Lattice Dynamics of Inert Gas Monolayers

Lattice dynamics of rare gas monolayers is discussed over a range of nearest-neighbor separations and temperatures. The self-consistent phonon method is used in its harmonic and cubic approximations. The floating phase, in which the atoms occupy sites of a two-dimensional triangular lattice is considered first. The quantum effects are seen to be large in neon at all temperatures, while rather insignificant in xenon at low temperatures. The phonon energies in the transverse and longitudinal modes are calculated. They are found to be more sensitive to temperature and lattice parameter than in three dimensions. Sound velocities and elastic constants are evaluated for the monolayers, as well as several dynamical quantities, zero-point energies, Debye frequencies and mean vibrational amplitudes. Thermodynamic quantities including pressure isotherms, specific heats, lattice compressibility constants and free energies are also presented. The monolayer is next pinned down by a graphite substrate to form a registered structure. In addition to the adatom-adatom interaction, the effect of the graphite surface is now included through a single particle potential, and a dispersive screening force. In this phase, owing to the lack of translational invariance, a band gap is established at the center of the Brillouin zone and the system displays no acoustic phonons. The band gaps are detected and the temperature at which they vanish, known as the floating transition temperature, is calculated for xenon and krypton. The krypton adsorbed monolayer presents a different behavior from its floating counterpart; the substrate increases its anharmonicity. The xenon monolayer, on the other hand, is seen to preserve its floating properties. The cubic theory is applied next to add the appropriate correction to the phonon spectrum, and the final energies turn out to be smaller than the ones predicted by the self -consistent harmonic approximation. The self-energy of the phonons and the dynamic structure factors result naturally from the theory.