Nonequilibrium thermodynamics of acoustic phonons in suspended graphene

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 ∆TLA+TA/∆TZA between 0.2 and 3.7. These deviations from the generally used local thermal equilibrium assumption (∆TLA+TA = ∆TZA) can affect the experimental analysis of thermal properties of 2D materials. arXiv:1909.11614v1 [cond-mat.mes-hall]

Phonon scattering at kinks in suspended graphene

“…whereŪ 1l is the average internal energy of the LA phonons over the surface of the drum. This ratio of the forces determines the mechanical out-of-plane response of the membrane, and should therefore match the force ratio observed in experiments 22 . Evaluation of the model requires several parameters from theory.…”

“…The transmission coefficient is minimal for a kink of 90 degrees. We compare the model to the experimental values of τ /a found in related works 15,22 . In Fig.…”

“…In this subsection, we calculate the ratio between the opposing thermal expansion forces in the steady-state regime, which are found in experiments in Ref. 22. As explained above and in the Supplemental information S2 27 , we expect the in-plane and flexural acoustic phonons to be at different temperatures and therefore require a twotemperature model to describe heat transport in the suspended graphene.…”

“…15 and the observation of the opposing thermal expansion forces in Ref. 22. We analyze the situation where a (optothermal) heat flux is incident at the center of a circular drum.…”

“…Here, we theoretically analyze phonon transport in suspended graphene membranes and compare this to experimental works 15,22 on devices as depicted in Fig. 1, to explain the large values of the thermal time constants.…”