CLASSICAL VIEWPOINT
FERMI-DIRAC STATISTICS
BOSE-EINSTEIN STATISTICS
BCS THEORY
MEISSNER EFFECT
SUPERCONDUCTOR TYPES
HISTORY
APPLICATIONS
Honors Contract Spring 2007
Brian Gustin
Mentor: Dr. Cristian Bahrim
1
RESISTANCE
e-
ρ = ρ 0 (1 + α ∗ ∆T )
where α is the temperature coefficient
of resistivity (α > 0)
ρ ≠0 because of impurities and defects
in the crystal lattice at T=0K.
R=ESISTIVITY
For conductors as temperature decreases resistivity
also decreases, but it reaches a constant value near
zero Kelvin due to impurities and imperfections in
the arrangement of atoms.
TEMPERATURE (K)
2
1
f FD (E ) = ( E − E )
F
kT + 1
e
E > EF @ T = 0K fFD = 0
E < EF @ T = 0K fFD = 1
T=0 Kelvin
T >> 0 Kelvin
EF
@ T ≠ 0K EF + kT
k = 8.6 x 10-2 meV/T (Boltzman constant)
@ T = 300K add kT = 25meV
3
1
f BE (E ) =
E
e
kT
−1
T=0K E=∞ → fBE = 0
E=0 → fBE = ∞
All bosons will condense on the lowest energy
level in the solid.
4
• Normal solid states:
p(E) = g(E) * fFD (E)
where for electrons in metals
g(E) ~ E1/2 (spin ↑/spin ↓)
EF
T = Tc
• Superconductor electronic states:
• If T > Tc then Cooper pairs form.
• Their binding energy Eg ~ 10-3 eV
• Eg can be broken with λ ~ 1.2 mm
• As T decreases towards Tc, the
energy gap Eg becomes smaller.
• If T < Tc then Eg 0 and Cooper
pairs are released.
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• Fermions are particles with a spin ½
• Bosons are particles with an integer spin.
(e.g. Cooper pairs have a spin of 0)
• In a normal conducting material electrons
collide with the crystal lattice creating resistance.
• In superconductors @ low T the electrons pair
into a new boson (the Cooper Pair).
• When an electron of a Cooper pair collides
with the lattice, it creates a disturbance that
is transmitted solely to the other electron in
the pair through the crystal lattice. This longrange interaction between electrons in the
Cooper pairs is because of the conservation
of linear momentum.
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•Effect: Superconductors
expel all magnetic field
lines of an external solid
magnet, and the magnet
levitates.
•If a large enough
magnetic field is applied
the superconductive
behaviour disappears.
•This value of B is known
as being the critical field. 7
Element
•Pure Elements
•When cooled below a critical
temperature, TC, these elements
exhibit zero resistance.
•These materials are usually
insulators in a normal state.
•Limited applicability and
practicality because of small
critical field values.
W
Ir
Lu
Hf
Ru
Os
Mo
Zr
Cd
U
Ti
Zn
Ga
Tc
0.015
0.1
0.1
0.1
0.5
0.7
0.92
0.546
0.56
0.2
0.39
0.85
1.083
Element
Th
Re
Ti
In
Sn
Hg
Ta
V
La
Pb
Tc
Nib
Tc
1.4
1.4
2.39
3.408
3.722
4.153
4.47
5.38
6
7.193
7.77
9.46
8
•Usually made from alloys
•Exhibit higher critical fields
•Co-exist in a normal and
superconducting state.
This is sometimes called
a vortex state because of the
vortices of superconducting
regions (small islands of
supercoductivity).
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•For T >> Tc normal states are closely packed
together and make the material insulating.
Normal Regions
Superconducting Region
•For T < Tc the normal states become smaller
and the magnetic field that penetrates these
small regions does not encounter any
resistance, so the material shows
superconductive behavior.
•The area of the normal states has radius of
about 300nm in type II superconductors .
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1. The phenomenom was first discovered in
1911 by a Dutch physicist, Keike Kamerlingh
Onnes.
a.Onnes used mercury as his
superconductor.
b.Critical temperature of Mercury is about
4Kelvin (liquid helium).
2. 1987 Dr. Ching Wu Chu reports a critical
temperature of 98 K
a.98 K was a breakthrough Tc because
liquid nitrogen (77 Kelvin) could now be
used to obtain a superconducting state.
Material
Tc(K)
Gallium
1.1
Aluminum
1.2
Indium
3.4
Tin
3.7
Mercury
4.2
Lead
7.2
Niobium
9.3
Niobium-Tin
17.9
La-Ba-Cu-oxide
30
Y-Ba-Cu-oxide
92
Tl-Ba-Cu-Oxide
125
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•“Space Efficieny”
e.g. 18000 pounds of copper wire
were replaced by 250 pounds of
superconductive cable.
•No energy loss due to heat
•Transformers can be made smaller
and last longer.
•An annual budget savings of
almost 40% could be obtained with
the replacement of copper wires
with superconducting cables.
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• Motors account for 70% of the power
consumption in domestic manufacturing
and 55% in the entire United States.
High power electric motor
produced for the US Navy
(July 2001).
• Using high-temperature superconducting
(HTS) coils instead of traditional copper
windings, this supermotor can produce
more power in less space, and use less
energy while doing it (high efficiency).
• Most cruise ships and large naval vessels
are switching to electric propulsion.
• These units are quieter than traditional
electric motors.
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• A superconducting processor does not
generate much heat.
• This processor is only four bits compared
with most of today’s 32 or 64 bit processors.
• However, this four bit processor is 500
times faster than today’s common Intel
processor.
Japan
•NASA and NSF are working for
developing a superconducting chip.
14
Home Page. Superconductors.org. 12 April 2007.
<http://www.superconductors.org>
Home Page. hyperphysics.com. 12 April 2007.
<http://www.hyperphysics.com>
Krane, Kenneth. Modern Physics: Second Edition. John Wiley
& Sons Inc, 1996.
Mayo, Jonathan L. Superconductivity: The Threshold of a New
Technology. TAB Books, 1988.
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