Surface and subsurface phonons of Bi(111) measured with helium atom scattering

Abstract

The surface phonon dispersion curves of Bi(111) have been measured by inelastic helium atom scattering (HAS) along the two symmetry directions. The complex set of observed dispersion curves, including several branches in the acoustic region, plus a localized and a resonant branch in the optical region, is interpreted by means of calculations based on density functional perturbation theory (DFPT). It is recognized that the upper phonon branches in the acoustic region starting at about $5.3$ meV and $4.3$ meV at zero wave vector correspond to shear-vertical and longitudinal modes localized on the third surface layer (second bilayer), respectively. The HAS ability of detecting subsurface phonons previously observed for Pb(111) multilayers is attributed to the comparatively strong electron-phonon interaction, and confirmed through a DFPT calculation of the phonon-induced surface charge-density oscillations. A comparison of the integrated HAS intensities with those of Pb(111) multilayers measured under similar kinematic conditions allows for an estimation of the electron-phonon mass-enhancement parameter for the Bi(111) surface. An anomaly at the $\overline{\mathrm{M}}$ point, quite sharp at 123 K but very broad at room temperature, is associated with recombination processes of bulk $\overline{\mathrm{M}}$-point pocket electrons with bulk pocket holes at either $\overline{\ensuremath{\Gamma}}$ or equivalent $\overline{\mathrm{M}}$ points.