BCS THEORY
BCS Theory
The theory of superconductivity proposed by Copper and Schrieffer now known as BCS theory can be thought of in terms of TWO FLUID picture. We need advanced quantum mechanics to understand BCS theory. However, we give only a sketch of theory quantitatively. In a super conducting material, a finite fraction of electrons are in a real sense condensed into a macromolecule or super fluid(Cooper pairs) which extends over entire volume of systems and is capable of motion as a whole. At low enough temperature the condensation is complete and all the electrons participate in forming the super fluid. As the temperature is increased , a fraction of electron evaporate from the condensate and forma weakly interacting gas of excitation that is NORMAL FLUID. This also extends throughout the entire volume of system, interpenetrating the superfluid tends to zero and the system undergoes a second order phase transaction from the superconducting to the normal state.
In a metallic conductor, the conduction electrons suffer scattering due to presence of imperfection in he crystal, lattice vibrations etc. As the temperature increase lattice ions vibrate with greater amplitude. This increase the resistance. It is interesting to know that lattice plays a crucial role in producing zero resistance! Consider an electron that moves through the array of ions(lattice). The positively charged ions come together and charge density increases (electron lattice interaction). The region of increased charge density attracts another electron (lattice electron interaction). These two electrons are coupled and are called Cooper pair or bound pair. Thus there is an lattice electron or bound pair interaction for a cooper pair. Since electron moves faster than the ions the electrons in the pair will be widely separated. The distance between the electron in the pair(coherence length) is about 1000 amstrong. This eliminates the objection against the repulsion between the electrons in a cooper pair.
Thus a kind of ordering occurs between electrons and atoms at low temperature that is the formation of super fluid. A single electron is a Fermion's that obeys Pauli's exclusion principle. But a Cooper pair is a Boson (that does not obey Pauli's exclusion principle) and hence any number of Cooper pair can be accommodated into a single quantum state. At very low temperature these particles can destroy the pair and hence the formation of normal electrons (that is normal fluid). The motion of normal electrons lead to resistance.
BCS theory shows that lowest state of system the one in which Cooper pairs are formed. The lowest state is separated from next state by gap which is of the order of milli electron volt. IT depends on the nature of the ions. Large number of cooper pair can occupy the ground state. Thus to carry the current . the Cooper pair need not move from an occupied state to unoccupied states. Since the excited state(normal electrons) is separated by an energy gap, as long as temprature is small enough, Cooper pair do not suffer scattering which is the source of resistance. The formation of Coopre pair has been varified experimentally. The BCS theory is successful in explaining metallic superconductivity, but certain facts remain unexplained by this theory.
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