Importance of the Electron-Phonon Interaction with the Forward   Scattering Peak for Superconducting Pairing in Cuprates
  Basic experimental facts related to ARPES, tunnelling, optics ad neutron scattering measurements are discussed. They give evidence for the relevance of the electron-phonon interaction (EPI) in pairing mechanism of HTSC cuprates. A controllable theory for strong correlations and their effects on EPI is discussed which is based on the 1/N expansion method in the t-J model. Strong correlations renormalize EPI and other charge-fluctuation properties (by including nonmagnetic impurity scattering) and the forward scattering peak (FSP) appears in the effective interactions. Pronounced FSP in EPI of HTSC cuprates reconciles many puzzling results. The theory of EPI with FSP gives that the couplings in the s- and d-wave pairing channel are of the same magnitude near and below the optimal hole doping. FSP in the nonmagnetic impurity scattering potential is responsible for robustness of d-wave pairing in cuprates. The ARPES kink and the isotope effect in the nodal and anti-nodal points and the collapse of the elastic impurity scattering in the superconducting state, are explained by this theory. It also explains why the nodal kink is not-shifted in the superconducting state while the anti-nodal kink is shifted by the maximal superconducting gap. In systems with FSP in EPI besides the classical phase fluctuations there are also internal fluctuations of Cooper pairs giving rise to an additional contribution to the pseudogap. 
Miodrag L. Kulic