Heat Transport in Mesoscopic Systems

TL;DR

This paper explores phonon heat transport in mesoscopic systems, deriving a universal conductance expression and analyzing effects of junction reflections and non-equilibrium phonon distributions.

Contribution

It introduces a universal heat conductance formula based on mode cutoff frequencies and examines the impact of junction reflections and phonon distribution shapes.

Findings

Universal heat conductance depends only on mode cutoff frequencies.

Reflections at junctions have minimal effect except at very low temperatures.

Narrow band phonon distributions produce quantized cooling steps.

Abstract

Phonon heat transport in mesoscopic systems is investigated using methods analogous to the Landauer description of electrical conductance. A "universal heat conductance" expression that depends on the properties of the conducting pathway only through the mode cutoff frequencies is derived. Corrections due to reflections at the junction between the thermal body and the conducting bridge are found to be small except at very low temperatures where only the lowest few bridge modes are excited. Various non-equilibrium phonon distributions are studied: a narrow band distribution leads to clear steps in the cooling curve, analogous to the quantized resistance values in narrow wires, but a thermal distribution is too broad to show such features.