Ultrasonic investigation of the P-T phase diagram of $\kappa$-(BEDT-TTF)$_{2}$X organic superconductors

Depending on the exact pressure conditions (hydrostatic or chemical by anion X substitution), the normal phase of the $\kappa $-(BEDT-TTF)$_{2}$X organic conductors is either a Mott insulator and/or an unconventional metal. Among them, $\kappa $-(BEDT-TTF)$_{2}$Cu[ N(CN)$_{2}$] Cl stands as the prototype material since it shows the complete sequence of states within a pressure interval of a few hundreds bars. Ultrasonic waves constitute excellent tools to probe such electronic states but experiments on organics are scarce due their brittleness and very small dimensions. We present a recent ultrasonic study of a few $\kappa $-(BEDT-TTF)$_{2}$X organic compounds under hydrostatic pressure conditions. Different phase transitions are identified trough several elastic anomalies characterized from isobaric and isothermal sweeps. Beyond the confirmation of the $P-T$ diagram of a typical Mott material, our ultrasonic data on the $\kappa $-(BEDT-TTF)$_{2}$Cu[ N(CN)$_{2}$] Cl conductor allows a detailed study of the critical point region. The very large softening of the velocity at the critical point corresponds to the predicted compressibility divergence of the electronic degrees of freedom and validates then, the DMFT picture of the Mott transition. Most importantly, our data reveal that the high pressure crossover line coincides with the pseudogap features previously observed in magnetic and transport properties. Impurity and crystal quality effects on the phase diagram will also be discussed. Key words. Organic – superconductivity – ultrasonics – Mott insulator