Relation of Extended Van Hove Singularities to High-Temperature Superconductivity within Strong-Coupling Theory

TL;DR

This paper investigates whether extended Van Hove singularities in cuprates can explain high-temperature superconductivity by analyzing their effects within a strong-coupling Eliashberg framework, finding limited influence on critical temperature.

Contribution

It demonstrates that strong-coupling effects diminish the impact of Van Hove singularities on superconducting transition temperatures, challenging their role as the primary cause.

Findings

Weak-coupling solutions show sensitivity to Van Hove singularity strength.

Strong-coupling solutions exhibit universal behavior regardless of singularity strength.

Band structure effects alone cannot account for high $T_c$ in cuprates.

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 $T_c$ 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 show universal behavior at very strong coupling.