Thermal transport of flexural phonons in a rectangular wire

TL;DR

This paper investigates quantum thermal transport of elastic flexural phonons in rectangular 2D waveguides, analyzing mode contributions and conductance to advance understanding of phonon-mediated heat flow in mesoscopic quantum devices.

Contribution

It provides a detailed analysis of phonon dispersion and transport in rectangular elastic waveguides using the Kirchhoff-Love equation and second quantization, highlighting mode contributions to thermal conductance.

Findings

Identification of key phonon modes affecting thermal transport

Quantitative analysis of temperature dependence of conductance

Insights into high-temperature limit behavior

Abstract

We study the quantum thermal transport of elastic excitations through a two-dimensional elastic waveguide between two thermal reservoirs. We solve the classical Kirchhoff-Love equation for rectangular wires and explore the dispersion relation for both the symmetric and antisymmetric solutions. Then, we study the phonon transport of these modes within the second quantization framework by analyzing the mean quadratic displacement, from which the energy density current, the temperature field, and conductance are determined. We identify the relevant modes contributing to thermal transport and explore the average temperature difference to reach the high-temperature limit. We expect our results to pave the way for understanding phonon-mediated thermal transport in two-dimensional mesoscopic quantum devices.