Akhiezer mechanism limits coherent heat conduction in phononic crystals

Abstract

Heat in phononic crystals (PnCs) is carried by phonons, which can behave coherently (wave-like) or incoherently (particle-like) depending on the modes, temperature, and length scales. By comparing the measured thermal conductivity of PnCs with theories, recent works suggest that thermal conductivity of PnCs can be explained by considering only surface and boundary scatterings, which not only backscatter phonons but also break their coherence. The logic here is that since average phonon wavelength at room temperature is only a few nanometers, the roughness at the surfaces and boundaries make the scattering diffusive (break the phase coherence of phonons), and thus only very long wavelength (low frequency) phonons with negligible contribution to total thermal conductivity remain coherent. Here, we theoretically show that in a thin film PnCs, the low frequency coherent phonons could significantly contribute to thermal conductivity when assuming the three-phonon scattering model for intrinsic scattering because of their extremely large density of states that result from the low dimensional nature. Yet, further analysis shows the contribution of the low frequency coherent phonons is still negligible within temperature range from 130 to 300 K due to the Akhiezer mechanism, which properly answers the question why the thermal conductivity of PnCs can be explained by considering only scattering of incoherent phonons at these temperatures.