Electron-Phonon Interaction and Strong Correlations in High-Temperature Superconductors: One can not avoid the unavoidable

Abstract

The important role of the electron-phonon interaction (EPI) in explaining the properties of the normal state and pairing mechanism in high-T$_{c}$ superconductors (HTSC) is discussed. A number of experimental results are analyzed such as: dynamical conductivity, Raman scattering, neutron scattering, ARPES, tunnelling measurements, isotope effect and etc. They give convincing evidence that the EPI is strong and dominantly contributes to pairing in HTSC oxides. It is argued that strong electronic correlations in conjunction with the pronounced (in relatively weakly screened materials) EPI are unavoidable ingredients for the microscopic theory of pairing in HTSC oxides. I present the well defined and controllable theory of strong correlations and the EPI. It is shown that strong correlations give rise to the pronounced \textit{forward scattering peak} in the EPI - the FSP theory. The FSP theory explains in a consistent way several (crucial) puzzles such as much smaller transport coupling constant than the pairing one ($\lambda_{tr}\ll \lambda$), which are present if one interprets the results in HTSC oxides by the old Migdal-Eliashberg theory for the EPI. The ARPES shift puzzle where the nodal kink at 70 meV is unshifted in the superconducting state, while the anti-nodal one at 40 meV is shifted can be explained at present only by the FSP theory. A number of other interesting predictions of the FSP theory are also discussed.