Electron localization in crystals with quasiperiodic lattice potentials

Abstract

Anderson's locator perturbation theory, used in the study of localization in disordered systems, is applied to the study of electron localization in tight-binding model lattices containing a periodic modulation potential incommensurate with the crystal lattice. Numerical studies of the convergence of the resulting continued fraction for the self-energy indicate that in one dimension there is a transition at a critical value of strength of the modulation from all states localized to all states extended, unlike the disordered crystal case. Studies in two and three dimensions show that there exists an intermediate range of modulation strength over which there can be mobility edges separating localized and extended states. Specific application is made of the results in one dimension to a system containing a superlattice modulation in one direction.