Resonant amplification of hydrodynamic temperature waves in graphite

Recent experiments have observed temperature waves in graphite, discussing how these appear when “normal” phonon scattering (which conserves phonons’ energy and crystal momentum) dominates over “umklapp” scattering (which conserves only energy). Under these conditions, the mesoscopic state of the system is described not only by temperature T (originating from the microscopic conservation of energy) but also from a drift velocity u (related to quasi conservation of momentum and bearing analogies to the velocity field in a fluid). The magnitude of these “hydrodynamic” phenomena is strongly affected by the relative strength of normal and umklapp scattering, and by the crystal’s purity, size, and shape; in practice such a magnitude is often weak and therefore measurement are challenging. Here we investigate from first principles the conditions determining the emergence and magnitude of temperature waves in graphite, also analyzing analogies and differences emerging from describing their evolution using Cattaneo’s equation [Comptes Rendus 247, 431(1958)] or the viscous heat equations [Phys. Rev. X 10, 011019 (2020)]. Finally, we show that temperature waves can be driven to resonance, thus the consequent amplification could facilitate their experimental detection.