Thermal response functions and second sound in graphene

The propagation of second sound, and more broadly the ballistic transport of heat, is of central importance in heat dissipation from electronic devices at very short length and time scales. Recently, we have developed thermal response functions appropriate for elucidating physics beyond the diffusive regime, including time-dependent sources and wave-like heat propagation. The methods are applied to graphene simulated using molecular-dynamics (MD) with empirical potentials. The simulations predict a strong oscillatory transport at T = 300 K for length scales equal to L = 68.1 nm and below. It is shown that at these temperatures and scales, the lifetime of the oscillatory transport is determined largely by wave coherence connected to the phonon band structure. While most Boltzmann transport equation (BTE) theories for second sound neglect this effect, and may not be suitable at very short length scales, they nevertheless are accurate for describing perturbations at longer length scales. Calculations using the linearized BTE are also presented, along with analysis of second sound. This approach results in significantly longer lifetimes for second sound in comparison to our MD simulation results. Predictions for the response due to time-dependent sources are also presented, including insight into how time-dependent experiments might probe the spectra associated with second sound. Results are discussed in relation to recent experiments on graphite.