On the influence of a square-root van Hove singularity on the critical temperature of high-T _c superconductors

Abstract

It is shown that the square-root van Hove singularity appearing in the density of states ν (E _F )∼(E _F −E ₀)^−1/2 as a result of extended saddle-point singularities in the electron spectrum of high-T _c superconductors based on hole-type cuprate metal-oxide compounds gives a nonmonotonic dependence of the critical temperature T _c on the position of the Fermi level E _F relative to the bottom E ₀ of the saddle. Because the divergence of ν(E _F ) is canceled in the electron-electron interaction constant renormalized by strong-coupling effects, T _c approaches zero as E _F →E ₀, in contrast to the weak-coupling approximation, where in this limit T _c approaches a finite (close to maximum) value. The dependence obtained for T _c as a function of the doped hole density in the strong-coupling approximation agrees qualitatively with the experimental data for overdoped cuprate metal oxides.