Vibrational modes of a simple-cubic layered superlattice

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Abstract
The matrix reduction method developed in an earlier paper is recast in a form useful for the study of layered superlattice structure. In particular, a rather general theorem relating the eigenvalues of a superlattice with those of the component lattice is proved for the model system of layered structure. Its most interesting feature is that the vibrational frequencies of the component lattice remain as those of the superlattice, consisting of repeated components, independent of the coupling strength between adjacent components. This analytical result is confirmed numerically by a series of frequency computations for the layered structures of type AB, ABAB and ABABAB, carried out without invoking the theorem.

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