On the emergence of heat waves in the transient thermal grating geometry

The propagation of heat in the transient thermal grating geometry is studied based on the phonon Boltzmann transport equation (BTE) in different phonon transport regimes. Our analytical and numerical results show that the phonon dispersion relation and temperature govern the emergence of heat waves. For the frequency-independent BTE, a heat wave manifests in both the ballistic and hydrodynamic regimes. For the frequency-dependent BTE, heat waves are present in the hydrodynamic regime but may be absent in the ballistic regime. In the context of real materials, we predict the emergence of heat waves in the suspended graphene (ballistic and hydrodynamic regimes) and silicon (ballistic regime) at extremely low temperatures.