt
dBA A
Therefore Li+ABA = constant (=total flux in loop)
i
Currents will flow to maintain the field in the loop….
So if R=0 the current will persist forever !!
forever
emfemf
Superconductivity and Superfluidity
……..and the corollary..and the corollary
Li+ABA = constant (=total flux in loop)
dtdi
LRidt
dBA A If
and Ri = 0 such that
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