Anomalous delay of phonons reflected from the surface of a superlattice

We study theoretically the propagation of acoustic phonons in a superlattice (SL) with a free surface. A phonon incident normally on the SL from a substrate is perfectly reflected, but it comes back to the substrate either with a time delay or with a time advance. Specifically the time delay is enhanced considerably if the frequency of the incident phonon coincides with an eigenfrequency of the vibrational modes localized at the surface of the SL. This suggests the observability of the surface vibrational modes by a time-resolved phonon reflection experiment.