The Effective Phonon Frequency and Mass Involved in Electron-Phonon Coupling at Metal Surfaces from Helium Atom...

In this work, we propose a new formulation of the classic Debye-Waller theory for the scattering of He atoms from metal surfaces. The probe atoms are repelled by the surface free-electron density just above the first surface atomic layer and the modulation of the surface charge density produced by lattice vibrations occurs via the electron-phonon coupling. In the Debye-Waller exponent, the surface-projected phonon spectrum is reduced to that of an effective single phonon branch responsible for the total electron-phonon coupling. This is characterized by an effective surface phonon frequency and an effective surface atom mass, which are extracted from the high and low surface temperature limits. Whether an acoustic or optical phonon branch is considered, a Debye or Einstein model for the surface can be assumed, respectively, leading to simple relationships between the effective parameters. The Einstein model is shown to work well for the copper surfaces (110), (113), (001) and (111), according to the HAS data reported by Lapujoulade et al., while for the clean and oxidized Nb(001) surfaces, the analysis of the HAS data recently reported by Arias, Sibener et al., suggests a dominant role of the surface acoustic phonons in the surface electron-phonon interaction.