Melting temperature of graphene

We present an approach to the melting of graphene based on nucleation theory for a first order phase transition from the 2D solid to the 3D liquid via an intermediate quasi-2D liquid. The applicability of nucleation theory, supported by the results of systematic atomistic Monte Carlo simulations, provides an intrinsic definition of the melting temperature of graphene, $ T_m $, and allows us to determine it. We find $T_m \simeq 4510$ K, about 250 K higher than that of graphite using the same interatomic interaction model. The found melting temperature is shown to be in good agreement with the asymptotic results of melting simulations for finite disks and ribbons of graphene. Our results strongly suggest that graphene is the most refractory of all known materials.