Is Thermal Conductivity of Graphene Divergent and Higher Than Diamond?

Abstract: The thermal conductivity of monolayer graphene is an outstanding challenge with no consensus reached on its exact value and length convergence so far. We consider four-phonon scattering, phonon renormalization, and an exact solution to phonon Boltzmann transport equation (BTE) from first principles. Using this computational formalism with unprecedented sampling grid, we show that when four-phonon scattering is included the thermal conductivity is convergent with system size at a room temperature value of 1300 W/(m$\cdot$K), which is lower than that of diamond. On the contrary, considering three-phonon scattering only yields divergence with size due to the momentum-conserving normal processes of flexural phonons.