Resonant enhancement of Anderson localization: Analytical approach

Abstract

We study localization properties of the eigenstates and wave transport in a one-dimensional system consisting of a set of barriers and/or wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced Anderson localization is the presence of the resonances emerging due to the coherent interaction of the waves reflected from the interfaces between the wells and/or barriers. Our theoretical approach allows to derive the localization length in infinite samples both out of the resonances and close to them. We examine how the transport properties of finite samples can be described in terms of this length. It is shown that the analytical expressions obtained by standard methods for continuous random potentials can be used in our discrete model, in spite of the presence of resonances that cannot be described by conventional theories. All our results are illustrated with numerical data manifesting an excellent agreement with the theory.

Transport through quasi-one-dimensional wires with correlated disorder

“…Moreover, recently a new approach has been developed in Ref. [6] allowing one to modify the standard perturbation theory in such a way that it gives good results also at the resonant energies. In particular, it was shown that Eq.…”

“…[6,7], outside the resonances the analytical results for the transmission coefficient and its variance, obtained for 1D continuous random potentials, can be safely used for tight-binding and KronigPenny models as well, provided the energy is not too close to the resonances. Moreover, it was shown that with specific methods one can effectively modify the theory and describe the global properties of the transmission within the whole energy region, including the resonance regions 6 .…”

“…[6,7], outside the resonances the analytical results for the transmission coefficient and its variance, obtained for 1D continuous random potentials, can be safely used for tight-binding and KronigPenny models as well, provided the energy is not too close to the resonances. Moreover, it was shown that with specific methods one can effectively modify the theory and describe the global properties of the transmission within the whole energy region, including the resonance regions 6 . For a long time the localization properties of weakly random potentials in the presence of correlations (colored-noise potentials) were discussed scarcely, in spite of the fact that the results developed for continuous 1D potentials have been obtained in the general form 8 , allowing to analyze the influence of both short and long-range correlations (see discussion in Ref.…”

Resonant Anderson localization in segmented wires

“…1b), a problem that was studied in Refs. [1][2][3][4]. In particular, we have followed the approach of Ref.…”

“…The electrical transport properties of bend semiconductor nanowires attracted much interest some years ago [1][2][3][4]. In particular, phenomena such as the formation of localized states and the scattering behavior of circular bends were considered.…”