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We develop a systematic typical medium dynamical cluster approximation thatprovides a proper description of the Anderson localization transition in threedimensions (3D). Our method successfully captures the localization phenomenonboth in the low and large disorder regimes, and allows us to study thelocalization in different momenta cells, which renders the discovery that theAnderson localization transition occurs in a cell-selective fashion. As afunction of cluster size, our method systematically recovers the re-entrancebehavior of the mobility edge and obtains the correct critical disorderstrength for Anderson localization in 3D.

A Typical Medium Dynamical Cluster Approximation for the Study of Anderson Localization in Three Dimensions