Thermal conductance of nanostructured phononic crystals

The thermal conductance of mechanically suspended nanostructures has recently received much attention, in part due to the recent prediction and observation of the quantum limit for thermal conductance, which is observed in long, thin insulating beams at very low temperatures [D. E. Angelescu, M. C. Cross, and M. L. Roukes, Superlattices Microstruct. 23, 673 (1998); K. Schwab, E. A. Henriksen, J. M. Norlock, and M. L. Roukes, Nature 404, 974 (2000); I. G. C. Rego and G. Kirczenow, Phys. Rev. Lett. 81. 232 (1998); M. P, Blencowe. Phys. Rev. B 59. 4992 (1999)]. In this brief report, we describe a model calculation where the simple beam used to calculate quantum conductance [L. G. C. Rego and G. Kirczenow, Phys. Rev. Lett. 81, 232 (1998)] is replaced by a beam made from an artificial one-dimensional phononic crystal. We find that at the lowest temperatures and longest thermal-phonon wavelengths, the quantum limit is recovered, while for intermediate temperatures, where the dominant phonon wavelength is of the order of the phononic-crystal repeat distance, a significant suppression of the conductance is predicted. At higher temperatures the conductance returns to that of a simple beam.