Calculations of properties in two-dimensional spin-fluctuation superconductors

The strong coupling Eliashberg equations for a superconductor stabilized through antiferromagnetic spin fluctuations involve three coupled nonlinear equations for the gap, the renormalization, and the energy shift. Each quantity depends on three variables, namely momentum in the two-dimensional Brillouin zone and on Matsubara frequencies accounting for retardation. Fast-Fourier-transform techniques are applied to generate numerical solutions based on the phenomenological form of the susceptibility suggested by Millis, Monien, and Pines (MMP). The calculated bare susceptibilities are not consistent with the input MMP form, and the unusual temperature dependence of the NMR below Tc is not reproduced in our calculations