Localization criteria and bethe lattices

Abstract

The problem of electron localization in static, cellularly disordered, tight-binding Bethe lattices is considered. Predictions of a localization criterion due to Economou and Cohen are developed for mobility edges and critical percolation concentrations, and compared with known exact results. The status of the criterion is critically discussed and several general limitations are illustrated. It is concluded that in some respects the criterion is coarsely representative for a range of real lattices but largely for fortuitous reasons.