Superconductors

Superconductors
o Abstract
o History
o Theory
 BCS Theory
 Cooper Pairs
o Experiment
 Thermocouples
 Multi-meters
o References
Abstract
This Wiki article was created give the reader a good understanding of how superconductors and
experimental devices such as thermocouples and multi-meters work. A superconductor is any
material that can reach a state where the electrical resistance the superconductor has while a
current is applied across it is always 0. A High Temperature Superconductor (HTS) is simply a
material that will exhibit superconductor properties if it is cooled with liquid nitrogen (around 77 K).
Currently BCS theory is generally accepted as the most powerful theory in describing lower
temperature superconductivity. High temperature superconductivy is not well understood so this wiki
will focus on explaining BCS theory instead.
History
The first superconductor was discovered by Heike Kamerlingh-Onnes in Holland in 1911. Onnes
took mercury and cooled it to around 4K using liquid helium and found that the mercury had no
resistance to electrical current. Onnes won a nobel prize for this 2 years later. In 1933 Walther
Meissner and Robert Ochsenfeld discovered that a superconductor will repel a magnetic field. In
1957 John Bardeen, Leon Cooper, and John Schrieffer created the BCS theory on superconductivity
which could explain superconductivity in elements and alloys. The theory breaks down however
when dealing with more complicated materials than elements and alloys and also at temperatures
higher than 30k. For the BCS theory, Bardeen, Cooper and Schrieffer were awarded a noble prize in
1972. Later, Brian Josephson predicted that electrical current would flow between 2 superconductors
even if there was an insulater between them. His predictions were true and in 1973 he won a nobel
prize for his work. In 1964 Bill Little suggested the existence of organic superconductors. Klaus
Bechgaard and a team of 3 french physicists formed the first organic superconductor ((TMTSF)2PF6)
which became a superconductor when kept at the very cold temperature of 1.2K and under high
pressure. In Switzerland, 1986, Alex Muller and George Bednorz created a ceramic material that
was a superconductor at 30k. This ceramic was surprisingly the highest temperature superconductor
of its time (ceramic materials are usually insulators!). Muller and Bednorz shared a nobel prize for
this discovery. Suddenly the scientific community started to make every possible combination of
ceramics in a quest to find the highest superconducting temperature (Tc). In 1987 YBa2Cu3O7 (the
compound used in this experiment) was found by an American research team to have a Tc of 92K.
This was a huge discovery because liquid nitrogen could be used instead of liquid helium (liquid
nitrogen was much cheaper, more abundant and had an easier experimental procedure assiciated
with it than liquid helium). Currently a molecule consisting of Mercury, Thallium, Barium, Calcium,
Copper and Oxygen holds the world record highest Tc of 138K. In 1997 a gold and indium alloy was
found to be both a superconductor and magnet at temperatures very close to 0k. This was thought to
be impossible. Recent years have given us around 50 new high temperature superconductors,
including the first high temperature superconductors without copper and some purely metal
superconductors. There is still no theory which can explain high temperature conductivity.
Theory
BCS Theory
This theory explains low temperature superconductivity but does not accurately describe the
phenomenon of HTS. The electrons in a superconductor while at or below the critical temperature
will pair to together, forming cooper pairs. These cooper pairs are in a lower energy state than any
unpaired electrons at low temperatures. Cooper pairs can form at very long ranges, so their
wavefunctions span a lot of space. The space taken up by one cooper pair will also be taken up by
many other cooper pairs so all of the independent wavefunctions overlap to create one big
complicated wavefunction. Normally, a free electron can take in a continuous amount of energy such
that any energy applied to the electron will cause a physical effect on the free electron. When
electrons are in a bound state such as the cooper pair, there is a discontinous range of energy
values that will cause an effect on the cooper pair; there becomes a minimal energy needed to
actually affect the cooper pair. Due to the low critical temperature of regular superconductors, the
kinetic energies of the particles which collide with the cooper pairs are too small to excite the lowest
energy state cooper pairs to their higher energy state (two free electrons). Then any collisions will
not have enough energy to raise the state of the cooper pairs therefore no energy is transfered. This
is why the paired electrons will theoretically remain in motion forever (as long as the superconductor
remains below the critical temperature) resulting in an electrical circuit with 0 resistance.
Cooper Pairs
Simplified Classical Explanation: The crystalline structure (lattice of positive nuclei) of a
superconductor at very low temperature bends towards a passing electron due to the coulomb
attraction of the negative electron and the positive lattice. This creates a higher positive charge
density and although electrons repel each other, this increased local positive charge density will
attract electrons from far away inside the superconductor. This effect is enough to cause the
electrons to pair up.
Attempted Quantum Explanation (I tried my best Joss!): The Pauli Exclusion Principle states that two
fermions (such as an electron) can not occupy the same quantum state. So this means that for a
superconductor, only one spin up and one spin down electron can be in the same energy state at the
same time. When the system is in the total lowest energy state, then all of the possible lowest
energy fermion states will be filled by one spin up and one spin down electron and all of the highest
energy states will be empty (just like the ground state in chemistry). The Fermi Energy is the energy
value of the highest energy states of fermions in a multi-fermion system at the total lowest energy
state. This means that if a superconductor(multi-fermion system) is cooled to around absolute 0
(lowest energy state) there will still be electrons in higher energy states (like the fermi energy state)
and therefore, some of the electrons are still moving. Electron-phonon interactions make the
electrons form cooper pairs at long range (a phonon is the particle embodyment of the small
vibrations in the positive lattice of a superconductor). Due to the long range, there will be many
cooper pair wavefunctions occupying the same space. A cooper pair has spin value 0 or 1 which
implies that the cooper pair has some boson properties. One of these properties is that a cooper pair
is symmetric under particle interchange. This means that many cooper pairs can occupy the same
quantum state at the same time. Due to this ability of cooper pairs to take up the exact same
quantum state, then all (or most) of the cooper pairs can take up the lowest energy state. Thus,
having cooper pairs will result in having a lower net energy than the free electrons (cooper pair state
energies are lower than the fermi energy) and this is why they will occur naturally at cold
temperatures inside superconductors.
Experiment
Thermocouples
A thermocouple is made of two different metal conductors and a junction which connects them. "A
temperature difference between any two points in a non-superconducting metal, when no current is
allowed to flow, will result in a electrostatic potential difference" (Experiment Guide for
Superconductor Demonstrations pg.44). If the two metal conductor leads were made of the same
material and had the same temperature gradient across their lengths, there would be no electric
potential since the potential gain going up one of the leads would exactly counter out the potential
loss going down the other. The potential difference generated across one of the leads is proportional
to the temperature difference between the two points in question. In order to read this potential
difference however, a voltmeter must be connected to the thermocouple in a series circuit. In order
to get an accurate voltage reading from the thermocouples, the wires connecting the thermocouple
to the voltmeter must be made of the same material. If these two wires are made of different
materials then they will have different potentials across them even if kept in the same temperature
gradient. Then when the circuit is formed, the voltage reading on the voltmeter would be incorrect by
an amount equal to the potential difference between the potential differences of the two wires! The
voltage reading on the voltmeter should only be the difference between the potential difference
generated by the temperature gradient across the first conducting lead, and the potential difference
generated by the temperature gradient across the second conducting lead. So by placing one end of
both of the conducting leads in a known temperature
(such as a 0C ice bath), and the other end
of each of the conducting leads (the end where both the leads are joined at the junction) in the
unknown temperature
, the voltage reading on the voltmeter will give us what
is and
since we already know what
is, the temperature
can be found.
Multi-meters
I thought it might be a good idea to talk about multi meters in the final wiki too, but it is already pretty
long so maybe i should leave it out?
References
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http://en.wikipedia.org/wiki/Superconductivity
http://en.wikipedia.org/wiki/Cooper_pair
http://www.superconductors.org/History.htm
http://www.abc.net.au/science/articles/2011/07/20/3273635.htm
Experiment Guide for Superconductor Demonstrations
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Superconductors

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