Approaches to the electronic structure of incommensurately modulated insulating crystals

A one-dimensional model of an incommensurately modulated insulator is investigated in perturbation theory using tight-binding theory with overlap. Results applicable in the sinusoidal regime are discussed in terms of the ‘‘structural resonance’’ of McConnell and Heine (Ref. ). The method of moments is used to explore ordering in one-dimensional chains, suggesting a novel electronic explanation of the driving force for the transition from disorder to order as a function of electron count (band filling).