Dependence of Tc on the physical parameters in single-layered copper oxides.

Abstract

From the superconducting gap equation that we have derived in a previous paper, we calculate the critical superconducting temperature ${\mathit{T}}_{\mathit{c}}$ of an itinerant electron gas in a ${\mathrm{CuO}}_{2}$ plane as a function of the occupancy of the d-p subband. This involves applying the Bogoliubov-Valatin mean-field approximation to a Hamiltonian including both the Hubbard intra-atomic repulsion U and an effective coupling constant V between electrons; the latter is assumed to be mediated by the electron-phonon interaction. As the Fermi level is shifted from the logarithmic Van Hove singularity in the electronic density of states, the calculated value of ${\mathit{T}}_{\mathit{c}}$ decreases much more slowly than the antiferromagnetic order parameter that we had previously calculated in the same model. This explains the existence of the superconducting phase largely outside of the domain of stability of the antiferromagnetic phase, when the compound is doped. Furthermore, we calculate the isotope effect, which exhibits a large variation with the doping x, showing a sharp peak for some critical value of x, in agreement with several independent experimental data. A very large influence of the Coulomb parameter U is found on the isotope effect which, in some cases, could vanish, or even be negative.