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

It is shown that the square-root van Hove singularity appearing in the density of states ?(E_F)~(E_F-E₀)^-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 E₀ of the saddle. Because the divergence of ?(E_F) is canceled in the electron-electron interaction constant renormalized by strong-coupling effects, T_c approaches zero as E_F?E₀, 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. © 1998 American Institute of Physics.