Abstract
We theoretically study the localized vibrational modes in a superlattice with a defect layer. In particular, we derive simple formulas for the eigenfrequency of this localized mode and the corresponding decay factor. Our formulas show explicitly how these quantities depend on the constituent layers of the superlattice and also the width of the defect layer. These formulas are useful for systematic understanding of the localized acoustic phonons in superlattice.
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