ON BCS THEORY OF SUPERCONDUCTIVITY IN SYSTEMS WITH OVERLAPPING BANDS .1. SIMPLE OVERLAP

A generalisation of Nambu representation of electron-pair states permits, following simple laws of matrix algebra, a Green's function reformulation of Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity in systems with an arbitrary number (N) of bands. Perceived inadequacies of the original Suhl-Matthias-Walker (SMW) formulation are reexamined. An energy symmetrization, which further simplifies the obtained mean-field Hamiltonian, is proposed. An approximate analytic solution of the resulting NXN determinantal equation yields an expression for T-c(N) similar to that by Jha and Rajagopal in their N-layer theory, and BCS and SMW results are, in appropriate limits, recovered. A new band-energy condition, presently found to be important and consistent with experiment on the oxide ceramics, is trivially obtained. In multiband systems, where bands may cluster and lose individual identities, the obtained approximate equality of band energies is interpreted as analogous to similar equality of energies of k- and k'-electrons whose wave functions overlap, the latter being at the heart of the conventional BCS criterion. The connection between multiband and multilayer models is discussed.