Antiferromagnetic spin-fluctuation effects on quasiparticle damping and superconductivity in high-Tcmaterials

Abstract

First we calculate the random-phase-approximation (RPA) dynamic spin susceptibility of a two-dimensional (2D) Hubbard model for different band fillings and on-site Coulomb couplings U. The q-averaged spectral function for antiparamagnon exchange interaction starts linearly in frequency and then becomes almost constant, in agreement with ‘‘nested Fermi-liquid theory.’’ Employing this interaction function we solve the Migdal-Eliashberg equations for the self-energy of quasiparticles in the 2D tight-binding band. In the normal state the damping rate of quasiparticles varies approximately linearly with frequency above ${\mathrm{\omega }}_{\mathit{c}}$ and linearly in temperature above ${\mathit{T}}^{\mathrm{*}}$, where ${\mathrm{\omega }}_{\mathit{c}}$ and ${\mathit{T}}^{\mathrm{*}}$ increase with decreasing degrees of nesting of the Fermi surface (${\mathrm{\omega }}_{\mathit{c}}$ and ${\mathit{T}}^{\mathrm{*}}$ denote the crossover values from quadratic to linear behavior). For a realistic choice of parameters we find qualitative agreement with inverse particle lifetimes obtained from infrared-reflectivity and photoemission data in the high-${\mathit{T}}_{\mathit{c}}$ materials. Within the RPA we find that the d-wave and extended s-wave pairing interactions due to exchange of one antiparamagnon is not strong enough to explain high-${\mathit{T}}_{\mathit{c}}$ behavior.