About the influence of the square-root van Hove singularity on the critical temperature of overdoped high-temperature superconductors

It is shown that the square-root van Hove singularity in the density of states ν(EF) ∼ (EF - 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 Tc on the position of the Fermi level EF with respect to the bottom E0 of the saddle. As a result of cancellation of the divergency of ν(EF) in the electron-electron coupling constant, renormalized due to the account of the strong coupling effects, Tc approaches zero in the limit EF → E0. This result contrasts that of the weak coupling approximation, which gives a finite value of Tc for EF → E0. The Tc on the concentration of doped holes, obtained in the strong coupling approximation, agrees qualitatively with the experimental data for the overdoped cuprate metal-oxides