Study of the Anderson localization in real materials using typical medium dynamical cluster approximation

We generalize the typical medium dynamical cluster approximation to multi-orbital disordered systems. Combining it with the first principals downfolding and unfolding methods to derive an effective low energy model, we apply our extended formalism to real materials where strong disorder exists. These include, e.g., the iron selenide superconductors K$_x$Fe$_{2-y}$Se$_2$ with Fe vacancies, Ga$_{1-x}$Mn$_x$N and S doped Si. By looking at the typical density of states, we study the mobility edge and the localization effects in these materials, which is useful to understand the mechanism of their insulating behavior. We find for example, that even the disorder associated with 12\% vacancies in K$_x$Fe$_{2-y}$Se$_2$ together with the anisotropy is not sufficient to cause localization.