Thermal Transport in Phononic Cayley Tree Networks

TL;DR

This paper provides an analytical study of heat current and fluctuations in a phononic Cayley tree network, revealing non-monotonic behavior and conditions for zero heat flow based on mass ratios.

Contribution

It introduces an analytical model for thermal transport in Cayley tree networks with harmonic masses, highlighting impedance mismatch effects and zero heat flow conditions.

Findings

Heat current and fluctuations are non-monotonic functions of mass ratio.

There exist critical mass ratios where heat flow becomes zero.

Impedance mismatch significantly affects thermal transport.

Abstract

We analytically investigate the heat current $I$ and its thermal fluctuations $\Delta$ in a branching network without loops (Cayley tree). The network consists of two type of harmonic masses: vertex masses $M$ placed at the branching points where phononic scattering occurs and masses $m$ at the bonds between branching points where phonon propagation take place. The network is coupled to thermal reservoirs consisting of one-dimensional harmonic chains of coupled masses $m$. Due to impedance missmatching phenomena, both ${\cal I}$ and $\Delta$, are non-monotonic functions of the mass ratio $\mu=M/m$. In particular, there are cases where they are strictly zero below some critical value $\mu^*$.