Non-equilibrium transport and phonon branch-resolved size effects based on a multi-temperature kinetic model

Non-equilibrium transport and phonon branch-resolved size effects in single-layer graphene materials are studied under a multi-temperature kinetic model, which is developed for capturing the branch-dependent electron-phonon coupling. Compared with typical macroscopic multi-temperature models, the assumption of diffusive phonon transport is abandoned in this model and replaced by the free migration and scattering of particles. The phonon branch- and size-dependent effective thermal conductivity is predicted in nanosized graphene as well as the temperature slips near the boundaries. Compared with other phonon branches, the ZA branch contributes the most to thermal conduction regardless of system sizes. Furthermore, in nanosized homogeneous graphene with a hotspot at the center, the branch-dependent thermal conductivity increases from the inside to the outside even if the system size is fixed. The thermal conductivity of ZA branch is even higher than the lattice thermal conductivity when the system size is hundreds of nanometers.