Phonon-induced surface charge density oscillations in quantum wells: a first-principles study of the (2 × 2)-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 SV-phonon displacements. These results apparently solve the long-standing question regarding helium atom scattering (HAS) experiments performed on the similar system (2 × 2)-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.