We present a first principle study of the electron-phonon ($e\mathrm{\text{−}}p$) interaction at the Be(0001) surface. The real and imaginary parts of the $e\mathrm{\text{−}}p$ self-energy ($\Sigma$) are calculated for the $\overline{\Gamma }$ surface state in the binding energy range from the $\overline{\Gamma }$ point to the Fermi level. Our calculation shows an overall good agreement with several photoemission data measured at high and low temperatures. Additionally, we show that the energy derivative of $\mathrm{R}\mathrm{e}\Sigma$ presents a strong temperature and energy variation close to $E_F$, making it difficult to measure its value just at $E_F$.

• Received 30 May 2003

DOI:https://doi.org/10.1103/PhysRevLett.91.166803