Dimensional crossover of thermal conductance in graphene nanoribbons: A first-principles approach

First-principles density-functional calculations are performed to investigate the thermal transport properties in graphene nanoribbons (GNRs). The dimensional crossover of thermal conductance from one to two dimensions (2D) is clearly demonstrated with increasing ribbon width. The thermal conductance of GNRs in a few nanometer width already exhibits an approximate low-temperature dependence of $T^{1.5}$, like that of 2D graphene sheet which is attributed to the quadratic nature of dispersion relation for the out-of-plane acoustic phonon modes. Using a zone-folding method, we heuristically derive the dimensional crossover of thermal conductance with the increase of ribbon width. Combining our calculations with the experimental phonon mean-free path, some typical values of thermal conductivity at room temperature are estimated for GNRs and for 2D graphene sheet, respectively. Our findings clarify the issue of low-temperature dependence of thermal transport in GNRs and suggest a calibration range of thermal conductivity for experimental measurements in graphene-based materials.