Origins of the attractive interactions for the Cooper pairs in dense Kondo systems

Abstract

Jichu, Matsuura, and Kuroda proposed a general procedure for treating the periodic Anderson model and showed that there exist quasiparticles with bandwidth of O($T_K$) ($T_K$ is the Kondo temperature), which account for the heavy fermions observed in the experiments. In the present study, we apply such a procedure to investigate the origins of the quasiparticle interaction for the Cooper pairing in the system. We find that (1) the Fermi-liquid interaction, specifically mediated by the spin-density and the charge-density fluctuations of the quasi-particles themselves, generally has strength of O($T_K$); (2) the quasiparticle-phonon coupling through modulation of the Kondo effect is proportional to the electronic energy above the Fermi level, which is in significant contrast to the models assumed in the earlier studies available in literature. Correspondingly, the phonon-mediated quasiparticle-pairing interaction has a peculiar frequency dependence, because of which the interaction plays an appreciable role only in strong-coupling cases. The superconductivity observed in the materials like ${\mathrm{CeCu}}_2$ ${\mathrm{Si}}_2$ can be examples for such cases.