Nearly antiferromagnetic Fermi liquids: An analytic Eliashberg approach

I study a model in which quasiparticles on a two-dimensional square lattice interact via exchange of antiferromagnetic spin fluctuations, determining when one may write the Eliashberg equations for the normal-state self-energy and for Tc. For parameters which have been argued to be appropriate for high-Tc superconductors, I find the mass enhancement and scattering rate to vary over the Fermi surface by a factor of the ratio of the antiferromagnetic correlations length {ξ} to the lattice constant. The pairing kernel is dominated by high-frequency spin fluctuations, and so Tc in the BCS approximation is essentially independent of {ξ}, explaining previous numerical work. The analytic solution suggests normal-state self-energy effects may not lower Tc as severely as in other models of d-wave superconductivity.