Influence of the substrate bands on the $sp$-levels topology of Ag films on Ge(111)

Angle-resolved photoemission spectroscopy and first-principles calculations were employed to analyze unusual features in the electronic structure of ultrathin Ag films grown on Ge(111). The Ag $sp$-derived quantum well states exhibit hexagonal-like constant energy contours with different in-plane orientations near the center of the surface Brillouin zone, in striking contrast to the expectations for a free-standing Ag(111) layer. The experimental observations are explained by taking into account the effects of hybridization of the Ag states with the star-like shaped Ge band edges on constant energy planes.

Figure 1

(Color online) First-principles electronic structure calculations for a free-standing 13 ML Ag(111) film. (a) QW band dispersion along the $\overline{M}\text{−}\overline{\Gamma }\text{−}\overline{K}$ line. Panels (b) and (c) display the $sp$-QW contours at $E_{\text{F}}$ and $E_{\text{F}}$−1 eV, respectively. Due to the interaction of the two surfaces of the film, the surface state splits into an even and odd branch.

Figure 2

(Color online) Constant energy cuts through the electronic structure of a 17 ML Ag film grown on Ge(111). The Ag and Ge surface Brillouin zones are displayed with thick and thin continuous lines, respectively. The Fermi surface of the system [panel (a)] displays a series of QW contours with common center at $\overline{\Gamma }$ and multiple ovals surrounding the ${\overline{M}}_{\text{Ge}}$ points. The $n=3\text{QW}$ contour appears to be a rounded hexagon at $E_{\text{F}}$−0.36 eV [panel (b)], clearly hexagonal at $E_{\text{F}}$−0.66 eV [panel (c)], round at $E_{\text{F}}$−0.81 eV [panel (d)], and again hexagonal-like at $E_{\text{F}}$−1.11 eV [panel (e)]. The symmetry axes of the hexagonal-like QW contours in panels (c) and (e) are clearly rotated by $30°$ with respect to each other. Dash-dotted and dotted lines in panels (b)–(e) indicate the onset of the heavy hole and light hole Ge band edges, respectively, as described in the text.

Figure 3

(Color online) Schematic energy-momentum dispersion relation of a QW state near the center of the surface Brillouin zone in the three-dimensional ($k_{\text{x}}$, $k_{\text{y}}$, $E$) space (band bottom view). (a) Nearly free electron-like case. (b) Interacting case. The complex band topology of the interacting case can be easily evaluated by following the isoenergetic lines labeled (b)–(e), which represent the experimental energy contours observed in the corresponding panels of Fig. 2.

Figure 4

(Color online) Photoemission intensity maps measured along the $\overline{M}\text{−}\overline{\Gamma }\text{−}\overline{K}$ line for (a) 9 and (b) 17 ML Ag films, respectively, displayed within the Ge(111) surface Brillouin zone. Panel (c) reports measured (full symbols connected by lines) and calculated (open symbols) edges of the substrate bands, which are classified as the HH, LH, and SO bands. The measured Ge band edges are also shown in panel (b) as dashed lines.

Figure 5

(Color online) Fermi surface of a 9 ML Ag film grown on Ge(111). The dotted line surrounding the bright (saturated) feature at the zone center highlights its hexagonal-like aspect.