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BCS Superconductivity Theory
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:
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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.
(You will need Apple's
QuickTime plugin to play all the animations on this page)
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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 to compare Cooper pair superconduction
and normal conduction.
High Temperature Superconduction
However, BCS theory predicted a theoretical maximum to Tc
of around 30-40K, as above this, thermal energy would cause electron-phonon
interactions of an energy too high to allow formation of or sustain Cooper
pairs.
1986 saw the discovery of high temperature superconductors (see History)
which broke this limit (the highest known today is in excess of 150K)
- it is in debate as to what mechanism prevails at higher temperatures,
as BCS cannot account for this. See High
Temperature Superconductivity Theory next for further details.
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