Evidence for power law localization in disordered systems

Abstract

Various lines of evidence are presented to show that for electrons in three-dimensional ordered systems there may be a regime intermediate between the extended states characteristic of weak disorder and the exponentially localized states characteristic of strong disorder. It is suggested that in the intermediate regime the wavefunctions may fall off from its maximum amplitude with a power law. A detailed study of the eigenstates of a system of 216 atoms arranged on a diamond lattice supports this suggestion. Consequences of this power law behaviour for the AC conductivity at zero temperature, the DC conductivity at low temperatures, and the AC hopping conductivity are derived.