Title:Oral: Migdal-Eliashberg superconductivity in a Kondo lattice

We apply the Migdal-Eliashberg theory of superconductivity to heavy-fermion and mixed-valence materials. Specifically, we extend the periodic Anderson model to a case when a strong coupling exists between itinerant electrons and lattice vibrations. Using the large-N approach within the saddle-point approximation, we derive a set of coupled nonlinear equations that describe the competition between the crossover to heavy-fermion or mixed-valence regimes and conventional superconductivity. We find that superconductivity at strong coupling emerges on par with the development of the many-body coherence in a Kondo lattice. Superconductivity is gradually suppressed with the onset of Kondo screening, and for strong electron-phonon coupling, the Kondo screening exhibits a characteristic re-entrant behavior. Even though the suppression of superconductivity is weaker in the mixed-valence regime for both weak and strong coupling limits compared to the local moment one, the superconducting critical temperature remains nonzero. In the weak coupling limit, the onset of the many-body coherence develops gradually; in the strong coupling limit, it emerges abruptly in the mixed valence regime, while in the local moment regime, the f-electrons remain effectively decoupled from the conduction electrons.