Electronic spectrum and superconductivity in the extended t–J–V model

•Extended t–J–V model with intersite Coulomb and electron-phonon interactions.•Spin-fluctuation pairing induced by the kinematical interaction for the Hubbard operators.•High-temperature d-wave superconductivity.•Suppression of intersite Coulomb and electron-phonon interactions for the d-wave pairing. A consistent microscopic theory of superconductivity for strongly correlated electronic systems is presented within the extended t–J–V model where the intersite Coulomb repulsion and the electron-phonon interaction are taken into account. The exact Dyson equation for the normal and anomalous (pair) Green functions is derived for the projected (Hubbard) electronic operators. The equation is solved in the self-consistent Born approximation for the self-energy. We obtain the d-wave pairing with high-Tc induced by the strong kinematical interaction of the order of the kinetic energy ∼t of electrons with spin fluctuations which is much larger than the exchange interaction J. The Coulomb repulsion and the electron-phonon interaction give small contributions for the d-wave pairing. These results support the spin-fluctuation mechanism of high-temperature superconductivity in cuprates previously proposed in phenomenological models.