Band structure and localization in incommensurate lattice potentials

A metal-insulator transition was found by Aubry in a one-dimensional tight-binding model containing a modulation potential incommensurate with the crystal lattice. In this article the extended bandlike states that occur in the metallic regime are studied using a quasiclassical approach. Near the metal-insulator transition the bands contain a hierarchy of gaps of ever decreasing magnitude. Although there is in principle a gap at every energy, since most gaps are negligible, the system is still expected to behave like a metal. In the insulating regime the wave functions were found to be exponentially localized with a localization length which approaches infinity at the metal-insulator transition. Possible experimental consequences of the predicted spectrum are discussed.