Stark-ladder resonances in ordered and disordered electrified chains

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Abstract
The electronic energy spectrum of a one-dimensional chain with periodic and disordered potentials in the presence of a constant electric field F is studied. Under certain conditions the spectrum shows the resonant states predicted by Wannier. These Stark-ladder resonances (SLR) are studied in detail for different potentials, amount of disorder, W, and length of the chains, L. Thermal population effects on the resonances are also considered. The different potentials correspond to rectangles with random widths and different heights, that include the extreme δ-function limit. The Poincaré-map method is used to calculate the reflectivity and transmittivity of the chains. Use is made of different scattering theory criteria to characterize the resonances. For electrons incident on the chain with energies, E≤FL, the electrostatic potential energy produced by the field, Levinson’s theorem is used to calculate the density of states from the derivatives of the phase shifts with respect to E. For energies E≥FL, the transmission coefficient T is calculated as a function of E, and the SLR appear as equally spaced maxima of T as E is varied.