Phonons and the coherence scale of models of heavy fermions

TL;DR

This paper investigates how phonons influence heavy fermion models, revealing that vertex corrections dominate and can cause Kondo breakdown even at weak couplings, challenging traditional approximations.

Contribution

It demonstrates the failure of Migdal's theorem in heavy fermion systems with phonons and shows how electron-phonon interactions reduce the coherence temperature leading to Kondo breakdown.

Findings

Vertex corrections dominate in heavy fermion models with phonons.

Electron-phonon interactions can cause Kondo breakdown at weak coupling.

Traditional approximations like Migdal-Eliashberg fail in this regime.

Abstract

We consider models of heavy fermions in the strong coupling or local moment limit and include phonon degrees of freedom on the conduction electrons. Due to the large mass or low coherence temperature of the heavy fermion state, it is shown that such a regime is dominated by vertex corrections which leads to the complete failure of the Migdal theorem. Even at weak electron-phonon couplings, binding of the conduction electrons competes with the Kondo effect and substantially reduces the coherence temperature, ultimately leading to the Kondo breakdown. Those results are obtained using a combination of the slave boson method and Migdal-Eliashberg approximation as well as the dynamical mean-field theory approximation.