Competition between disorder and Coulomb interaction in a two-dimensional plaquette Hubbard model

We have studied a disordered ${N}_{\mathrm{c}}\ifmmode\times\else\texttimes\fi{}{N}_{\mathrm{c}}$ plaquette Hubbard model on a two-dimensional square lattice at half-filling using a coherent potential approximation (CPA) in combination with a single-site dynamical mean field theory (DMFT) approach with a paramagnetic bath. Such a model conveniently interpolates between the ionic Hubbard model at ${N}_{\mathrm{c}}=\sqrt{2}$ and the Anderson model at ${N}_{\mathrm{c}}=\ensuremath{\infty}$ and enables the analysis of the various limiting properties. We confirmed that within the CPA approach a band insulator behavior appears for noninteracting strongly disordered systems with a small plaquette size ${N}_{\mathrm{c}}=4$, while the paramagnetic Anderson insulator with nearly gapless density of states is present for large plaquette sizes ${N}_{\mathrm{c}}=48$. When the interaction $U$ is turned on in the strongly fluctuating random potential regions, the electrons on the low energy states push each other into high energy states in DMFT in a paramagnetic bath and correlated metallic states with a quasiparticle peak and Hubbard bands emerge, though a larger critical interaction $U$ is needed to obtain this state from the paramagnetic Anderson insulator (${N}_{\mathrm{c}}=48$) than from the band insulator (${N}_{\mathrm{c}}=4$). Finally, we observe a Mott insulator behavior in the strong interaction $U$ regions for both ${N}_{\mathrm{c}}=4$ and ${N}_{\mathrm{c}}=48$ independent of the disorder strength. We discuss the application of this model to real materials.