Dynamics of xenon, krypton, and methane monolayers in registry with graphite

The self-consistent phonon (SCP) theory is used to study the dynamics of monolayers of xenon, krypton, and methane adsorbed on graphite. Only the √3 × √3 solid phase is considered. It is shown that the phonon energies of the Xe monolayers are very similar to those of their floating counterparts, while the interaction of the Kr and ${\mathrm{CH}}_4$ monolayers with the graphite significantly affects the phonon dispersion curves. The gap in the phonon dispersion curves at the center of the Brillouin zone is computed as a function of temperature. At a critical temperature, the gap goes spontaneously to zero and a transition from a locked-in commensurate phase to a floating phase takes place. This transition appears to describe the commensurate to floating transition in ${\mathrm{CH}}_4$ well. A simple model of the floating transition is compared to the full SCP calculations. The one-phonon dynamic form factor, including the cubic anharmonic term, and phonon lifetimes are also evaluated for Kr and ${\mathrm{CH}}_4$.