Ballistic length scale of heat transport in the subwavelength limit

We present a comprehensive study of phonon ballistic length scale using a Casimir--Rayleigh model of heat transport. This model incorporates temperature-dependent Casimir radiation and wavelength-dependent Rayleigh scattering. We exploit this definition to understand heat transport in newly synthesized silicon metalattices, which consist of a finely controlled, three-dimensional arrangement of nanometer-sized cavities in crystalline silicon. Through computational simulation and experimental validation, we show that the heat conductivity of metalattices exhibits a minimum as a function of the cavity diameter at constant porosity. This departure from Casimir's linear scaling law can be understood in terms of the geometry dependence of the phonon mean free path in a network of cavities.