Phase Separation close to the density-driven Mott transition in the Hubbard-Holstein model

The density driven Mott transition is studied by means of Dynamical Mean-Field Theory in the Hubbard-Holstein model, where the Hubbard term leading to the Mott transition is supplemented by an electron-phonon (e-ph) term. We show that an intermediate e-ph coupling leads to a first-order transition at T=0, which is accompanied by phase separation between a metal and an insulator. The compressibility in the metallic phase is substantially enhanced. At quite larger values of the coupling a polaronic phase emerges coexisting with a non-polaronic metal.