Localization by electric fields in one-dimensional tight-binding systems

Abstract

We show that upon including an electric field within the class of one-dimensional single-orbital, nearest-neighbor, tight-binding models for a general nonperiodic potential, all eigenstates are localized. Irrespective of the details of the potential, the energy eigenstates show factorial localization and the eigenvalue spectrum is discrete, characterizable as a Stark ladder with nonuniform spacing. As an example, all eigenstates of the Aubry model become localized by the electric field, whatever the strength ${\varepsilon }_0$ of the incommensurate potential, whereas in the field-free case this occurs only if ${\varepsilon }_0$ exceeds the Aubry critical value. We also present detailed results for the Koster-Slater single-impurity model in an electric field. We indicate briefly some necessary conditions for observing field-enhanced localization.