Apical oxygen vibrations dominant role in d-wave cuprate superconductivity and its interplay with spin fluctuations

Microscopic theory of a high Tc cuprate BiSCO based on main pairing channel of electrons in CuO planes due to 40meV lateral vibrations of the apical oxygen atoms in adjacent the SrO ionic insulator layer is proposed. The separation between the vibrating charged atoms and the 2D electron gas creates the forward scattering peak leading in turn to the d-wave pairing within Eliashberg formalism. The phonon mode naturally explain the kink in dispersion relation observed by ARPES and the and effect of the O16 to O18 isotope substitution in the normal state. To describe the pseudogap physics a single band fourfold symmetric Hubbard model, with the hopping parameters t' = - 0.17t and the on site repulsion U = 6t was used. It described the Mott insulator at low doping, while at higher dopping the pseudogap physics (still strongly correlated) can be be approximated by the symmetrized mean field model and with renormalized U incorporating screening. The location of the transition line between the locally antiferromagnetic pseudogap and the paramagnetic overdoped phases and susceptibility (describing spin uctuations coupling to 2DEG) are also obtained within this approximation. The superconducting d-wave gap mainly due to the phonon channel but is assisted by the spin fluctuations (15-20%). The dependence of the gap and Tc on doping and effect of the isotope substitution are obtained and is consistent with experiments.