Phonon anomalies due to strong electronic correlations in layered organic metals

We show how the coupling between the phonons and electrons in a strongly correlated metal can result in phonon frequencies which have a non-monotonic temperature dependence. Dynamical mean-field theory is used to study the Hubbard-Holstein model that describes the \kappa-(BEDT-TTF)_2 X family of superconducting molecular crystals. The crossover with increasing temperature from a Fermi liquid to a bad metal produces phonon anomalies that are consistent with recent Raman scattering and acoustic experiments.