Energy-momentum mapping of $d$-derived Au(111) states in a thin film

The quantum well states of a film can be used to sample the electronic structure of the parent bulk material and determine its band parameters. We highlight the benefits of two-dimensional film band mapping, with respect to complex bulk analysis, in an angle-resolved photoemission spectroscopy study of the $5d$ states of Au(111). Discrete $5d$-derived quantum well states of various orbital characters form in Au(111) films and span the width of the corresponding bulk bands. For sufficiently thick films, the dispersion of these states samples the bulk band edges, as confirmed by first-principles calculations, thus providing the positions of the critical points of bulk Au in agreement with previously determined values. In turn, this analysis identifies several $d$-like surface states and resonances with large spin splittings that originate from the strong spin-orbit coupling of the Au $5d$ atomic levels.

Figure 1

(a) ARPES spectra for a 24-ML Au film on Ag(111) measured along the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ direction at 45 eV photon energy. (b) Energy distribution curves relative to the area enclosed in a white box in panel (a). Vertical ticks mark the band dispersion of five B4-derived QW states. (c–f) Second derivative ARPES spectra of the same energy-momentum region acquired with photon energies of (c) 35, (d) 45, (e) 65, and (f) 80 eV.

Figure 2

(a) DFT calculations for a freestanding 24-ML slab of Au(111) along the $\overline{\mathrm{M}}–\overline{\mathrm{\Gamma }}–\overline{\mathrm{K}}–\overline{\mathrm{M}}$ direction. The gray shaded region indicates the surface-projected Au bulk states. (b–d) Bulk bands of Au(111) along (b) $\mathrm{\Gamma }L$, (c) $LX$, and (d) $A_1{A}_2$ lines [35]. Red dots indicate the experimental critical points. The irreducible representations at $\mathrm{\Gamma },L$, and $X$ are reported [34].

Figure 3

Second derivative photoemission spectra and corresponding DFT calculations (shifted down by 0.27 eV) for the 24-ML Au(111) film. (a,b) $\overline{\mathrm{K}}–\overline{\mathrm{\Gamma }}–\overline{\mathrm{K}}$ direction, 65 eV photon energy. (c,d) $\overline{\mathrm{K}}–\overline{\mathrm{M}}–\overline{\mathrm{K}}$ direction, 65 eV photon energy. (e,f) $\overline{\mathrm{\Gamma }}–\overline{\mathrm{M}}–\overline{\mathrm{\Gamma }}$ direction, 55 eV photon energy. (g,h) $\overline{\mathrm{\Gamma }}–\overline{\mathrm{K}}\text{−}\overline{\mathrm{M}}$ direction, 45 eV photon energy.

Figure 4

DFT band structure for a 24-ML Au(111) film on a 6-ML Ag(111) substrate. The color scale represents the spatial localization of the states inferred from their total weight on all Au layers. The gray shaded region shows the surface-projected Au bulk bands.

Figure 5

(a) Second derivative ARPES spectra at 65 eV photon energy and (b) corresponding DFT calculations for the 24-ML Au(111) film along the $\overline{\mathrm{\Gamma }}–\overline{\mathrm{M}}$ direction. No energy shift is applied to the calculated bands. Black dots mark the experimental band dispersion of surface-related features.

Figure 6

Second derivative ARPES spectra acquired along the $\overline{\mathrm{\Gamma }}–\overline{\mathrm{K}}–\overline{\mathrm{M}}$ direction in the vicinity of $\overline{\mathrm{K}}$ and corresponding DFT calculations for a 24-ML Au(111) film. (a,b) Photon energy 80 eV. Calculated bands are shifted downwards by 0.27 eV. (c,d) Photon energy 65 eV. Calculated bands are shifted downwards by 0.18 eV. (e,f) Photon energy 65 eV. No energy shift is applied. Black dots mark the experimental band dispersion of surface-related features.