Pentegov V. Properties of cuprate metal-oxides determined by the anisotropy of the electronic spectrum and Coulomb correlations

It is shown that the key role in the formation of the properties of cuprate metal-oxide compounds is played by the extended saddle points in the band spectra of the 2D layers of CuO2, which lead to the strong anisotropy of the quasiparticles' effective mass and group velocity, as well as to the appearance of the damped long-wave charge density oscillations with acoustic dispersion (acoustic plasmons) in the collective electron spectrum. The low-angle scattering of the current carriers on such collective excitations is manifested in suppression of the Coulomb repulsion for small transferred momenta, resulting in the effective attraction between quasiparticles in the d-wave Cooper channel. It is shown also that the many-body correlations, described by the Coulomb vertex function, are crucial in these systems and work to amplify the electron-electron interaction. The self-consistent numerical solution of the set of nonlinear integral equations for the normal and anomalous self-energies of the electron Green functions and the calculation of the critical temperature of superconducting transition, along with the isotopic effect exponent, show that the results obtained in the framework of the Fermi-liquid approach agree quite satisfactory with the experiments for the optimally doped and overdoped cuprate metal-oxides, provided the anisotropy of the quasi-2D electron spectrum in the plane of cuprate layers and the square-root Van Hove singularities in the density of states due to the extended saddle points are taken into account.