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

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; the latter is particularly important for spin-fluctuation-mediated pairing mechanisms. 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 Eliashberg theory, which accounts for the full momentum structure of the pairing potential and the energy dependence of the density of states. Our computations employ band structures chosen to model both the La2Sr2−xCuO4 and YBa2Cu3O7−δ families. For our spin fluctuation calculations, we take the dynamical susceptibility to be the pairing potential and examine two models of this susceptibility in the cuprates. We compare and contrast these models with available magnetic neutron-scattering data, since these data provide the most direct constraints on the susceptibility. We conclude that a model constrained by neutron-scattering measurements will not yield the observed 90-K Tc’s regardless of the strength of the electron-spin fluctuation coupling, even when the Van Hove singularity and momentum-space structure are accounted for; moreover, when transport constraints are applied to this type of model, we expect Tc≊10 K, as was found in an earlier paper. We also find that the Van Hove singularity enhances Tc much less effectively than weak-coupling calculations would suggest.

Source-reported materials — not catalogue approval

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