Localized vibrational modes in superlattices

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Abstract
The effect of an impurity cell on the vibrational properties of superlattices is studied theoretically. The continuous equation governing the elastic-wave motion in a superlattice is transformed exactly to a discrete form which is analogous to the equation for the displacement in one-dimensional discrete lattices. With the use of this equation isolated frequencies associated with the vibrations localized near the impurity cell are predicted in the band gaps at the center and boundary of the folded Brillouin zone of the host superlattice. Numerical calculation reveals further the existence of impurity states in the intrazone gaps due to intermode Bragg reflection. The calculated phonon transmission rate shows local enhancements due to these localized states, suggesting their observability by phonon spectroscopic experiment with a quasimonochromatic phonon detector.