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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

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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.

( )T∆∗+= αρρ 10

R=

ES

IST

IVIT

Y

TEMPERATURE (K)

where α is the temperature coefficient

of resistivity (α > 0)

ρ ≠0 because of impurities and defects

in the crystal lattice at T=0K.

e-

RESISTANCE

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E > EF @ T = 0K � fFD = 0

E < EF @ T = 0K � fFD = 1

@ T ≠ 0K � EF + kT

k = 8.6 x 10-2 meV/T (Boltzman constant)

@ T = 300K add kT = 25meV

( ) ( )1

1

+

=−

kTFEEFD

e

Ef

EF

T=0 Kelvin

T >> 0 Kelvin

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T=0K �E=∞→ fBE = 0

E=0 → fBE = ∞

All bosons will condense on the lowest energy level in the solid.

( )1

1

−=

kTEBE

e

Ef

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• Normal solid states:

• Superconductor electronic states:

• If T > Tc then Cooper pairs form.

• Their binding energy Eg ~ 10-3 eV

• Eg can be broken with

• As T decreases towards Tc, the

energy gap Eg becomes smaller.

• If T < Tc then Eg � 0 and Cooper

pairs are released.

EF

T = Tc

p(E) = g(E) * fFD (E)

where for electrons in metals

g(E) ~ E1/2 (spin ↑/spin ↓)

λ ~ 1.2 mm

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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 long-

range 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.

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•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 0.015 Th 1.4

Ir 0.1 Re 1.4

Lu 0.1 Ti 2.39

Hf 0.1 In 3.408

Ru 0.5 Sn 3.722

Os 0.7 Hg 4.153

Mo 0.92 Ta 4.47

Zr 0.546 V 5.38

Cd 0.56 La 6

U 0.2 Pb 7.193

Ti 0.39 Tc 7.77

Zn 0.85 Nib 9.46

Ga 1.083

Element Tc Element Tc

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•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).

•For T >> Tc normal states are closely packed

together and make the material insulating.

•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 .

Normal Regions Superconducting Region

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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

•“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.12

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• Motors account for 70% of the power

consumption in domestic manufacturing

and 55% in the entire United States.

• 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.

High power electric motor

produced for the US Navy

(July 2001).

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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.

•NASA and NSF are working for

developing a superconducting chip.Japan

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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.