## BCS Theory of SuperconductivityThe properties of Type I superconductors were modeled successfully by the efforts of John Bardeen, Leon Cooper, and Robert Schrieffer in what is commonly called the BCS theory. A key conceptual element in this theory is the pairing of electrons close to the Fermi level into Cooper pairs through interaction with the crystal lattice. This pairing results from a slight attraction between the electrons related to lattice vibrations; the coupling to the lattice is called a phonon interaction. Pairs of electrons can behave very differently from single electrons which are fermions and must obey the Pauli exclusion principle. The pairs of electrons act more like bosons which can condense into the same energy level. The electron pairs have a slightly lower energy and leave an energy gap above them on the order of .001 eV which inhibits the kind of collision interactions which lead to ordinary resistivity. For temperatures such that the thermal energy is less than the band gap, the material exhibits zero resistivity. Bardeen, Cooper, and Schrieffer received the Nobel Prize in 1972 for the development of the theory of superconductivity.
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## Experimental Support: BCS TheoryElectrons acting as pairs via lattice interaction? How did they come up with that idea for the BCS theory of superconductivity? The evidence for a small band gap at the Fermi level was a key piece in the puzzle. That evidence comes from the existence of a critical temperature, the existence of a critical magnetic field, and the exponential nature of the heat capacity variation in the Type I superconductors. The evidence for interaction with the crystal lattice came first from the isotope effect on the critical temperature. The band gap suggested a phase transition in which there was a kind of condensation, like a Bose-Einstein condensation, but electrons alone cannot condense into the same energy level (Pauli exclusion principle). Yet a drastic change in conductivity demanded a drastic change in electron behavior. Perhaps coupled pairs of electrons with antiparallel spins could act like bosons?
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## Measured Superconductor Bandgap
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## Energy Gap in Superconductors as a Function of TemperatureThe effective energy gap in superconductors can be measured in microwave absorption experiments. The data at left offer general confirmation of the BCS theory of superconductivity. The data is attributed to Townsend and Sutton.
| Index Superconductivity concepts References Blatt, Ch 13 Kittel, Solid State, Ch 12 | ||

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## Vanadium Heat Capacity
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## Exponential Heat CapacityAs it is warmed toward its critical temperature, the heat capacity of vanadium increases 100-fold in just 4 K. This exponential increase suggests an energy gap which must be bridged by thermal energy. This energy gap evidence was part of the experimental motivation for the BCS theory of superconductivity.
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