Charge fluctuations, spin fluctuations, and superconductivity in the Anderson lattice model of heavy-fermion systems

Abstract

We determine the quasiparticle-quasiparticle interaction within the U\ensuremath{\rightarrow}\ensuremath{\infty} Anderson lattice model via an auxiliary boson (1/N) expansion to order (1/N${)}^{2}$. At leading order the interaction which is mediated by the exchange of a single zero-frequency fluctuation of the Bose field is repulsive in the p channel and attractive in the d channel. The dominant contribution to the interaction at order (1/N${)}^{2}$, which is due to spin fluctuations involving high-frequency, \ensuremath{\omega}>${T}_{K}$, fluctuations of the Bose field, is attractive in both p and d channels. The strength of this term relative to the charge fluctuation contribution is of order (${m}^{\mathrm{*}}$/m)${\mathrm{ln}}^{\mathrm{\ensuremath{-}}2}$(${\mathrm{Nm}}^{\mathrm{*}}$/m), where ${m}^{\mathrm{*}}$ is the heavy-fermion mass. Thus, for parameters corresponding to the majority of systems of interest, pairing in this model is allowed in both p and d channels; the origin of the attractive interaction, as in $^{3}\mathrm{He}$, is in the exchange of spin fluctuations.