Electronic Band Structure of Incommensurate Systems.

A method first developed by Dy, Wu and Wongtawatnugool (J. of Phys. C. 14, L781 (1981)) in the study of disordered systems is extended and applied in conjunction with direct diagonalization to study various tight binding hamiltonians with incommensurability. The methods used to study these systems are compared. These include various phases of the method of continued fraction which are often used in studying the localization behavior of states of disordered systems. One-dimensional systems with site potential and hopping integral modulations are studied in detail and a concept of quasi-localization is introduced to reconcile the controversies on the existence of mobility edges. Narrow bands are found in general exterior to broad bands which have narrow gaps embedded in them. The DWW method is also generalized to higher dimensional cases and shown to be pertinent by applying to special systems with known results.