Phonon anomalies due to strong-electronic correlations in layered organic metals

We show how the coupling between the phonons and electrons in a strongly co rrelated metal can result in phonon frequencies that have a nonmonotonic te mperature dependence. Dynamical mean-field theory is used to study the Hubb ard-Holstein model that describes the kappa-(BEDT-TTF)(2)X [where BEDT-TTF is bis-(ethylenedithia-tetrathiafulvalene)] family of superconducting molec ular crystals. The crossover with increasing temperature from a Fermi liqui d to a bad metal produces phonon anomalies that are relevant to recent Rama n scattering and acoustic experiments.