The role of weak interactions on the mobility-edge of strongly disordered electron systems

New insights into the nature of the mobility edge of a weakly correlated, disordered Anderson spectra will be presented within the typical medium dynamical cluster approximation (TMDCA). The TMDCA systematically incorporates non-local spatial correlations (beyond the single-site approximations) treating the disorder to all orders and the interacting, non-local cluster self-energy up to second order in the perturbation expansion of the interactions, $U$. An arbitrary small interaction is found to lead to an exponential fast crossover of the sharp mobility edge that separates the localized and extended states in the non-interacting regime below the critical disorder strength $W_c^{U=0}$ whenever the chemical potential of the non-interacting typical density of states is below the mobility edge energy. This smearing of the mobility edge is ascribed to the inelastic scattering due to $U$. However, as the chemical potential, $\mu$ approaches the smeared edge, reduction of the phase space for scattering by $U$ causes the edge to once again become sharp. A concomitant soft-pseudogap is found at energy, $\omega=0$ independent of filling, which is linear rather than quadratic in $\omega$, due to the lack of momentum conservation. The method is demonstrated on realistic low-dimensional structures.