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

We have studied a disordered $N_{\rm c} \times N_{\rm c}$ 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 $N_{\rm c}=\sqrt{2}$ and the Anderson model at $N_{\rm c} = \infty$ and enables the analysis of the various limiting properties. We confirmed that within the CPA approach a band insulator behavior appears for non-interacting strongly disordered systems with a small plaquette size $N_{\rm c} = 4$, while the paramagnetic Anderson insulator with nearly gapless density of states is present for large plaquette sizes $N_{\rm c}=48$. 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 ($N_{\rm c}=48$) than from the band insulator ($N_{\rm c}=4$). Finally, we observe a Mott insulator behavior in the strong interaction $U$ regions for both $N_{\rm c}=4$ and $N_{\rm c}=48$ independent of the disorder strength. We discuss the application of this model to real materials.