Electron-phonon coupling on the Mg(0001) surface

We have studied the $\overline{\Gamma }$ surface state on the Mg(0001) surface by angle-resolved photoemission spectroscopy. An analysis of the temperature-dependent linewidth of this state within the Debye model yields a value of $\lambda =0.27\left(2\right)$ for the electron-phonon coupling constant which is in good agreement with available data for bulk Mg. The $\text{electron-electron}+\text{electron-defect}$ scattering contribution is found by subtracting the electron-phonon contribution from the measured hole linewidth. Its value compares well with the computed result. The analysis of the role of two- and three-dimensional effects in the hole dynamics shows that interband transitions from bulk states to the hole are the dominant mechanism of the hole decay.

Figure 1

Dispersion of the Mg(0001) surface state around the center of the surface Brillouin zone. The grey-scale image shows the photoemission intensity as a function of binding energy and momentum parallel to the surface ($h\nu =44\mathrm{eV}$, $T=73\mathrm{K}$). The horizontal axis is the crystal momentum parallel to the surface calculated for a binding energy of 0 eV. The white dotted line shows the result of a parabolic fit of the surface state dispersion (see text for details).

Figure 2

(Color online) EDCs at $\overline{\Gamma }$ for three different temperatures $(h\nu =44\mathrm{eV})$. The blue circles are the experimental data points; the red solid line is a result of the fit; dashed lines give the fit Lorentzians and the green dotted line is a background multiplied on a Fermi function.

Figure 3

(Color online) Temperature dependence of the surface state linewidth at $\overline{\Gamma }$. The open circles give the experimental results. The solid line is the result of the three-dimensional (3D) Debye model fit (see text for details). The inset shows the reduced ${\chi }^2$ value ${\chi }_{\nu }^2$ and the coupling constant $\lambda$ as a function of the Debye temperature used in the fit.

Figure 4

(Color online) Left axis: Calculated probability density for the surface-state wave function as a function of distance from the surface (in units of atomic layers, layer 1 being the surface layer). Right axis: Layer-resolved Debye temperature from a dynamical LEED study (Ref. 38).