Steady-state phonon heat currents and differential thermal conductance across a junction of two harmonic phonon reservoirs

Abstract

We study phonon transport in junctions of two harmonic reservoirs coupled together by a spring. The exact steady-state heat currents and thermal conductance are calculated using nonequilibrium Green's functions. We find that the heat currents follow Fourier's law and the thermal conductance has a peak whenever the phonon spectra match. At lower temperatures, however, the thermal conductance maximum may not coincide with the spectra-matching peak due to the exclusion of higher-frequency phonons, whose spectra may match, from participating in the transport. Furthermore, we find that increasing the coupling spring constant increases the thermal conductance. Lastly, the magnitude of the steady-state heat currents and thermal conductance are the same whether the direction of phonon flow is from left to right or vice versa, even with mass and spring constant asymmetry. The properties of this basic model can serve as a reference for more complicated setups of phonon transport in molecular junctions.