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

1986; American Physical Society; Volume: 34; Issue: 6 Linguagem: Inglês

10.1103/physrevb.34.3674

1095-3795

Marshall Luban, James H. Luscombe,

Cold Atom Physics and Bose-Einstein Condensates

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 ${\ensuremath{\varepsilon}}_{0}$ of the incommensurate potential, whereas in the field-free case this occurs only if ${\ensuremath{\varepsilon}}_{0}$ 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.