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

We determine the quasiparticle-quasiparticle interaction within the U→∞ 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, ω>$T_K$, 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)${\ln }^{\mathrm{-}2}$(${\mathrm{Nm}}^{\mathrm{*}}$/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.