Role of Van Hove singularities and momentum-space structure in high-temperature superconductivity.

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, the latter being particularly important for spin-fluctuation-mediated pairing mechansims. We examine these ideas by calculating the critical temperature Tc for model Einstein-phononand 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. Our calculations employ band structures chosen to model both the La2Sr2−xCuO4 and YBa2Cu3O7−δ families. 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 magnetic neutron scattering data, since these data provide