Electron-phonon superconductivity mechanisms in the Hubbard model

An electron–phononpairing mechanism in the Hubbard model on a square lattice is considered. The method of two-time Green's functions is used to calculate the critical temperature of the superconducting transition. The limiting case $U\to\infty$ is considered, and expressions are obtained for the dependences on the concentration of particles of the temperatures of the superconducting and Peierls transitions and the exponent of the isotopic effect. It is shown that the inclusion of Coulomb correlations leads to a displacement of the Van Hove singularity in the quasiparticle spectrum and to a change in the dependences of the isotopic effect and the temperatures of the superconducting and Peierls transitions on the carrier concentration compared with an ordinary Fermi system.