Quantized thermal conductance of dielectric quantum wires

Using the Landauer formulation of transport theory, we predict that dielectric quantum wires should exhibit quantized thermal conductance at low temperatures in a ballistic phonon regime. The quantum of thermal conductance is universal, independent of the characteristics of the material, and equal to π2k2 BT/3h where kB is the Boltzmann constant, h is Plank’s constant and T is the temperature. Quantized thermal conductance should be experimentally observable in suspended nanostructures adiabatically coupled to reservoirs, devices that can be realized at the present time. PACS: 85.30.Vw, 73.23.Ad, 63.22.+m Typeset using REVTEX 1 During the last two decades, the physics of electron transport in one dimension has attracted a great deal of attention. Some remarkable associated phenomena have been the quantum Hall effect discovered by von Klitzing, Dorda and Pepper [1] and the quantized conductance of ballistic point contacts discovered by van Wees et al. [2] and Wharam et al. [3] Here the signature of one-dimensional conduction has been the quantization of the twoterminal and Hall electrical conductances in multiples of the fundamental quantum e/h, as has been understood within the framework of Landauer theory, [4] and of Büttiker-Landauer theory, [5] respectively. One-dimensional phonon transport should also be possible. However, despite the long standing theoretical interest in this topic that goes back to the 1920’s, [6] the question whether the phonon thermal conductance should be quantized in one dimension has to our knowledge not been addressed either theoretically or experimentally. Recent advances in nanotechnology, and especially the work of Seyler and Wybourne [7] and of Tighe, Worlock and Roukes [8] have made experimental investigation of this question feasible. The purpose of this Letter is to demonstrate theoretically that in a low temperature regime dominated by ballistic massless phonon modes the phonon thermal conductance of a one dimensional quantum wire is quantized, the fundamental quantum of thermal conductance being πk BT/3h, where kB is the Boltzmann constant, h is Plank’s constant and T is the temperature. We also establish the conditions that should be met for the experimental observation of this novel phenomenon. Our starting point is the Landauer energy flux