We show that simple band models of the electronic structure of disordered systems have features exhibiting two distinct classes of behavior, universal, and non-universal, depending on dimensionality. The universal features become independent of structure and disorder after all lengths and energies have been appropriately scaled, provided energies are restricted to the vicinity of the band edges, and the disorder is small relative to the band width, and lengths are large on an atomic scale. This universal structure is shifted in energy for more than two dimensions in a readily calculable non-universal way. Deep in the tail non-universal behavior emerges as the localized states become sensitive to potential fluctuations on individual sites. Deep in the band non-universal behavior emerges at electron energies comparable in scale to the transfer matrix elements.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Ceramics and Composites
- Condensed Matter Physics
- Materials Chemistry