Absence of localization in certain statically disordered lattices in any spatial dimension

We present a statically disordered electronic system in which under certain circumstances an initially localized particle necessarily becomes delocalized at long times regardless of the spatial dimension and the magnitude of the disorder. The model is based on correlations between diagonal and off-diagonal matrix elements and is shown to be applicable to structurally induced disorder in solids. Numerical and analytical calculations in one dimension indicate that transport is superdiffusive, with the mean-square displacement growing in time as $t^{3/2}$, regardless of the magnitude of the disorder. Transport is shown to arise in this model from a set of measure-zero unscattered states at a particular energy in the parent-ordered band. It is argued that, when the Fermi level coincides with the energy of the unscattered states, an enhancement of transport should obtain. In addition, it is shown that superdiffusive motion persists for a wide range of correlations between the diagonal and off-diagonal matrix elements when the disorder is structurally induced and chosen from a bivalued distribution. The relevance of these results to transport experiments is discussed.