Discontinuity effect on the phonon transmission and thermal conductance in a dielectric quantum waveguide

We investigate the effect of the discontinuity on the acoustic phonon transmission and thermal conductance in a dielectric quantum waveguide at low temperatures by using the scattering matrix method. It is found that the total transmission coefficient versus the reduced frequency exhibits strong resonant behavior. The reduced thermal conductance exhibits a universal quantization at low enough temperatures, independent of the parameters of structure, and decreases below the ideal universal value for the low temperatures due to the strong scattering of phonons by the discontinuity. A comparison between different discontinuity structures is made. Our results show that the transmission coefficient and thermal conductance sensitively depend on the geometric configurations.