Relationship To Superconductivity
Cooper originally considered only the case of an isolated pair's forming in a metal. When one considers the more realistic state of many electronic pair formations, as is elucidated in the full BCS Theory, one finds that the pairing opens a gap in the continuous spectrum of allowed energy states of the electrons, meaning that all excitations of the system must possess some minimum amount of energy. This gap to excitations leads to superconductivity, since small excitations such as scattering of electrons are forbidden. The gap appears due to many-body effects between electrons feeling the attraction.
Herbert Fröhlich was first to suggest that the electrons might act as pairs coupled by lattice vibrations in the material. This was indicated by the isotope effect observed in superconductors. The isotope effect showed that materials with heavier ions (different nuclear isotopes) had lower superconducting transition temperatures. This can be explained by the theory of Cooper pairing: since heavier ions are harder to move they would be less able to attract the electrons resulting in a smaller binding energy for Cooper pairs.
The theory of Cooper pairs is quite general and does not depend on the specific electron-phonon interaction. Condensed matter theorists have proposed pairing mechanisms based on other attractive interactions such as electron–exciton interactions or electron–plasmon interactions. Currently, none of these alternate pairing interactions has been observed in any material.
It should be mentioned that Cooper pairing does not really involve individual electrons pairing up to form "quasi-bosons". The paired states are energetically favored, and electrons go in and out of those states preferentially. This is a fine distinction that John Bardeen makes:
- "The idea of paired electrons, though not fully accurate, captures the sense of it."
The mathematical description of the second-order coherence involved here is given by Yang.
Read more about this topic: Cooper Pair
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