After a review of the fundamental properties of the high-Tc cuprate superconductors, we evaluate and study the major parameters of these compounds. In this approach, we consider the attractive interaction is due to the phonons at low temperature, but at high temperature it is related to the magnetic excitations. Analytical expressions for the coherence length , the isotope coefficient and the superconducting gap ratio R = 2 (0) /kBTc are obtained for the case where the Fermi level is close to the van Hove singularity. This model explains simultaneously high Tc, large gap energy (0), short coherence length and small values of the isotope coefficient . Our theoretical values are in a good agreement with experimental results.

The isotope coefficient α has been studied in the context when the Fermi level is close to the van Hove singularity. In this approach, we consider the interaction is related to the magnetic excitations at high temperature. An analytical expression for the isotope effect is obtained in the weak coupling limit. Our results show that when the superconducting transition temperature increases the isotope coefficient decreases in qualitative agreement with experimental results.

Analytical expressions for the superconducting transition temperature Tc and the isotope coefficient α have been obtained for the case where the Fermi level is close to the van Hove singularity. In this approach, we consider two interactions, the first related to the phonons and the second relevant to the magnetic excitations. Our result shows that the isotope coefficient α decreases with the superconducting transition temperature Tc in qualitative agreement with experimental data.

The superconducting gap ratio R = 2Δ(0)/kBTc has been studied in the context when the Fermi level is close to the van Hove singularity. In this approach, we consider the interaction is related to the phonons at low temperature but at high temperature, it is relevant to the magnetic excitations. Our results show that the superconducting gap ratio R takes large values in qualitative agreement with experimental data.

The model recently developed by Getino et al. to study the gap energy in the van Hove scenario in high-T c oxides is extended to study the isotope effect and the coherence length in these materials. We propose a more realistic model by: (1) adding a constant term to the singular logarithmic contribution, within the weak coupling BCS theory and a phonon mediated interaction; (2) assuming the Fermi level lies close to a van Hove singularity for optimal doping. The equations obtained from this approach, are applicable to low as well as high temperature superconductors successfully the superconducting temperature transition T c , the gap energy Δ, the isotope effect α and the coherence length ξ. For high-T c oxides, it is found that when the effective mass of carriers tends to be large, α and ξ tend to be small where T c and Δ became larges. We shown that when the effective mass of carriers is enclosed between 5 m e and 15 m e , the values obtained for these parameters are in agreement with experimental data.