Statics and dynamics of multivalley charge density waves in Sb(111)

Charge density waves (CDWs), periodic modulations of the charge density, are among the most abundant and non-trivial ordered phases in condensed matter. Here we demonstrate the occurrence of multi-valley charge density waves (MV-CDW) on the semimetal Sb(111), a phenomenon previously observed at semiconductor surface inversion layers. The topological nature of the pocket surface states in Sb(111) ensures perfect nesting conditions giving rise to sharp peaks in helium atom scattering (HAS) diffraction spectra. The peculiar temperature dependence permits to distinctly associate the diffraction peaks with surface electron and hole-pocket states due to the non-trivial surface electronic band structure known from recent experimental data and present ab-initio calculations. Inelastic HAS spectra, besides providing the surface phonon dispersion curves in agreement with density functional perturbation theory calculations, reveal two additional dispersion curves of elementary excitations in the gap well below Rayleigh waves. They are attributed to collective excitations of the quasi-commensurate MV-CDWs associated with the surface electron M-pocket states at the Fermi level. These findings suggest that HAS can be regarded as a choice spectroscopy for the investigation of surface electronic excitations in the THz domain, opening up a new window for the search of collective phases at surfaces.