Interfacial three-phonon processes: Application to pulse experiments and the Kapitza conductance

We have studied interfacial three-phonon processes as a mechanism to explain the enhanced transmission of acoustic energy across the interface between (high phonon velocity) "classical" and (low phonon velocity) "quantum" systems. Because of phase-space considerations, decay of a phonon from the "classical" material to two phonons in the "quantum" material is possible for reasonable values of the interfacial cubic anharmonicity (1-10 eV/${\mathrm{\AA }}^2$). The transmission rate, for an interaction depending on the cube of the surface strain, varies as ${\omega }^6$, for an incident phonon frequency $\omega$, so that the process rapidly "turns on" and then must saturate, in agreement with experiment. The mechanism causes most of the transmission to occur outside the critical cone, in agreement with experiment. The mechanism is also consistent with the observed frequency conversion of the incident phonon. When the characteristic wavelength of the transmitted phonons is considered (∼16 Å), one can account for experiments showing that a 3-layer (12 Å) ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ film behaves like bulk liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The mechanism appears to be consistent with a wide variety of experimental results, including recent pulse work on solid surfaces cleaved in situ. It is suggested that experiments be performed to verify the predicted ${\omega }^6$ onset rate, perhaps by studying the transmitted energy outside the critical cone.