Flexural phonons and thermal transport in graphene

Abstract

We show through an exact numerical solution of the phonon Boltzmann equation that the lattice thermal conductivity of graphene is dominated by contributions from the out-of-plane or flexural phonon modes, previously thought to be negligible. We connect this unexpected result to the anomalously large density of states of flexural phonons compared to their in-plane counterparts and to a symmetry-based selection rule that significantly restricts anharmonic phonon-phonon scattering of the flexural modes. The result is found to hold in the presence of the ripples known to occur in graphene, phonon-isotopic impurity scattering, and rigidity of the flexural phonon branch arising from the long-wavelength coupling between flexural and in-plane modes. Finally, accurate inclusion of the momentum conserving Normal phonon-phonon scattering processes within the context of a full solution of the phonon Boltzmann equation are shown to be essential in accurately describing the graphene thermal conductivity, in contrast to the more commonly used relaxation time and long wavelength approximations.

Ab initiothermal transport in compound semiconductors

“…Similar behavior has been previously noted in Si and Ge [7,30]. For systems with very strong N scattering relative to U scattering, such as in diamond [9][10][11], graphene [31,32] and carbon nanotubes [22,33], the full solution to the BTE is required to accurately determine κ L .…”

Thermal conductivity of graphene mediated by strain and size

“…from the iterative approach is several-fold higher than those from the SMRTA [22,24], confirming previous findings [21,23] that both N-and U-processes and their relationship influencing the nonequilibrium populations of phonon modes are important for determining k of graphene. The convergence of k in our calculations for infinite unstrained graphene also justifies that intrinsic three-phonon scatterings can confine k, i.e., higher-order inter-phonon scatterings are not required for convergence of k as was previously suggested for k of unstrained single-walled carbon nanotubes [38,39]. Under different strains  = 0.0025, 0.01 and 0.1, k increases nearly linearly with increasing N 1 and at a fixed N 1 a larger  gives a higher k, indicating non-negligible contributions from longer-wavelength phonon modes and the divergence of k with system size under strain.…”

Morphing Graphene-Based Systems for Applications: Perspectives from Simulations

“…Its dispersion law is parabolic, implying that these modes are the lowest energies of the spectrum, and are the easiest to be excited. The very low phonon-phonon scattering rate and the large thermal population have as a consequence that the flexural phonons give a fundamental contribution to thermal conductivity both for graphene monolayer [95] and multilayers [96]. Moreover, they are responsible of the negative thermal expansion coefficient observed in a wide temperature interval, up to an inversion temperature value, which is still controversial [94][95][96].…”