  Motivated by the current interest in the understanding of the Mott insulators
away from half filling, observed in many perovskite oxides, we study the Mott
metal-insulator transition (MIT) in the doped Hubbard-Holstein model using the
Hatree-Fock mean field theory. The Hubbard-Holstein model is the simplest model
containing both the Coulomb and the electron-lattice interactions, which are
important ingredients in the physics of the perovskite oxides. In contrast to
the half-filled Hubbard model, which always results in a single phase (either
metallic or insulating), our results show that away from half-filling, a mixed
phase of metallic and insulating regions occur. As the dopant concentration is
increased, the metallic part progressively grows in volume, until it exceeds
the percolation threshold, leading to percolative conduction. This happens
above a critical dopant concentration $\delta_c$, which, depending on the
strength of the electron-lattice interaction, can be a significant fraction of
unity. This means that the material could be insulating even for a substantial
amount of doping, in contrast to the expectation that doped holes would destroy
the insulating behavior of the half-filled Hubbard model. Our theory provides a
framework for the understanding of the density-driven metal-insulator
transition observed in many complex oxides.
