Importance of the Electron–Phonon Interaction with the Forward Scattering Peak for Superconducting Pairing in Cuprates

We discuss first some basic experimental facts related to ARPES, tunnelling, optics and neutron scattering measurements. They give evidence for the relevance of the electron–phonon interaction (EPI) in pairing mechanism of HTSC cuprates. A controllable and very efficient theory for strong correlations and their effects on EPI is discussed. The theory is based on the 1/N expansion method in the t–J model without using slave bosons (or fermions). The remarkable prediction is that strong correlations renormalize EPI and other charge-fluctuation properties (by including nonmagnetic impurity scattering) in such a way that the forward scattering peak (FSP) appears in the corresponding effective interactions. The existence of FSP in EPI is additionally supported by the weakly screened Madelung interaction in the ionic–metallic structure of layered cuprates. Pronounced FSP in EPI of HTSC cuprates reconciles many puzzling results, which could not be explained by the old theory with the momentum independent EPI. For instance, 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. It is shown that FSP in the impurity scattering potential is responsible for robustness of d-wave pairing in cuprates with nonmagnetic impurities and other defects. The ARPES kink and the isotope effect in the nodal and anti-nodal points, as well as the collapse of the elastic nonmagnetic impurity scattering in the superconducting state, are explained by this theory in a consistent way. The proposed theory 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. It turns out, that in systems with FSP in EPI besides the classical phase fluctuations there are also internal fluctuations of Cooper pairs. The latter effect is pronounced in systems with long-ranged pairing forees, thus giving rise to an additional contribution to the pseudogap behavior.