Enhanced Valence Fluctuations Caused by f-c Coulomb Interaction in Ce-Based Heavy Electrons: Possible Origin of Pressure-Induced Enhancement of Superconducting Transition Temperature in \Ge and Related Compounds

Properties of an extended periodic Anderson model with the f-c Coulomb interaction $\text{Ufc}$ is studied as a model for \Ge and related compounds which is cosidered to exhibit a sharp valence change under pressure. The problem is treated by extending the {\it slave-boson} and large-N expansion method to treat the present system. It is shown that, as the f-level ${ϵ}_{\mathrm{f}}$ is increased relative to the Fermi level, the sharp valence change is caused by the effect of $\text{Ufc}$ with moderate strength of the order of the bandwith of conduction electrons. The superconducting transition temperature $T_{\text{rc}}$ due to the valence-fluctuation exchange is estimated on the slave-boson fluctuation approximation. In the model with spherical Fermi surface, $T_{\text{rc}}$ exhibits sharp peak as a function of ${ϵ}_{\mathrm{f}}$, simulating the effect of pressure, for the d-wave pairing channel.