Acoustic interference in random superlattices

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Abstract
We study theoretically the interference effects and the resulting transmission of acoustic phonons in random superlattices, i.e., multilayered systems in which two kinds of building blocks A and B are stacked at random. We derive (i) the recursion relations satisfied by the superlattice structure factors, and (ii) an analytic expression for the ensemble-averaged intensity of phonons reflected from layer interfaces of an infinite system. We predict a number of sharp features in the intensity versus frequency, which appear rather regularly. Furthermore, numerical calculations for both the double- and single-layer random superlattices indeed exhibit distinctive dip structures in phonon transmission spectra which are in good agreement with the analytical results. We also find that the single-layer random superlattices show an effective phonon-filtering action as the system size is increased, i.e., they prevent the transmission of phonons except for those satisfying resonance conditions.

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