Competition between phonon superconductivity and Kondo screening in mixed valence and heavy fermion compounds

We consider competition of Kondo effect and s-wave superconductivity in heavy fermion and mixed valence superconductors, using the phenomenological approach for the periodic Anderson model. Similar to the well known results for single-impurity Kondo effect in superconductors, we have found principal possibility of a re-entrant regime of the superconducting transition temperature, $T_c$, in heavy fermion superconductors in a narrow range of model parameters and concentration of f-electrons. Suppression of $T_c$ in mixed valence superconductors is much weaker. Our theory has most validity in the low-temperature Fermi liquid regime, without re-entrant behavior of $T_c$. To check its applicability, we performed the fit for the $x$-dependence of $T_c$ in Ce$_{1-x}$La$_x$Ru$_3$Si$_2$ and obtained an excellent agreement with the experimental data, although no re-entrance was found in this case. Other experimental data are discussed in the light of our theoretical analysis. In particular, we compare temperatures of the superconducting transition for some known homologs, i.e., the analog periodic lattice compounds with and without f-elements. For a few pairs of homologs superconductivity exists only in the heavy fermion materials, thus confirming uniqueness of superconductivity mechanisms for the latter. We suggest that for some other compounds the value of $T_c$ may remain of the same order in the two homologs, if superconductivity originates mainly on some light Fermi surface, but induces sizable superconducting gap on another Fermi surface,for which hybridization or other heavy fermion effects are more significant.