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Introduction to Superconductivity
---------------------------------
Certain metals and alloys, when cooled to extremely
low temperatures, suddenly lose all their electrical
resistance and become superconductors. The temperature
at which the transition to the superconducting state
occurs is referred to as the critical temperature, T_{c}.
Superconductors also exhibit remarkable magnetic behavior
and they can have their superconductivity destroyed by
the application of a sufficiently large magnetic field.
For many purposes a superconductor can be viewed as
consisting of two interpenetrating fluids. One of the
fluids is the normal fluid composed of normal conduction
electrons obeying Fermi-Dirac statistics and the other
is the superfluid. According to the BCS theory, the
superfluid consists of pairs of electrons (Cooper pairs)
of equal but opposite momentum and spin. The pairing
is between electrons which lie near the Fermi energy
of the normal metal and arises because of a subtle
interaction between these electrons and the lattice.
The resulting pairs are in an energy state lower then
the Fermi energy by an amount corresponding to the
binding energy of the pair. It can be shown from
Quantum Mechanics that it is energetically favourable
for all the Cooper pairs to be in the same quantum
state and have the same momentum. This is possible
because a Cooper pair having integral (zero) spin can
be thought of as a Bose-Einstein particle. This means
that the only scattering process which can reduce the
current flow in a superconductor is one in which the
pairs are broken up, a process which requires at least
an energy equal to the binding energy of the pair.
For low current densities there is noway in which this
energy can be imparted to the pairs and consequently
the specimen has no resistance. As with ordinary
particles it is possible to represent the motion of a
Cooper pair by a wavefunction whose gradient determines
the magnitude of the current flowing in the superconductor.
This wavefunction has the form of a travelling wave whose
phase coherence extends over indefinitely large distances.
When superconductivity is destroyed, for example by a
large current or magnetic field, this phase coherence
is lost.