Coherent heat transport in 2D phononic crystals with acoustic impedance mismatch

In this work we have calculated the cumulative thermal conductivities of micro-phononic crystals formed by different combinations of inclusions and matrices at a sub-Kelvin temperature regime. The low-frequency phonon spectra (up to tens of GHz) were obtained by solving the generalized wave equation for inhomogeneous media with the plane wave expansion method. The thermal conductivity was calculated from Boltzmann transport theory highlighting the role of the low-frequency thermal phonons and neglecting phonon-phonon scattering. A purely coherent thermal transport regime was assumed throughout the structures. Our findings show that the cumulative thermal conductivity drops dramatically when compared with their bulk counterpart. Depending on the structural composition this reduction may be attributed to the phonon group velocity due to a flattening of the phonon dispersion relation, the extinction of phonon modes in the density of states or due to the presence of complete band gaps. According to the contrast between the inclusions and the matrices, three types of two dimensional phononic crystals were considered: carbon/epoxy, carbon/polyethylene and tungsten/silicon, which correspond respectively to a moderate, strong and very strong mismatch in the mechanical properties of these materials.