Enhanced electron-phonon coupling at the Au/Mo(112) surface

A detailed investigation of the electronic structure and electron-phonon coupling for a Au monolayer on the Mo(112) surface is presented. The electronic states of bulk Mo and the (112) surface-derived states are seen to strongly hybridize with those of the Au overlayer, resulting in the formation of surface resonance states localized near the surface and the interface of Au/Mo(112). The experimentally extracted self-energy due to the electron-phonon coupling on one of the surface resonance bands gives a good quantitative agreement with the calculations. The strength of electron-phonon coupling for Au/Mo(112) is discussed in terms of the mass enhancement factor and is considerably larger than for the Mo(112) surface. Such an increase in the mass enhancement factor in the vicinity of the Fermi level likely derives from the soft surface phonon modes created upon Au adsorption.

Figure 1

The schematic illustration of Au/Mo(112) at the coverage of nominal 1 ML (a). The corresponding SBZ is illustrated in (b) with the approximate dimensions along the $\overline{\Gamma }-\overline{X}$ and $\overline{\Gamma }-\overline{Y}$ lines.

Figure 2

The ARPES band mapping taken along the $\overline{\Gamma }-\overline{X}$ line with the incident photon energy of 22 eV with $p$ polarization geometry (i.e., only the states with even reflection parity about $\overline{\Gamma }-\overline{X}$ are visible) for (a) Mo(112) (reprinted from Ref. 22) and (b) 1 ML Au/Mo(112). (c) This shows the band structure along the $\overline{\Gamma }-\overline{X}$ line of the free-standing ML of Au with the same structure as the topmost layer of Mo(112). The band with the Fermi-level crossing of $k_F=0.64$ Å${}^{-1}$ can be identified and is expected to hybridize with the Mo bulk state with nearly the same Fermi momentum $k_F$. The band structure calculated from the seven-layer slab model is overlaid for 1 ML Au/Mo(112) in (d). For (d), the significantly surface-weighted states with even reflection parity are marked with yellow circles.

Figure 3

(a) The ARPES spectrum taken along the $\overline{\Gamma }-\overline{X}$ line in the vicinity of the Fermi level. The surface resonance band with $k_F=0.64$ Å${}^{-1}$ is seen to exhibit band renormalization (a mass enhancement in the dispersion) due to electron-phonon coupling within ∼50 meV below the Fermi level. The peak positions obtained in the MDCs are indicated with circles ($•$), and the expected unrenormalized band dispersion is indicated with a blue broken curve. (b) The spectral function weighted with the Fermi function at $T=60$ K in the vicinity of Fermi level calculated from the theoretically determined Eliashberg function and experimentally determined bare band dispersion $E$($k$) and the impurity scattering rate (estimated to be ∼78-meV contribution to ${\Sigma }_I$). The experimental MDC peak positions ($•$), determined from ARPES, are overlaid for the comparison and are seen to agree well with the theoretically expected renormalization. The peaks of the calculated spectral functions are denoted as a red solid curve as a visual guide. (c) The calculated spectral function in which impurity scattering is turned off (band renormalization is solely due to electron-phonon coupling). The agreement between the ARPES-determined MDC peak positions ($•$) and the calculated band distortion is more apparent. Note that the change to the Fermi edge cutoff at finite temperature (60 K) is also turned off for the visual clarity.

Figure 4

The phonon band structure calculated using the seven-layer slab model is shown in (a), where the surface-weighted modes are marked with a thick dotted line (blue = longitudinal mode; red = vertical mode; brown = horizontal mode). The isotropic Eliashberg function, ${\alpha }^{2}F$(ω), calculated from the seven-layer slab model is shown in (b). Note that the Eliashberg function is dimensionless.

Figure 5

The plots of the real part (a), and the imaginary part (b) of self-energy for the surface resonance band with $k_F=0.64$ Å${}^{-1}$. The experimental data points ($•$) for ${\Sigma }_R$ are obtained from the deviation of the ARPES peak positions from the expected unrenormalized band dispersion [see Fig. 3a], and those for ${\Sigma }_I$ are obtained from the width of the photoemission peaks as described in the text. The calculated self-energy due to electron-phonon coupling was obtained using Eqs. (3) and (5), from the calculated isotropic Eliashberg function at $T$ = 60 K and plotted as solid curves. The calculated ${\Sigma }_I$ is rigidly shifted up by 171 meV, so as to fit the experimental data (interpreted as deriving from the electron-impurity coupling and instrumental broadening as discussed in text). The dotted curves represent the self-energy obtained from the free-parameter Eliashberg function that gives the best fit to the experimental data.