We show how the coupling between the phonons and electrons in a strongly correlated metal can result in phonon frequencies that have a nonmonotonic temperature dependence. Dynamical mean-field theory is used to study the Hubbard-Holstein model that describes the $\kappa -(\mathrm{BEDT}-\mathrm{TTF}{)}_{2}X$ [where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene)] family of superconducting molecular crystals. The crossover with increasing temperature from a Fermi liquid to a bad metal produces phonon anomalies that are relevant to recent Raman scattering and acoustic experiments.

• Received 6 September 2000

DOI:https://doi.org/10.1103/PhysRevB.62.16442