Thermal conductivity of monolayer graphene: Convergent and lower than diamond

The thermal conductivity of monolayer graphene is widely believed to surpass that of diamond even for few-micron-size samples and was proposed to diverge with system size. Here, we predict the thermal conductivity from first principles by considering four-phonon scattering, phonon renormalization, an exact solution to the phonon Boltzmann transport equation (BTE), and a dense enough sampling grid. We show that at room temperature, the thermal conductivity saturates at 10 $\textmu{}\mathrm{m}$ system size and converges to 1300 W/($\mathrm{m}\phantom{\rule{0.16em}{0ex}}\mathrm{K}$), which is lower than that of diamond. This indicates that four-phonon scattering overall contributes 57% to the total thermal resistance and becomes the leading phonon scattering mechanism over three-phonon scattering. On the contrary, considering three-phonon scattering only yields higher-than-diamond values and divergence with size due to the momentum-conserving normal processes of flexural phonons.