RELATION OF EXTENDED VANHOVE SINGULARITIES TO HIGH-TEMPERATURE SUPERCONDUCTIVITY WITHIN STRONG-COUPLING THEORY

Recent angle-resolved photoemission (ARPES) experiments have indicated that the electronic dispersion in some of the cuprates possesses an extended saddle point near the Fermi level which gives rise to a density of states that diverges like a power law instead of the weaker logarithmic divergence usually considered. We investigate whether this strong singularity can give rise to high transition temperatures by computing the critical temperature T(c) and isotope effect coefficient alpha within a strong-coupling Eliashberg theory which accounts for the full energy variation of the density of states. Using band structures extracted from ARPES measurements, we demonstrate that, while the weak-coupling solutions suggest a strong influence of the strength of the Van Hove singularity on T(c) and alpha, strong-coupling solutions show less sensitivity to the singularity strength and do not support the hypothesis that band-structure effects alone can account for either the large T(c)'s or the different T(c)'s within the copper oxide family. This conclusion is supported when our results are plotted as a function of the physically relevant self-consistent coupling constant, which shows universal behavior at very strong coupling.