Surface electronic band structure and $Ā$ surface state lifetimes at the $\mathrm{Be}\left(101\mathrm{}¯0\right)$ surface: Experiment and theory

The surface electronic band structure of the $\mathrm{Be}\left(101\mathrm{}¯0\right)$ surface is experimentally determined by angle-resolved photoemission and calculated by using density-functional theory. The experimental results agree well with the calculations, except for the fact that we were only able to resolve three surface states in the gap at $\overline{L},$ instead of four as predicted by the calculations. Through the temperature-dependent study, the phonon contribution subtracted width $(ħ$ times inverse lifetime) of the shallow surface state at $Ā$ is found to be $51\pm 8\hspace{0.5em}\mathrm{meV}.$ This is compared with the electron-electron interaction contribution to the width (53 meV) of the shallow surface state at $Ā$ obtained from model potential calculations.