Surface relaxation of topological insulators: Influence on the electronic structure

The surface structure of topological insulators Bi${}_2$Te${}_3$(111) and a single bilayer bismuth on it was studied by low-energy electron-diffraction analysis. The topmost quintuple layer of Bi${}_2$Te${}_3$ showed only a slight relaxation ($\sim 1\%$ contraction). On the other hand, the bilayer Bi was strongly distorted compared to bulk Bi (3.5 $\%$ in-plane contraction and $\sim 7\%$ out-of-plane expansion). First-principles calculation reveals that this distortion has a large influence on the electronic structure and can enlarge the band gap.

Figure 1

(a) LEED pattern of the 1$\times$1 Bi${}_2$Te${}_3$(111) surface at 80 K. [(b), (c)] Top (b) and side (c) view of the Bi${}_2$Te${}_3$(111) surface. The orange (light gray) circles represent Bi and blue (dark gray) ones represent Te. (d) $IV$ curves of the Bi${}_2$Te${}_3$(111) surface. The solid lines are experimentally obtained ones and dashed lines are calculated ones.

Figure 2

$R$ factor vs the out-of-plane lattice compression of Bi${}_2$Te${}_3$. The dashed line indicates the upper limit of the reliability of $R$${}_p$. The data points below this line is the uncertainty of the lattice constant.

Figure 3

(a) LEED pattern of the bilayer Bi on Bi${}_2$Te${}_3$. [(b),(c)] Top (b) and side (c) view of the Bi bilayer on Bi${}_2$Te${}_3$. The orange (light gray) circles represent Bi and the blue (dark gray) ones represent Te. (d) $IV$ curves of the bismuth bilayer on Bi${}_2$Te${}_3$. The solid lines are experimentally obtained ones and the dashed lines are calculated ones.

Figure 4

$R$ factor as a function of the lattice expansion for the intrabilayer Bi distance (red or dark gray circles) and the distance between the bottom of the Bi bilayer and the topmost Te layer of Bi${}_2$Te${}_3$ (green or light gray triangles). The values are compared to bulk Bi values. The dashed line indicates the upper limit of the trustworthy $R$${}_p$ value.

Figure 5

Calculated band structures of the single bilayer Bi with various lattice constants. $a$ is the in-plane lattice constant and $d$ is the distance between the two bismuth layers. The inset in (a) shows the Brillouin zone with high symmetry points.