Energy spectrum, transmittance, and localization in an incommensurate nonanalytic potential

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Abstract
The energy spectrum, localization properties of eigenstates, and transmittance are calculated for a one-dimensional incommensurate chain with a potential which is the absolute value of the cosine potential used in the Aubry model. This nonanalytical potential, which has cusps, has previously been proposed by Bardeen as a model for the effective pinning potential for the motion of charge-density waves. Results show that, contrary to what happens in the Aubry model, a sharp mobility edge exists for intermediate values of the modulation and separates extended low-energy states from high-energy localized states. The first three terms in the Fourier expansion of the studied potential correspond very closely to the Soukoulis-Economou potential. Compared to that later model, the effect of the nonanalyticity in the Bardeen potential, represented by the infinite rest of the above-mentioned Fourier expansion, is found to be small.