Localization in One-Dimensional Lattices in the Presence of Incommensurate Potentials

Abstract

The density of states and the localized or extended nature of the eigenstates is investigated in one-dimensional crystals with a modulation potential incommensurate with that of the underlying lattice. Studies of the transmission coefficient $T$ and of the spatial dependence of the eigenstates show that even in one dimension it is possible to have a mobility edge. The implications of these results on experimentally measured quantities are also discussed.