Lattice thermal conductance in nanowires at low temperatures: Breakdown and recovery of quantization

Abstract

The quantization of lattice thermal conductance $g$ normalized by ${g}_{0}={\ensuremath{\pi}}^{2}{k}_{B}^{2}T∕3h$ (the universal quantum of thermal conductance) was recently predicted theoretically to take an integer value over a finite range of temperature and then observed experimentally in nanowires with catenoidal contacts. The prediction of this quantization by Rego and Kirczenow [Phys. Rev. Lett. 81, 232 (1998)] relies on a study of only dilatational (longitudinal) vibrational mode in the wires. We study the thermal conductance in catenoidal wires by explicitly calculating the transmission rates of the six distinct vibrational modes (four acoustic and two low-lying optical modes) and applying the Landauer formula for the one-dimensional thermal transport in the ballistic regime. In a temperature range similar to the one predicted by Rego and Kirczenow, we find the presence of a plateau in $g∕{g}_{0}$. However, below this temperature range $g∕{g}_{0}$ is modified---that is, the quantization is broken---due to imperfect transmission of the acoustic modes of vibration. Our new observation is that, as temperature goes down further, the recovery of the quantization of $g∕{g}_{0}$ should occur. These results are found assuming GaAs as a wire material, but we also make similar calculations for silicon nitride wires used experimentally.