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Metal-Insulator-Transition in a Weakly interacting Disordered Electron System

The interplay of interactions and disorder is studied using the Anderson-Hubbard model within the typical medium dynamical cluster approximation. Treating the interacting, non-local cluster self-energy ($Σ_c[{\cal \tilde{G}}](i,j\neq i)$) up to second order in the perturbation expansion of interactions, $U^2$, with a systematic incorporation of non-local spatial correlations and diagonal disorder, we explore the initial effects of electron interactions ($U$) in three dimensions. We find that the critical disorder strength ($W_c^U$), required to localize all states, increases with increasing $U$; implying that the metallic phase is stabilized by interactions. Using our results, we predict a soft pseudogap at the intermediate $W$ close to $W_c^U$ and demonstrate that the mobility edge ($ω_ε$) is preserved as long as the chemical potential, $μ$, is at or beyond the mobility edge energy.