Heat conduction measurements in ballistic 1D phonon waveguides indicate breakdown of the thermal conductance quantization

Adib Tavakoli,Kunal Lulla,Olivier Bourgeois,Natalio Mingo,Eddy Collin,Thierry Crozes

doi:10.1038/s41467-018-06791-0

Abstract

Emerging quantum technologies require mastering thermal management, especially at the nanoscale. It is now accepted that thermal metamaterial-based phonon manipulation is possible, especially at sub-kelvin temperatures. In these extreme limits of low temperatures and dimensions, heat conduction enters a quantum regime where phonon exchange obeys the Landauer formalism. Phonon transport is then governed by the transmission coefficients between the ballistic conductor and the thermal reservoirs. Here we report on ultra-sensitive thermal experiments made on ballistic 1D phonon conductors using a micro-platform suspended sensor. Our thermal conductance measurements attain a power sensitivity of 15 attoWatts sqrt {{mathrm{Hz}}} ,^{ - 1} around 100 mK. Ballistic thermal transport is dominated by non-ideal transmission coefficients and not by the quantized thermal conductance of the nanowire itself. This limitation of heat transport in the quantum regime may have a significant impact on modern thermal management and thermal circuit design.

Highlights

Emerging quantum technologies require mastering thermal management, especially at the nanoscale
The thermal conductance and the transmission coefficient are measured as a function of temperature in the ballistic regime
The low transmission coefficients suggest that different mechanisms are at stake preventing a perfect transmission of phonons between the reservoirs

Summary

Introduction

Emerging quantum technologies require mastering thermal management, especially at the nanoscale. In a one dimensional (1D) quantum channel connecting two reservoirs, the heat current is related to the probability for a phonon of being transmitted from one heat bath to the other when they are kept at different temperatures This is well described by the Landauer formalism, which expresses thermal conductance in terms of transmission between reservoirs[6,7,8,9,10,11,12,13,14]. Many experiments have been done for electrons[15,16,17] or photons[18,19], very few experimental attempts have been made to probe this limit for phonons[20,21,22] This leaves open crucial questions like: where is the temperature drop located, where does the thermal resistance appear, or where do the phonons scatter?. The Landauer expression for the heat flux in a ballistic 1D nanowire between two reservoirs is given by[8,9,10,23]: Q_ 1⁄4 X Z α

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Conclusion