Acoustic phonon modes and dispersion relations of nanowire superlattices.

We study theoretically acoustic phonon modes in nanowire superlattices (NWSLs) composed of cubic materials. We classify the acoustic phonon modes in rectangular and square cross-section NWSLs, based on group theory. For NWSLs consisting of GaAs and AlAs, we calculate numerically the dispersion relations of each phonon mode and corresponding displacement fields. We examine the effects of both the lateral confinement and superlattice modulation along the wire axis. The results suggest that peculiar electron-phonon interactions occur because the vibrations of both the lateral and longitudinal confining potentials induce scattering potential in addition to the deformation and piezoelectric potentials.