Evolution of the electronic structure in ultrathin Bi(111) films

By combining angle-resolved photoemission spectroscopy and first-principles calculations, we systematically studied the electronic structures of ultrathin Bi(111) films ($\le 5$ bilayers) epitaxially grown on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. High-resolution low-energy band dispersions and Fermi surfaces of ultrathin $\mathrm{Bi}\left(111\right)/{\mathrm{Bi}}_2{\mathrm{Te}}_3$ films as a function of thickness were experimentally determined. Our results also indicate that the electronic structures of epitaxial Bi films are strongly influenced by the substrate compared with freestanding films. The substrate effects mainly include two aspects. First, the in-plane lattice constant of Bi(111) films is compressed, which increases the bandwidth of the surface-state-like bands. Furthermore, the band dispersion near the $\overline{\Gamma }$ point is significantly modified as well. Second, there exists a strong hybridization at the $\mathrm{Bi}/{\mathrm{Bi}}_2{\mathrm{Te}}_3$ interface, and the hybridization effects spatially extend to three Bi bilayers.

Figure 1

RHEED patterns of (a) 40-QL ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ grown on Si(111), and (b) 1-BL Bi(111) and (c) 5-BL Bi(111) films on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. (d) RHEED intensity line profiles with the increase of film thickness. The position where the intensity line profile was taken is marked by red dashed line in (a). (e) In-plane lattice constant of Bi films as a function of film thickness. Solid line is a guide for the eye.

Figure 2

(a) ARPES spectra of 40-QL ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111) film along $\overline{K}-\overline{\Gamma }-\overline{K}$ direction. Blue dashed lines mark the surface states and valence bands. (b)–(f) ARPES spectra of 1-BL Bi(111) to 5-BL Bi(111) films along $\overline{K}-\overline{\Gamma }-\overline{K}$ directions. (g)–(k) ARPES spectra of 1-BL Bi(111) to 5-BL Bi(111) films along $\overline{M}-\overline{\Gamma }-\overline{M}$ direction. The green dashed lines are the calculated spectra from top 2 Bi BLs. White arrows in (b) and (g) mark the bands that cross the Fermi level to form Fermi surface. Blue dashed lines in (c) are from (a). Quantum well states are marked by “QWS”. Outermost holelike band and Rashba-type splitting bands are marked by “S1” and “X”. Red dotted lines in (i) and (j) present the hybridization bands. (l) The side view of 3-BL Bi(111) on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ and differential charge density near interface. 1 QL is 1 nm and 1 BL is 0.4 nm. $Z=0$ is the interface.

Figure 3

(a) Fermi surface of 1-BL and (b) 2-BL Bi(111) films. White arrows mark the outer and inner Fermi surface sheets. (c) Experimental FS and (d) the calculated bands along the $\overline{M}-\overline{\Gamma }-\overline{M}$ direction of 3-BL Bi(111)/${\mathrm{Bi}}_2{\mathrm{Te}}_3$ film. (e) Experimental FS and (f) the calculated bands along the $\overline{M}-\overline{\Gamma }-\overline{M}$ direction of 4-BL Bi(111)/${\mathrm{Bi}}_2{\mathrm{Te}}_3$ film. (g) Experimental FS and (h) the calculated bands along the $\overline{M}-\overline{\Gamma }-\overline{M}$ direction of 5-BL Bi(111)/${\mathrm{Bi}}_2{\mathrm{Te}}_3$ film. Calculated bands only include the contributions from top 2-BL Bi. The Fermi levels (green lines) in calculated bands are adjusted based on the size of FS originating from S1 band.

Figure 4

(a) Calculated band structures of 5-BL Bi(111) with uncompressed in-plane lattice constant ($a_{\text{Bi}}=4.54$ Å) (from Ref. [5]) and of 5-BL Bi(111)/${\mathrm{Bi}}_2{\mathrm{Te}}_3$ with compressed in-plane lattice constant ($a_{\text{Bi}}=4.38$ Å) along the $\overline{\Gamma }-\overline{M}$ direction. (b) The sketch of the strain effect on S1 band. (c) Calculated band structures near $\overline{\Gamma }$ point of 20-BL and 5-BL Bi(111)/${\mathrm{Bi}}_2{\mathrm{Te}}_3$ with compressed in-plane lattice constant ($a_{\text{Bi}}=4.38$ Å). (d) Experimental FS of 20-BL Bi(111)/${\mathrm{Bi}}_2{\mathrm{Te}}_3$ with ($a_{\text{Bi}}=4.5$ Å).

Figure 5

(a) Side view of 4-BL Bi(111) film on ${\mathrm{Bi}}_2{\mathrm{Te}}_3$. The calculated spectra projected onto (b) top 1 BL, (c) bottom 1 BL, (d) top 2 BLs, (e) 4 BLs plus 1-QL ${\mathrm{Bi}}_2{\mathrm{Te}}_3$(111), and (f) 4 BLs along $\overline{M}-\overline{\Gamma }-\overline{M}$ directions in 4-BL Bi(111)/${\mathrm{Bi}}_2{\mathrm{Te}}_3$. The spectra caused by hybridization between Bi and ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ are marked by “H1” and “H2” in (c). The Dirac-cone surface states of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ are marked by “D” in (e). (g)–(k) The calculated spectra projected onto the top 1 BL, bottom 1 BL, top 2 BLs, 4 BLs plus 1 QL, and 4 BLs along $\overline{K}-\overline{\Gamma }-\overline{K}$ direction.