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 = 2 k B 2 T /3h ͑the universal quantum of thermal conductance͒ 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 ͑1998͔͒ relies on a study of only dilatational ͑longitudinal͒ 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 modes͒ 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 brokendue 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.

Heat transmission between a profiled nanowire and a thermal bath

“…Below 1 K, the thermal conductance decreases below the value of the universal thermal conductance as expected in different models at intermediate temperature. 15,24 Only one sample (P1) exhibits a thermal conductance that is relatively close to four times the universal quantum of thermal conductance (4K q ) as predicted by Rego and Kirczenow,14 and in a work by Tanaka et al 15 However, this is not a general behavior because samples P2 and P3 have a thermal conductance even lower than in the case of the abrupt junction. The dispersion of the experimental results is intriguing because it only occurs for temperature below 1 K. This may be due to varying roughness from one sample to the other, giving different value of mean free path.…”

“…A way to improve the thermal contact consists in profiling the shape at the interface nanowire-thermal reservoir. Rego and Kirczenow, 14 and then Tanaka, Yoshida, and Tamura, 15 demonstrated that a catenoidal profile allows a transmission coefficient close to one for a large range of frequencies. In this particular case, and for the massless mode, the thermal conductance becomes an integer multiple of K q ¼ p 2 k 2 B T=3h, known as the universal quantum of thermal conductance.…”

“…The half lengths k of the catenoidal nanowires are the following: k P1 ¼ 3:5 lm; k P2 ¼ 2:6 lm, and k P3 ¼ 2:9 lm; this represents the straight part of the nanowire where the crosssection can be seen as uniform (see, for instance, Ref. 15). The roughness of the flanks of these wires is estimated to be of few nanometers 6 due to the RIE etching.…”

Thermal transport associated with ballistic phonons in asymmetric quantum structures

“…The situation is similar to the SV mode. Then, the mixing of P and SV modes occurs and could lead to the appearance of the more modes [35,56]. However, considering our assumption that regions I, II, and III have the same thickness and is small with respect to the other dimensions and also to the wavelength of the elastic waves, the horizontally polarized shear SH mode are decoupled from the phonon mode P (or SV ).…”

Multimode quantized thermal conductance tuned by electric field in a composite polymer

“…[17,18] Clearly alternative approaches have to be explored in order to open multiple phononic channels.…”