Phonon-mediated thermal conductance of mesoscopic wires with rough edges

TL;DR

This paper analyzes how acoustic phonons propagate in long, rough-edged insulating wires, revealing a transition from ballistic to diffusive behavior affecting thermal conductance, with potential saturation at certain temperatures.

Contribution

It provides a detailed analysis of phonon transport regimes in mesoscopic wires with rough edges, highlighting the crossover phenomena affecting thermal conductance.

Findings

Phonon propagation transitions from ballistic to diffusive with increasing frequency.

Thermal conductance tends to saturate around specific temperature ranges.

Re-entrant quasi-ballistic regime observed at higher frequencies.

Abstract

We present an analysis of acoustic phonon propagation through long, free-standing, insulating wires with rough surfaces. Due to a crossover from ballistic propagation of the lowest-frequency phonon mode at $\omega <\omega _{1}=\pi c/W$ to a diffusive (or even localized) behavior upon the increase of phonon frequency, followed by re-entrance into the quasi-ballistic regime, the heat conductance of a wire acquires an intermediate tendency to saturate within the temperature range $T\sim \hbar \omega_{1}/k_{B}$.