06-07-2012, 11:55 AM
BCS Superconductivity Theory
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In 1957, Bardeen, Cooper and Schrieffer (BCS) proposed a theory that explained the microscopic origins of superconductivity, and could quantitatively predict the properties of superconductors. Prior to this, there was Ginzburg-Landau theory, suggested in 1950, which was a macroscopic theory. This will not be dealt with here, but Ginzburg-Landau theory can be derived from BCS theory.
Cooper Pair Formation
Mathematically, BCS theory is complex, but relies on an earlier 'discovery' by Cooper (1956), who showed that the ground state of a material is unstable with respect to pairs of 'bound' electrons. These pairs are known as Cooper pairs and are formed by electron-phonon interactions - an electron in the cation lattice will distort the lattice around it, creating an area of greater positive charge density around itself. Another electron at some distance in the lattice is then attracted to this charge distortion (phonon) - the electron-phonon interaction. The electrons are thus indirectly attracted to each other and form a Cooper pair - an attraction between two electrons mediated by the lattice which creates a 'bound' state of the two electrons:
Left: Cooper pair formation - electron-phonon interaction: the electron is attracted to the positive charge density (red glow) created by the first electron distorting the lattice around itself.
The formation of Cooper pairs is supported by the fact that BCS and the Ginzburg-Landau theories predict the charge and mass of the supercurrent 'particle' to be 2e and 2Me respectively.
Cooper Pairs - BCS Theory Supercurrent Carriers
The Cooper pairs within the superconductor are what carry the supercurrent, but why do they experience such perfect conductivity?
Mathematically, because the Cooper pair is more stable than a single electron within the lattice, it experiences less resistance (although the superconducting state cannot be made up entirely of Cooper pairs as this would lead to the collapse of the state).
Physically, the Cooper pair is more resistant to vibrations within the lattice as the attraction to its partner will keep it 'on course' - therefore, Cooper pairs move through the lattice relatively unaffected by thermal vibrations (electron-phonon interactions) below the critical temperature. Play the animations below by clicking the 'play' icon in the corner to compare Cooper pair superconduction and normal conduction.
High Tc Superconductivity Theory
With the discovery of materials that went superconducting at temperatures above the theoretical limit imposed by BCS theory (see History), there was (and still is) much debate as to what the mechanism of superconduction in these compounds might be.
One explanation involves the use of holes within the superconductor - many high Tc superconductors are compounds such as YBa2Cu3O7-x (see Making Your Own Superconductors) or La(2-x)SrxCuO4, where the metal ion (in these cases, copper) will be partially oxidised; obviously, each metal ion cannot be physically partially oxidised, rather, the lattice will be comprised of a ratio of Cu2+ to Cu3+ ions, depending on x.
This means that there are 'holes' of positive charge (Cu3+ ions) within the lattice. This type of superconductor is hence referred to as a p-type superconductor; Compounds can also be doped to insert extra electrons into the lattice (i.e. a reduction), e.g. La2CuO(4+x) - this is called an n-type superconductor.
Although the positive 'holes' are usually stabilised by surrounding counterions (such as oxygen in the cases above), the highly charged ions will still ideally want to reduce (e.g. Cu3+ to Cu2+), however, they cannot gain an electron from neighbouring (Cu2+) ions, as this does not solve the problem.
When a current is applied to the superconductor, the electrons travel along the ion planes in the lattice. As an electron passes a hole in a neighbouring plane, it will push negative charge from orbitals on a reduced cation towards the hole (due to electrostatic repulsion), by distorting the lattice.
The oxidised cation (Cu3+) then reduces, and the reduced ion (Cu2+) oxidises - effectively, the hole moves backwards (as an electron moves forwards). This 'extra' current that is caused by the normal current is the supercurrent.
Above: Click play to see a visualisation of the high temperature superconduction discussed above. Because the hole moves backwards, an electron (current) moves forwards - this is the extra supercurrent generated.
The theory is supported by the fact that Tc varies with the amount of doping (x) - too many or too few holes destroys the effect.
You can see the copper planes in YBa2Cu3O7-x in the VRML strucutre included in the Uses section (on the Making Your Own Superconductors page).
Uses of Superconductors
Efficient Electricity Transportation
Superconductors have many uses - the most obvious being as very efficient conductors; if the national grid were made of superconductors rather than aluminium, then the savings would be enormous - there would be no need to transform the electricity to a higher voltage (this lowers the current, which reduces energy loss to heat) and then back down again.
Superconducting magnets are also more efficient in generating electricity than conventional copper wire generators - in fact, a superconducting generator about half the size of a copper wire generator is about 99% efficient; typical generators are around 50% efficient.
The US Department of Energy are actively encourages the use of superconductors as energy efficient devices.
At the moment, the problem lies with the critical temperature - unless a material is found that can superconduct above 300K, some sort of cooling system needs to be employed, which would be expensive, although companies are developing prototypes - in December 1998, Pirelli Wire built a test 150ft cable that transmitted electricity using high temperature superconducting materials.
Magnetic Levitation
Above: The Yamanashi MLX01 MagLev test vehicle achieved a speed of 343 miles per hour on April 14, 1999.
So-called 'MagLev' trains such as the Yamanashi MLX01 train show above have been under development in Japan for the past two decades - the train floats above the track using superconducting magnets; this eliminates friction and energy loss as heat, allowing the train to reach such high speeds.
Visit the MagLev R&D Department Home Page to find out more about the project.
Magnetic Resonance Imaging (MRI)
Above: MRI scan of a human skull
MRI is a technique developed in the 1940s that allows doctors to see what is happening inside the body without directly performing surgery. The development of superconductors has improved the field of MRI as the superconducting magnet can be smaller and more efficient than an equivalent conventional magnet.
Check out the University of Texas Austin's NMRI Lab for more information and links.
Synchrotrons and Cyclotrons (Particle Colliders)
Particle Colliders like CERN's Large Hadron Collider (LHC) are like very large running tracks that are used to accelerate particles (i.e. eletrons, positrons, hadrons and more) to speeds approaching the speed of light before they are collided with one another or other atoms, usually to split them (this was how many sub-nuclear particles such as taus and neutrinos were discovered).
They do this by cycling the particle using magnetic fields, continually increasing the speed of the particle.
The first project to use superconducting magnets was the proton-antiproton collider at Fermilab.