Figure 3: Experimental and simulation results on length-dependent thermal conductivity.

(a) Length dependence of the extracted intrinsic thermal conductivity when assuming R_c contributes negligible (red squares), 5% (blue circles) and 11.5% (brown diamonds) to the total measured thermal resistance in a 9-μm-long sample. The linear solid lines are guides to the eyes. The red diagonal lines indicate the average/effective phonon mean free path (MFP), which is 240 nm and 80 nm obtained by experiment and simulation, respectively. Inset: illustration of logκ~logL scaling behaviour for one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) systems, where thermal conductivity scales as ~L^0.33, ~logL and constant, respectively. Also see Supplementary Fig. 8. (b)Thermal conductivity of graphene as a function of the distance between the hot and the cold reservoir, obtained with direct (black circles) and reverse non-equilibrium molecular dynamics (NEMD) (red squares and green diamonds) methods at T=300 K and reverse NEMD at 1,000 K (blue triangles). Results obtained with supercells with square aspect ratio (green diamonds) agree well with those obtained with elongated supercells (all others). Dashed lines indicate the logarithmic fit. The dotted and dashed vertical lines indicate the limit of the ballistic transport regime obtained by experiment and simulation, respectively.