Dynamics of rare-gas floating monolayers in the self-consistent phonon theory

The dynamics of floating two-dimensional (2D) monolayers of Xe, Kr, Ar, and Ne are explored over a range of lattice spacings and temperature using the self-consistent phonon theory. Phonon dispersion curves and the zero-point energy are calculated and appropriate Debye temperatures and rms vibrational amplitudes 〈$u^2$〉 estimated at T=0 K. The results show that floating monolayers of Ar and Xe represent their physisorbed counterparts well. They also show that Xe and Kr are effectively harmonic at T≤25 K while Ne is a strongly anharmonic 2D crystal at all T. The self-consistent harmonic frequencies in Ne at T=0 K are nearly twice the harmonic values. Ar is an intermediate case. The effective Debye temperature is ${\Theta }_D$≊65 K in all cases and the Lindemann ratio γ=〈$u^2$〉/R varies from 3% in Xe to 9% in Ne at T=0 K, similar to 3D crystal values. The phonon frequencies depend sensitively on lattice parameter and temperature, more so than in 3D crystals.