Role of Spin-Orbit Coupling and Hybridization Effects in the Electronic Structure of Ultrathin Bi Films

The electronic structure of Bi(001) ultrathin films (thickness $\ge 7$ bilayers) on $\mathrm{Si}(111)\mathrm{\text{−}}7\times 7$ was studied by angle-resolved photoemission spectroscopy and first-principles calculations. In contrast with the semimetallic nature of bulk Bi, both the experiment and theory demonstrate the metallic character of the films with the Fermi surface formed by spin-orbit-split surface states (SSs) showing little thickness dependence. Below the Fermi level, we clearly detected quantum well states (QWSs) at the $\overline{M}$ point, which were surprisingly found to be non-spin-orbit split; the films are “electronically symmetric” despite the obvious structural nonequivalence of the top and bottom interfaces. We found that the SSs hybridize with the QWSs near $\overline{M}$ and lose their spin-orbit-split character.

Figure 1

(a) The Fermi surface of bulk Bi depicted in bulk (orange) and its projection to the surface (red) Brillouin zone of $\mathrm{Bi}(001{)}_{\mathrm{hex}}$, or $(111{)}_{\mathrm{rhom}}$. Electron (hole) pockets are filled with light blue (purple). The size of the pockets are scaled by a factor of 3. (b), (c) Schematic drawing of the Bi bulk band projection near the Fermi level $E_F$ before (b) and after (c) the SMSC transition as predicted in Ref. 5.

Figure 2

The Fermi surfaces of ultrathin Bi(001) films for 6.8 (a), 10 (b), and 17 BL (c) films. (d) The schematic drawing of the Fermi surface of ultrathin Bi(001) films in the SBZ. Electron pockets are colored in light blue and hole pockets in purple. (e) The close up of the band dispersion image near the $\overline{\Gamma }$ point in the vicinity of the Fermi level along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction for the 10 BL film. The solid lines through the dots are the results of the first-principles calculation with one side of the film terminated with H. Red circles are surface states and pink ones surface resonances.

Figure 3

(a) The band structure of a 10 BL Bi(001) film for the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction. (b) Calculated band dispersion for the 10 BL Bi film with one side of the film H terminated. Red represents surface states, pink the states close to the surface, and white the states located inside the film.

Figure 4

Calculated band structure for freestanding Bi(001) films assuming space-inversion symmetry for 7 (a), 10 (b), and 17 (c) BL Bi(001) films together with the measured band dispersion [6.8 BL for the experimental data of (a)] along the $\overline{\Gamma }\mathrm{\text{−}}\overline{M}$ direction for $k>0.3{\AA }^{-1}$. For the two uppermost bands close to $E_F$, the states whose electron density is localized at the surface are represented in red, and those localized weaker at the surface are shown in pink. The states localized inside the film are shown in white. The yellow circle in (c) is used in (f). (d) The bulk band dispersion along the $L\mathrm{\text{−}}X$ direction and the calculated positions of QWS for the 17 BL film. (e) STM image of the rugged wetting layer at the Bi-Si interface taken after peeling off the Bi film. (f) The layer-resolved electron density (17 BL film) for the surface state [yellow circle in (c), the same band as $n=17$] and those for QWSs ($n=1$, 3, 17) at $\overline{M}$.