Theory of high-Tc superconductivity in layered cuprates

A model of superconductivity in high-temperature superconducting layered cuprates is proposed, based on the extended saddle point singularities in the electron spectrum, weak screening of the Coulomb interaction and phonon-mediated interaction between electrons plus a small short-range repulsion of Hund's, or spin-fluctuation, origin. This permits to explain the large values of T-C, features of the isotope effect on oxygen and copper, the existence of two types of the order parameter, the peak in the inelastic neutron scattering, the positive curvature of the upper critical field, as function of temperature, etc. The resonant tunneling mechanism for the c-axis transport is proposed. Real physical properties are calculated and compared with experimental data. These include the temperature dependence of the static c-axis conductivity in the normal state, frequency dependence of the optical conductivity and stationary supercurrent along the c-axis. It is demonstrated that for the latter the coherence of resonant tunneling through different centers is of primary importance. The resonant tunneling idea is used for description of the origin and some properties of the "pseudogap phase". The superconducting critical temperature in this picture is defined at low doping by establishment of a 3-dimensional phase correlation between the layers, and at high doping by destruction of a d-wave superconductivity by disorder. The result is a nonmonotonic dependence of T c on doping. The pseudogap phase is described on the basis of the Franz-Millis model of superconducting fluctuations, consisting of small superconducting domains with uncorrelated supercurrents. The calculated characteristics, namely, the spectral function, the inelastic neutron scattering cross section, and the spin susceptibility agree with experimental data.