Phonon-Induced Surface Charge Density Oscillations in Quantum Wells: A First-Principles Study of the (2x2)-K Overlayer on Be(0001)

Density functional perturbation theory has been applied to study the surface vibrations of (2 2)-K monolayer on the Be(0001) surface. We present the full phonon dispersion curves along the high symmetry directions of the surface Brillouin zone (SBZ) together with the layer-projected phonon density of states and the phonon-induced surface charge density oscillations at Γ and M for the alkali SV and L modes. Surprisingly, at the M point, the L-phonon displacements produce a more pronounced perturbation on the surface charge density than the SVphonon displacements. These results apparently solve the long-standing question regarding helium atom scattering (HAS) experiments performed on the similar system (2x2)-K on graphite, where the alkali SV phonon mode is not observed. Moreover, this result confirms the previous finding that HAS from free-electron metal surfaces probes directly the phonon-induced charge density oscillations and the related electron phonon interaction.