Fluctuation subharmonic and multiharmonic phonon transmission and Kapitza conductance between crystals with very different vibrational spectra

The existence of low-frequency, almost dispersionless intrinsic resonant vibrational modes in a transition layer at clean interface between two media (a rigid and a soft crystal) with very different elastic properties is predicted. It is shown that nonlinear interaction of bulk acoustic phonons with fluctuation resonant vibrations of a two-dimensional transition layer leads to subharmonic transmission across the interface of acoustic phonons incident from a rigid crystal with frequencies above the highest frequency in a soft crystal, and to the second- (and multiple-) harmonic transmission of acoustic phonons incident from a soft crystal. It is shown that contrary to subharmonic and multiharmonic generation of coherent acoustic waves, the coefficients of fluctuation subharmonic and multiharmonic phonon transmission do not depend on the amplitude of incident acoustic wave and are determined by temperature-dependent mean-square amplitudes of relative interface fluctuation displacements. It is emphasized that fluctuation subharmonic phonon transmission is a nonthreshold dynamical phenomenon which is significant for its contribution to Kapitza thermal boundary conductance across the interface. In both cases of fluctuation subharmonic and multiharmonic phonon transmission, two-dimensional resonant interface transition layer leads to the considerable enhancement of the coupling between phonons in the media with very different elastic properties. It is shown that inelastic interface dynamical phenomena can substantially contribute at elevated temperatures to the Kapitza conductance between solids with very different vibrational spectra (such as diamond and soft crystal) and to the thermal conductance across a helium-solid interface also.