Localization of electrons in ordered and disordered systems II. Bound bands

The question is: how should we describe the electron states in an assembly of `atoms' with overlapping bound-state wave functions? In a regular lattice, these states are non-localized Bloch functions, forming a band of width B, say. Attention is focused on the effects of `cellular disorder', where a statistical variation wl is imposed on the energy of the bound state of the lth atom. A very simple version of the argument of Anderson (1958) demonstrates his conclusion that the states should all become localized if wl is distributed uniformly over a range of width somewhat greater than B. The same argument applied to the `equiconcentration binary alloy', where wl takes the values ±½W at random, shows that the band of propagating states is not destroyed, but splits into two narrower bands when W>>B.