Effect of pseudogap and van Hove singularity density of state on the isotope effect coefficient of superconductor

This research was to study the isotope effect coefficient of high temperature superconductors taking into account the pseudogap. We used the BCS-like model including the effect of the vHs density of state and pseudogap. The isotope effect coefficient was derived to the analytical and the approximation form. For the effect of vHs density of state, we found that the isotope effect coefficient increased as the critical temperature increased. For the pseudogap effect, as the critical temperature increased, the isotope effect coefficient decreased to the BCS value, 0.5. For the effect of the vHs density of state and pseudogap, we found that when the critical temperature increased, the isotope effect coefficient decreased. Finally, we showed our numerical results that can fit well with the experimental data of YBa2-xLaxCu3O7-delta and Y1-xPrxBa2Cu3O6.92 superconductors.