Electron-phonon coupling and temperature-dependent shift of surface states on Be(101¯0)

Abstract

The temperature dependence of two Schockley surface states $(S1$ and $S2)$ on $\mathrm{Be}(101\ifmmode\bar\else\textasciimacron\fi{}0),$ located in a wide bulk projected band gap from $\ifmmode \bar{A}\else \={A}\fi{}$ to $\overline{\ensuremath{\Gamma}},$ has been investigated with angle-resolved photoemission spectroscopy. The electron-phonon coupling of the surface states $S1$ and $S2$ at the zone boundary $(\ifmmode \bar{A}\else \={A}\fi{})$ were determined using both Debye and Einstein phonon models. Based on fitting, this analysis indicates that the surface optical phonon mode located around 64 meV contributes most strongly to the electron-phonon coupling of the $S1$ surface state, which is highly localized in the surface layer. The determined electron-phonon coupling parameter \ensuremath{\lambda} of $S1$ and $S2$ (0.647 and 0.491, respectively) is distinct from the bulk value $({\ensuremath{\lambda}}_{\mathrm{bulk}}=0.24).$ Both surface states $S1$ and $S2$ are observed to shift linearly with the temperature, but in opposite directions at the rates of $(\ensuremath{-}0.61\ifmmode\pm\else\textpm\fi{}0.3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\mathrm{e}\mathrm{V}/\mathrm{K}$ and $(1.71\ifmmode\pm\else\textpm\fi{}0.8)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}\mathrm{e}\mathrm{V}/\mathrm{K},$ respectively. The different behavior of the two surface states, with respect to both the electronic-phonon coupling and temperature-dependent shift of initial energy, is attributed to the higher surface charge localization of $S1$ than $S2.$