Unusually weak electron-phonon coupling in the Shockley surface state on Pd(111)

Electron-phonon $\left(e\text{−}ph\right)$ coupling in the $\overline{\Gamma }$ unoccupied surface state on Pd(111) is studied using density-functional perturbation-theory calculation and two-photon photoemission measurements. Also, an ab initio GW calculation is performed to combine it with the $e\text{−}ph$ coupling evaluation in the study of the surface-state linewidth. We show that the $e\text{−}ph$ coupling in the surface state is unusually weak. It is smaller by a factor of 5 than that at the Fermi surface of bulk Pd. Temperature-dependent two-photon photoemission measurements confirm this result indicating an important role of interband scattering from surface to bulk states.

Figure 1

(Upper panel) The Shockley surface electronic state (black circles) on Pd(111). The gray background represents bulk Pd bands projected onto the two-dimensional Brillouin zone. (Lower panel) The calculated total density of electronic states, DOS (solid line) and DOS of $d$ states only (dotted line) for a nine-layer Pd slab.

Figure 2

Electron-phonon Eliashberg spectral function ${\alpha }^{2}F\left(\omega \right)$ for the $\overline{\Gamma }$ unoccupied surface state. The contribution from the Rayleigh surface mode is indicated by hatched area. Phonon density of states for a nine-layer Pd slab, $F\left(\omega \right)$, is shown by dashed line.

Figure 3

Temperature dependence of the lifetime broadening for the unoccupied surface state at $\overline{\Gamma }$. The solid curve shows the calculated electron-phonon contribution plus the electron-electron contribution (dashed line). The symbols present two experimental data sets with the corresponding fits including the contribution by thermally generated defects.

Figure 4

Two-photon photoemission spectra for the unoccupied surface state at the $\overline{\Gamma }$ symmetry point for different temperatures. The kinetic energy is relative to the vacuum level of the analyzer. The inset shows the energy diagram of the two-photon photoemission process.