Anomalous Fermi liquid and strong-coupling superconductivity in cuprate perovskites

Abstract

We use the Eliashberg formalism for calculating T c in the 2D t- J model supplemented by an interaction with full-symmetric apex-oxygen vibrations. It is shown that in this model holes form an anomalous 2D Fermi liquid with a Fermi surface which is also two-dimensional in some range of hole concentrations x. This Fermi surface is a part of a large nearly flat region around the boundaries of the magnetic Brillouin zone. This region produces a pronounced maximum in the density of states near the Fermi level. However, in spite of this favorable condition for superconductivity, created by the hole-magnon interaction, we found this interaction alone to be unable to yield a high T c. Together with a moderate hole-phonon interaction it does lead to d-wave superconductivity at temperatures and hole concentrations observed in cuprates. High T c are connected with the large density of states in the nearly flat region, a conformity of the two interactions for the d x 2− y 2 symmetry, and the high-phonon frequency. The obtained dependences of T c on x and on the phonon frequency are in close agreement with observations in cuprates.