Theory of hopping conductivity of a suspension of nanowires in an insulator

Thermal conductivity (kappa) of the Al-based Mackay-type 1/1-cubic approximants (alpha-phase) was investigated over a wide temperature range from 2 K to 300 K. Behaviors of kappa(T) observed for these 1/1-cubic approximants were essentially the same with those reported for the corresponding icosahedral quasicrystals; very small magnitude lower than 4.5 W/m K, small contribution of electrons, and possession of a local maximum and a local minimum around 30-50 K and 100-200 K, respectively. By analyzing measured lattice thermal conductivity kappa(lat)(T) in terms both of local atomic arrangements and phonon dispersions, we revealed that kappa(lat)(T) is greatly reduced by combination of the small group velocity of phonons and the enhanced umklapp process of phonon scattering. Those characteristics are brought about by the large lattice constant and vacancies in the structure.