Nonequilibrium Thermodynamics of Acoustic Phonons in Suspended Graphene

TL;DR

This study experimentally determines the temperature differences between in-plane and out-of-plane acoustic phonons in suspended graphene, revealing significant deviations from thermal equilibrium assumptions and impacting 2D material thermal analysis.

Contribution

It introduces a novel method to measure phonon bath temperatures in suspended graphene using frequency-dependent mechanical response to laser modulation.

Findings

In-plane and out-of-plane phonons have significantly different temperatures in steady state.

The temperature ratio between in-plane and out-of-plane phonons ranges from 0.2 to 3.7.

Deviations from local thermal equilibrium affect thermal property measurements of 2D materials.

Abstract

Recent theory has predicted large temperature differences between the in-plane (LA and TA) and out-of-plane (ZA) acoustic phonon baths in locally-heated suspended graphene. To verify these predictions, and their implications for understanding the nonequilibrium thermodynamics of 2D materials, experimental techniques are needed. Here, we present a method to determine the acoustic phonon bath temperatures from the frequency-dependent mechanical response of suspended graphene to a power modulated laser. The mechanical motion reveals two counteracting contributions to the thermal expansion force, that are attributed to fast positive thermal expansion by the in-plane phonons and slower negative thermal expansion by the out-of-plane phonons. The magnitude of the two forces reveals that the in-plane and flexural acoustic phonons are at very different temperatures in the steady-state, with typically observed values of the ratio $\Delta T_{\mathrm{LA+TA}}/\Delta T_{\mathrm{ZA}}$ between 0.2 and 3.7. These deviations from the generally used local thermal equilibrium assumption ($\Delta T_{\mathrm{LA+TA}}=\Delta T_{\mathrm{ZA}}$) can affect the experimental analysis of thermal properties of 2D materials.