Dielectric Catastrophe at the Mott Transition

A Mott insulator becomes metallic when the effect of correlations decreases. In the case of full frustration, a first-order phase transition is expected up to some critical endpoint. Above $T_{\rm crit}$ there might be some crossover and quantum critical behavior. But what happens below?

We start with the quantum spin liquid $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$ and tune the electronic bandwidth either by external pressure or by chemical substitution. DC resistivity confirms the insulator-metal transition (and even superconductivity in between). Optical spectroscopy reveals the development of the Drude-like contribution given evidence for coherent transport. Most surprising, however, is the divergency of the dielectric permittivity at the Mott insulator-to-metal transition at temperatures $T < T_{\rm crit} \approx 20$ K with $\epsilon_1 \approx 10^5$ and more. We show that the dielectric catastrophe is a fingerprint of the first-order phase transition where metallic and insulating regions coexist spatially. The percolative nature of the Mott transition dominates the low-frequency behavior compared to the closing of the Mott-Hubbard gap seen in the infrared range. All experimental trends are captured by dynamical mean-field theory of the single-band Hubbard model supplemented by percolation theory.