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The propagation of heat in the transient thermal grating geometry is studiedbased on phonon Boltzmann transport equation (BTE) in different phonontransport regimes. Our analytical and numerical results show that the phonondispersion relation and temperature play a significant role in the emergence ofheat wave. For the frequency-independent BTE, the heat wave appears as long asthe phonon resistive scattering is not sufficient, while for thefrequency-dependent BTE, the heat wave could disappear in the ballistic regime,depending on the grating period and temperature. We predict that the heat wavecould appear in the suspended graphene and silicon in extremely low temperaturebut disappear at room temperature.

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