| Summary: | 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 ỚSelectronỚ<U+00fd> and ỚSholeỚ<U+00fd> kinetic energies and a pairing interaction with the phonon variables eliminated. These ỚSelectronsỚ<U+00fd> and ỚSholesỚ<U+00fd> were introduced formally in terms of a free-electron model, which we consider unsatisfactory. We define ỚSelectronsỚ<U+00fd> and ỚSholesỚ<U+00fd> in terms of the cur- tures of the Fermi surface. ỚSElectronsỚ<U+00fd> (1) and ỚSholesỚ<U+00fd> (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.
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