Quantum size effects in quasi-free-standing Pb layers

Quantum well states in thin metal films are strongly influenced by the electronic and geometric structure of the underlying substrate. This impedes a comparison to ab initio calculations generally based on free-standing films. Here we show that Pb films deposited on single-crystalline, epitaxial graphite are an excellent approximation to free-standing metal films. We find Pb islands of four monolayer height to be most stable, followed by other even-numbered islands, in excellent agreement with theoretical predictions for the formation of preferred island heights.

Figure 1

(Color online) Cut through the SBZ for 2 ML of Pb on graphitized SiC. The lines represent the DFT calculations for a 2-ML- [blue (dark gray)] and a 4-ML- [red (light gray)] thick free-standing Pb slab, with spin-orbit coupling taken into account. (Inset) LEED image obtained at $90\mathrm{eV}$ after deposition of 2 ML of Pb.

Figure 2

(Color online) Magnified area from Fig. 1. Inserted are DFT calculations for a 2-ML-thick free-standing Pb incorporating [blue (dark gray) line] and ignoring spin-orbit coupling [green (light gray) line].

Figure 3

Energy distribution curves extracted from the images at $k_{\Vert }=0$ for increasing coverage. Indicated are the island heights that the QWSs are derived from.

Figure 4

(Color online) (a) Fitted spectrum for 4 ML Pb on graphite. (b) Ratio of the total Pb covered area for 2- [blue (dark gray) diamonds and solid line], 4- [green (light gray) upwards triangles and solid line], 6- [red (dark gray) downwards triangles and dashed line], and 8- (black squares and dashed line) ML-high islands. (c) Surface energy per unit cell as a function of layer thickness obtained with the values described in the text. The solid (blue) line and (green) circles represent a free-standing Pb film; for the dashed (red) line and black diamonds an artificial phase shift of 0.3 ML has been incorporated.