Poster
The mass correction factor λ of conducting surfaces directly determined from the Helium atom scattering Debye-Waller exponent
1Department of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA
2Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal, 4, 20018 Donostia-San Sebastian, Spain
3Dipartimento di Scienza dei Materiali, Universitá di Milano-Bicocca, Via Cozzi 53, 20125 Milano, Italy
4Instituto de Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid, Spain
An atom at thermal energy scattered by a conducting surface can exchange energy with the phonon gas of the solid through the oscillations of the electron gas density produced at the surface by the vibrational displacements of the atomic cores. Thus the inelastic atom scattering intensity where a phonon is excited was shown to be approximately proportional to the electron-phonon coupling strength (mass correction factor) for that specific phonon (mode-λ), which enables a mode-λ spectroscopy for the determination of the individual phonon contributions to the mass correction factor. Applying the standard approximations of electron-phonon coupling theory for metals to the distorted wave Born approximation for the atom scattering from the surface potential leads to expressions which relate the elastic and inelastic scattering intensities, as well as the Debye-Waller factor, to the well known mass correction factor of superconductivity theory. This treatment, besides reproducing the previously obtained result that the intensities for single phonon inelastic peaks in the scattered spectra are proportional to the respective mass correction components, leads to a useful result for the Debye-Waller factor W(T). The intensities of elastic diffraction peaks are proportional to exp[-2W(T)] and their logarithmic temperature dependence is a linear function of the absolute temperature with a slope roughly proportional to the total mass-correction factor λ. As a first application an analysis is presented of such temperature dependence for grapheme on different substrates. The relative size of λ is shown to nicely correlated with that of Kohn anomalies eventually observed in the dispersion curves of the optical branches. The dependence of the elastic and inelastic scattering, and that of the Debye-Waller factor, on the mass correction factor shows that measurements of elastic and inelastic spectra of atomic scattering are capable of revealing detailed information about the electron-phonon coupling mechanism in the surface electron density.