Mott and Wigner-Mott transition away from half-filling

We study the Mott transition in strongly correlated electron systems away from half-filling in the presence of finite-range Coulomb interaction and/or a superstructure associated with an inhomogeneous electronic state. Using a cluster Gutzwiller approach, we map a minimal single band $t$-$U$-$V$-$\Delta$ model with nearest neighbor Coulomb repulsion $V$ and superlattice potential $\Delta_i$ to a two-orbital Hubbard model with intra and interorbital Coulomb repulsion $U$ and $U^\prime$ and a crystal field splitting $\Delta$. We obtain the Mott transition at quarter-filling from both uniform and $\sqrt{2}\times\sqrt{2}$ charge density wave metals and discuss the physics of the Mott and Wigner-Mott metal-insulator transition.