On the importance of collective excitations for thermal transport in graphene

Abstract

We use equilibrium molecular dynamics (MD) simulations to study heat transport in bulk singlelayer graphene. Through a modal analysis of the MD trajectories employing a time-domain formulation, we find that collective excitations involving flexural acoustic (ZA) phonons, which have been neglected in the previous MD studies, actually dominate the heat flow, generating as much as 78% of the flux. These collective excitations are, however, much less significant if the atomic displacements are constrained in the lattice plane. Although relaxation is slow, we find graphene to be a regular (non-anomalous) heat conductor for sample sizes of order 40 lm and more. V C 2015 AIP Publishing LLC. . [http://dx.Heat transport in graphene has raised considerable interest recently, for both practical and theoretical reasons. 1 Yet, some basic questions remain unanswered. Experimental values for the heat conductivity of bulk suspended single-layer graphene around room temperature, for example, have been reported in the wide range of 600-5300 W/m K (Refs. 2-6) with recent results even suggesting that it diverges logarithmically with the length of the samples. 7 Therefore, it is fair to say, that a definitive value is still to be found. To address this point, many theoretical investigations using various transport equations 8-12 and molecular dynamics (MD) schemes 7,13-20 have been carried out. In particular, much attention has focused on the relative conductivities of the various phonon branches, especially the flexural acoustic (ZA) branch. Early studies concluded that these were negligible in view of their low group velocity and high Gruneisen parameter. 21,22 More recently, and in contrast, full solutions of the linearized phonon Boltzmann equation suggest that the contribution of ZA modes is dominant and amounts to 88% 10 or 76% 11 of the total conductivity. However, these results rely on symmetrybased selection rules which reduce ZA phonon scattering but are likely broken in real materials. Modal analyses of MD simulations, finally, conclude that the contributions of the three acoustic branches are similar, about 30% each. 13,16,19 Below, we demonstrate that this last result is erroneous and due to a theoretical oversight and that ZA phonons actually dominate the heat flow.An interesting possibility recently raised by Fugallo et al. 12 is that collective phonon excitations in graphene lead to greatly enhanced thermal conductivity as opposed for considering single-mode excitations only. Such collective modes have already been observed in polyethylene chains, 23 in various one-dimensional models, 24 as well as in the twodimensional triangular Lennard-Jones lattice. 25 To investigate this possibility, we have performed modal analysis of equilibrium MD simulations, which naturally allows the treatment of scattering mechanisms to all orders. Modal analyses of MD trajectories in graphene have already been reported, 13,19,26 as noted above. However, these calculations used a frequency-domain formulation which, we demonstrate in this ...

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

“…Mode-coupling theory [6] predicts a divergent t −1 scaling of the HCACF for strictly 2D systems and a convergent t for the out-of-plane component, which means that both components eventually saturate and κ for pristine graphene is finite, in agreement with several recent theoretical studies using other approaches [10][11][12][13]34,42], although it is found experimentally that κ is still increasing up to 9 microns [9]. Our results show clearly that the slow convergence of the thermal conductivity is due to the flexural phonons: The convergence of κ out (t) takes a few ns, while κ in (t) converges within a few hundred ps.…”

“…Apart from holding great prospects for thermal management applications in nanoelectronic devices, graphene also serves as a benchmark for investigating fundamental questions regarding thermal transport in lowdimensional systems. Anomalous thermal transport, such as logarithmic divergence of thermal conductivity with respect to system size, has been long predicted for 2D lattice models [6][7][8] and it has been debated whether or not this divergence can occur in graphene [9][10][11][12][13]. It has also been predicted that hydrodynamic phonon transport can occur in graphene in a much wider temperature range than in three-dimensional (3D) materials [14,15].…”

Phonons and thermal transport in graphene and graphene-based materials

“…From the review of these theoretical and computational results we can conclude that the studies, independend MD studies, predicting larger contribution to TC from the in-plane acoustic phonons [133,138,144]. However, other MD studies demonstrate opposite view [158,[161][162]. Including collective excitations in the thermal transport models significantly change the final concluions [132,[161][162].…”

“…The decrease of the contribution of ZA modes in defected graphene was explained by the breakdown of reflection symmetry in the direction perpendicular to graphene layer [138]. At the same time, Gill-Comeau and Levis [161][162], considering the collective phonon excitations in graphene, concluded that ZA phonons dominate the thermal transport, carrying ~ 78 % of heat. Figure 14 illustrate how sensitive the relative contribution of each phonon polarization branch can be to the amount and nature of the defects in graphene.…”

“…However, other MD studies demonstrate opposite view [158,[161][162]. Including collective excitations in the thermal transport models significantly change the final concluions [132,[161][162]. Another reasons for scatter of thermlal conductivity data in diffrent models are (i) various interatomic potentials used, (ii) difference in the simulation domain size in MD approaches and (iii) different formulation of the heat auto-correlation functions.…”