Anderson localization in topologically disordered systems: The effects of band structure

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Abstract
A self-consistent theory of localization in a tight-binding model of topologically disordered systems is developed, which explicitly incorporates the influence of irreducible many-body interactions. These interactions are responsible for the detailed band structure of the system and stem from many-body terms in the renormalized perturbation series for the self-energy. The theory employs our previously developed disordered reference system in which the structure of the medium is taken into account, and makes considerable use of statistical mechanical methods which have direct parallels in conventional applications of liquid state theory. The resultant formulation leads to a self-consistent theory for the density of states and the localization characteristics of the system. The central notion of screening is introduced, whereby the simple transfer matrix element is replaced by an energy and density dependent renormalized transfer matrix element. The effect of screening on the mobility edge trajectories is found to be pronounced, and leads to substantially enhanced (diminished) stability of localized state near the upper (lower) band edge in the density of states.