Phonon and magnon mediated d-wave superconductivity in cuprates

We use the Eliashberg formalism for calculating Tc in the 2D t-J model supplemented by an interaction with fully-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 a certain 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. Extended saddle points, analogous to those observed in angle-resolved photoemission spectra, form the main part of this region. It 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 high Tc. Only together with a moderate hole-phonon interaction does it lead to d-wave superconductivity at temperatures and hole concentrations observed in cuprates. High Tc are connected with a large density of states in the nearly flat region, a conformity of the two interactions for the dx2-y2 symmetry, and a high phonon frequency Ω. The obtained dependences of Tc on x and on Ω are in close agreement with observations in cuprates