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Using the scattering-matrix cascading method, we investigate the effect of structural defect on the acoustic phonon transmission and thermal conductance in the superlattice nanowire at low temperatures. In the present system, the phonon transmissions exhibit quite complex oscillatory behaviour. It is found that a lateral defect in an otherwise periodic structure significantly decrease the thermal conductance and completely washes away the transmission quantization. However, the appreciable transmission quantization survives in the presence of a longitudinal defect whereas a good quantization plateau of thermal conductance emerges below the universal level in a wide temperature range with the lateral defect.

Employing the transfer matrix method, we investigate the property of the interface optical-phonon modes (IOPMs) in a finite superlattice with a cap layer and a structural defect layer in the dielectric continuum approximation. In the present structure, there exist two types of defect IOPMs: localized modes and surface modes. The evolution of extended, localized and surface IOPMs can be clearly tracked with the thickness of the defect or cap layer. In some cases, degeneracy between surface IOPMs may occur, but the conservation of the total number of the IOPMs is always kept for every value of the transversal wave number. These results show that the spectra of these localized or surface IOPMs can be engineered by adjusting structural parameters.