Phonon dispersion at the Be(0001) surface

Electron-phonon coupling in a system with broken symmetry: Surface ofBe(0001)

“…7, the solid (open) dots indicated the calculated modes with large (small) surface amplitude [12]. The solid triangles at the bottom indicate the measured FWHM of the RW using high-resolution electron energy loss spectroscopy (HREELS) [13]. It is clear that peak #4 can be associated with high density of states in the surface RW (flat region) at ; while peak #5 could be associated with the shear horizontal mode at [13,43] .…”

“…The solid triangles at the bottom indicate the measured FWHM of the RW using high-resolution electron energy loss spectroscopy (HREELS) [13]. It is clear that peak #4 can be associated with high density of states in the surface RW (flat region) at ; while peak #5 could be associated with the shear horizontal mode at [13,43] . Experimentally the energy of the shear horizontal mode was determined to be ~50.5 meV, which is very close to energy of peak #5 (49.0 meV).…”

“…As stated previously, there is a remarkable connection between the energies of these peaks in the ELF and the measured line width changes in the RW surface phonon mode [13]. The abrupt increase in the RW line-width at in the Γ K direction must be associated with in the Γ M , so a contour in k-space for this behavior should be continuous, which we have attempted to draw in Fig.…”

“…The contribution of the surface phonon modes to the ELF can be determined by comparing , to the calculated surface phonon dispersion by Lazzeri and de Gironcoli [12] and measured dispersion by Hannon et al [13]. In the right panel of Fig.…”

“…The wave functions of the surface states are exponentially damped into the solid [11]. There are also localized surface phonon modes (Rayliegh waves) split off from the bottom of the bulk phonon bands [12,13]. The degree of localization of surface phonons or surface states will depend upon the nature of the mode -its energy and wave vector.…”