Imperfect phonon transmission and quantized thermal conductance in dielectric nanowires

We study the thermal conductance g in catenoidal wires by explicitly calculating the transmission rates of 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 [Phys. Rev. Lett. 81, 232 (1998)], we find the presence of a plateau in g/g₀ (g₀ = π²k²_BT/3h is the thermal conductance quantum), indicating the quantization of thermal conductance. However, below this temperature range g/g₀ is modified, that is, the quantization is broken, due to imperfect transmissions of the acoustic modes of vibration. As temperature goes down further, the recovery of the conductance, which suggests the quantization at T = 0 K, is predicted. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)