Phonon transmission across superfluid helium-solid interfaces using intermediate antireflection nanolayers

Based on the wave nature of phonons, we present a study of phonon transmission from superfluid 4He across a bilayered solid, made up of a film layer, of a few tens of nanometers in thickness, deposited on a solid. The main focus is aimed at suppressing the thermal boundary resistance between superfluid helium and the solid by introducing an intermediate film that acts as an antireflection layer. We derive a relationship showing that the maximum transmission is reached for film thicknesses which are comparable to the phonon wavelengths in the film layer. The analysis is carried out within the framework of the acoustic mismatch model and considers phase coherence due to interference effects arising from multiple reflections of phonons inside the intermediate layer.