Phonon universal-transmission fluctuations and localization in semiconductor superlattices with a controlled degree of order

Abstract

We study both analytically and numerically phonon transmission fluctuations and localization in partially ordered superlattices with correlations among neighboring layers. In order to generate a sequence of layers with a varying degree of order we employ a model proposed by Hendricks and Teller as well as partially ordered versions of deterministic aperiodic superlattices. By changing a parameter measuring the correlation among adjacent layers, the Hendricks-Teller superlattice exhibits a transition from periodic ordering, with alternating layers, to the phase separated opposite limit; including many intermediate arrangements and the completely random case. In the partially ordered versions of deterministic superlattices, there is short-range order (among any N consecutive layers) and long range disorder, as in the N-state Markov chains. The average and fluctuations in the transmission, the backscattering rate, and the localization length in these multilayered systems are calculated based on the superlattice structure factors we derive analytically. The standard deviation of the transmission versus the average transmission lies on a universal curve irrespective of the specific type of disorder of the SL. We illustrate these general results by applying them to several GaAs-AlAs superlattices for the proposed experimental observation of phonon universal transmission fluctuations. 62.65.+k, 63.50.+x, 68.65.+g, 71.55.Jv

Controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers

“…In this case, the power-law decrease of the transmission coefficient with an increase of the sample length should be observed. 16,38 Moreover, experimental and theoretical studies of JPW propagation in 2D Josephson arrays could be a useful tool to study wave localization in 2D structures.…”

“…Previous related work on acoustic wave propagation in semiconductor multilayers appears in Ref. 16. Using our Eqs.…”

“…If the correlations are long-range ͓e.g., ͑r͒ decays as a power law͔, a continuum of extended states can appear in the energy spectrum, 16,25,33 since ˜͑ q͒ can vanish in an interval of q. In other words, controllable long-range correlations facilitate the observation of the metal-insulator transition.…”

“…These phenomena involving disorder can be conveniently described using 1D tight-binding models ͑see, e.g., Refs. [16][17][18]20, and 21͒. For a long time, it was believed that localized and extended states in 1D potentials did not coexist and 1D systems could not display complex dynamic features such as the metal-insulator transition.…”

Transport and localization in periodic and disordered graphene superlattices

“…25,26 ). Additional analogies, not discussed here, also exist with the transport and localization of phonons in different kinds of periodic and random one-dimensional structures 27,28,29 .…”