  We report on a possibility of efficient engineering of the acoustic phonon
energy spectrum in multishell tubular structures produced by a novel high-tech
method of self-organization of nano- and micro-architectures. The strain-driven
roll-up procedure paved the way for novel classes of metamaterials such as
single semiconductor radial micro- and nano-crystals and multi-layer spiral
micro- and nano-superlattices. The acoustic phonon dispersion is determined by
solving the equations of elastodynamics for InAs and GaAs material systems. It
is shown that the number of shells is an important control parameter of the
phonon dispersion together with the structure dimensions and acoustic impedance
mismatch between the superlattice layers. The obtained results suggest that
rolled up nano-architectures have potential for thermoelectric applications
owing to a possibility of significant reduction of the thermal conductivity
without degradation of the electronic transport.
