Flux quantization experiments indicate that the carriers, Cooper pairs
(pairons), in the supercurrent have charge magnitude 2e, and that they
move independently. Josephson interference in a Superconducting Quantum
Int- ference Device (SQUID) shows that the centers of masses (CM) of
pairons move as bosons with a linear dispersion relation. Based on this
evidence we develop a theory of superconductivity in conventional and
mate- als from a unified point of view. Following Bardeen, Cooper and
Schrieffer (BCS) we regard the phonon exchange attraction as the cause
of superc- ductivity. For cuprate superconductors, however, we take
account of both optical- and acoustic-phonon exchange. BCS started with
a Hamiltonian containing "electron" and "hole" kinetic energies and a
pairing interaction with the phonon variables eliminated. These
"electrons" and "holes" were introduced formally in terms of a
free-electron model, which we consider unsatisfactory. We define
"electrons" and "holes" in terms of the cur- tures of the Fermi surface.
"Electrons" (1) and "holes" (2) are different and so they are assigned
with different effective masses: Blatt, Schafroth and Butler proposed to
explain superconductivity in terms of a Bose-Einstein Condensation (BEC)
of electron pairs, each having mass M and a size. The system of free
massive bosons, having a quadratic dispersion relation: and moving in
three dimensions (3D) undergoes a BEC transition at where is the pair
density.
