Electronic plus phonon-exchange mechanism for high-temperature superconductivity in layered crystals

Abstract

A general mathematical formulation is developed for calculating the effective electron-electron interaction in layered crystals like YBa₂Cu₃O₇-δ, and for finding the resulting superconducting transition temperature T_c in such systems within the framework of the conventional BCS pairing arising from various possible excitations in the medium. This differs considerably from the usual case of an effective three-dimensional homogeneous system, and should be relevant in the calculation of T_c for the new class of high-T_c perovskites in which oxygen deficiencies in Cu-O layers and their distribution in the crystal play a crucial role. The explicit form of the effective interaction V_jj(q _t,ω) in a given layerj in the unit cell of the crystal is found to be determined not only by the true polarization function Π_j(q _t,ω) of that layer, but also of other layers. The exchange of electronic excitations of a nearby insulating layer by carriers in a conducting layer thus becomes possible to get high T_c, with or without the usual phonon exchange.