About the Influence of the Square-Root Van Hove Singularity on the Critical Temperature of Overdoped High-Temperature Superconductors

Abstract

It is shown that the square-root van Hove singularity in the density of states ν(E F )~ (E F -E0)-1/2, associated with the extended saddle-point singularities in the electron spectra of the cuprates, leads to a nonmonotonic dependence of the critical temperature T c on the position of the Fermi level E F with respect to the bottom E0 of the saddle. As a result of cancellation of the divergency of ν(E F ) in the electron–electron coupling constant, renormalized due to the account of the strong coupling effects, T c approaches zero in the limit E F → E0. This result contrasts that of the weak coupling approximation, which gives a finite value of T c for E F → E0. The T c on the concentration of doped holes, obtained in the strong coupling approximation, agrees qualitatively with the experimental data for the overdoped cuprate metal-oxides.