  Understanding the mechanisms of thermal conduction in graphene is a
long-lasting research topic, due to its high thermal conductivity.
Peierls-Boltzmann transport equation (PBTE) based studies have revealed many
unique phonon transport properties in graphene, but most previous works only
considered three-phonon scatterings and relied on interatomic force constants
(IFCs) extracted at 0 K. In this paper, we explore the roles of four-phonon
scatterings and the temperature dependent IFCs on phonon transport in graphene
through our PBTE calculations. We demonstrate that the strength of four-phonon
scatterings would be severely overestimated by using the IFCs extracted at 0 K
compared with those corresponding to a finite temperature, and four-phonon
scatterings are found to significantly reduce the thermal conductivity of
graphene even at room temperature. In order to reproduce the prediction from
molecular dynamics simulations, phonon frequency broadening has to be taken
into account when determining the phonon scattering rates. Our study elucidates
the phonon transport properties of graphene at finite temperatures, and could
be extended to other crystalline materials.
