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Title: 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 Anderson lattice model to a case when there exists a strong coupling between itinerant electrons and lattice vibrations. Using the saddle-point approximation, we derive a set of coupled nonlinear equations which describe competition between the crossover to a 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 the Kondo screening and for strong electron-phonon coupling the Kondo screening exhibits a characteristic re-entrant behavior. Even though for both weak and strong coupling limits the suppression of superconductivity is weaker in the mixed-valence regime compared to the local moment one, superconducting critical temperature still 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. Possibility of experimental realization of these effects in Ce-based compounds is also discussed.  more » « less
Award ID(s):
2002795
PAR ID:
10545036
Author(s) / Creator(s):
;
Publisher / Repository:
IOP
Date Published:
Journal Name:
Journal of Physics: Condensed Matter
Volume:
36
Issue:
32
ISSN:
0953-8984
Page Range / eLocation ID:
325602
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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