Relation of extended Van Hove singularities to high-temperature superconductivity within strong-coupling theory

Abstract

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 ${\mathit{T}}_{\mathit{c}}$ and isotope effect coefficient \ensuremath{\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 ${\mathit{T}}_{\mathit{c}}$ and \ensuremath{\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 ${\mathit{T}}_{\mathit{c}}$'s or the different ${\mathit{T}}_{\mathit{c}}$'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.