Role of Van Hove Singularities and Momentum Space Structure in High-Temperature Superconductivity

TL;DR

This paper investigates the influence of Van Hove singularities and momentum space structure on high-temperature superconductivity, finding that energy dependence in the density of states is more crucial than Van Hove singularities or momentum structure.

Contribution

The study compares Eliashberg and mean field theories to assess the impact of Van Hove singularities and momentum structure on Tc in cuprates, revealing their secondary role.

Findings

Van Hove singularities do not significantly change Tc.

Energy dependence of the density of states is more important than momentum structure.

Results are consistent across different models of spin-fluctuation pairing.

Abstract

There is a great deal of interest in attributing the high critical temperatures of the cuprates to either the proximity of the Fermi level to a van Hove singularity or to structure of the superconducting pairing potential in momentum space far from the Fermi surface. We examine these ideas by calculating the critical temperature Tc for model Einstein-phonon- and spin-fluctuation-mediated superconductors within both the standard, Fermi-surface-restricted Eliashberg theory and the exact mean field theory, which accounts for the full momentum structure of the pairing potential and the energy dependence of the density of states. By using two models of spin-fluctuation-mediated pairing in the cuprates, we demonstrate that our results are independent of the details of the dynamical susceptibility, which is taken to be the pairing potential. We also compare these two models against available neutron scattering data, since these data provide the most direct constraints on the susceptibility. We conclude that the van Hove singularity does not drastically alter Tc from its value when the density of states is constant and that the effect of momentum structure is significant but secondary in importance to that of the energy dependence in the density of states.