  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.
