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

We consider competition of the 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 the single-impurity Kondo effect in superconductors, we have found the principal possibility of a reentrant 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 the most validity in the low-temperature Fermi liquid regime, without reentrant behavior of T_c . To check its applicability, we performed the fit for the x dependence of T_c in Ce_1-xLa_xRu₃Si₂ and obtained an excellent agreement with the experimental data, although no reentrance 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 the 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 a sizable superconducting gap on another Fermi surface, for which hybridization or other heavy fermion effects are more significant. By passing, we cite the old results that show that the jump in the specific heat at the transition reflects the heaviness of carriers on this Fermi surface independently of mechanisms responsible for superconductivity.