Lattice vibrations in the Frenkel-Kontorova Model. II. Thermal conductivity

We applied the formulas for the phonon spectral-density function that we presented in the previous paper of this series to analyze the thermal conductivity of the lattice in the framework of the Frenkel-Kontorova (FK) model. We found that two extra mechanisms of phonon scattering (different from the point impurities, three-phonon processes, and boundary scattering typical of all crystals), viz., resonance, and anharmonic scattering, that mainly influences the thermal conductivity of the lattice. The frequencies of resonance scattering are discrete, and their number increases from a finite number to infinity with their transition from the commensurate to the incommensurate state. Changing the amplitude and period of the FK model changes the frequencies and the frequency number of resonance scattering and the intensity of anharmonic scattering. We analyze these changes in detail. Our theory can explain all existing numerical results on this problem and suggest strategies to reduce the thermal conductivity of the lattice of layered materials.