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 T(c). For parameters which have been argued to be appropriate for high-T, 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-xi to the lattice constant. The pairing kernel is dominated by high-frequency spin fluctuations, and so T(c) in the BCS approximation is essentially independent of xi, explaining previous numerical work. The analytic solution suggests normal-state self-energy effects may not lower T(c) as severely as in other models of d-wave superconductivity.