Localization in Spatially Disordered Systems: Screening and Band Structure Effects at the EMA Level

Abstract

An analysis is given of Anderson localization in a one-band tight-binding model with off-diagonal disorder characteristic of a quenched liquid-like structure. We extend a localization criterion due to Logan and Wolynes, based on a self-consistent determination of the most probable value of the imaginary part of the site self-energy, to include screening arising from many-body terms in the renormalized perturbation series. Liquid state methods are used to examine screening, as embodied in an effective energy and density dependent transfer matrix element, at the level of the effective medium approximation. It is shown that this effective transfer matrix element is screened in high energy regions and anti-screened in low energy regions, so that extended states tend to occur in the low energy low density of states regime. Theoretical predictions for the mobility edge trajectories are found to be in reasonable agreement with recent computer simulations. The effects of the short-ranged structure of the system are also examined.

Key Words:

• Anderson localization
• screening
• effective medium approximation