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 a 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 nonpolaronic metal.