Intrinsic thermal conductivity in monolayer graphene is ultimately upper limited: A direct estimation by atomistic simulations

In the sample size domain so far explored, the thermal conductivity of graphene shows an intriguing dependence on the sample length Lz along the heat flux direction. An extrapolated infinite value for such a thermal conductivity is sometimes suggested for infinite samples, while other investigations predict anyway an upper limit for it. We address this issue by avoiding any guess or approximation on the underlying microscopic heat transport mechanisms; we rather perform direct atomistic simulations aimed at estimating thermal conductivity in samples with increasing size up to the unprecedented value of Lz=0.1 mm. Our results provide evidence that thermal conductivity in graphene is definitely upper limited in samples long enough to allow a diffusive transport regime for both single and collective phonon excitations.