Topological insulators are now being investigated enthusiastically for their peculiar properties which stem from the inverted parity band structure. For example, previous researches found that surface states of a topological insulator form a spin polarized Dirac cone with a linear dispersion. The electronic structures of topological insulators have been studied extensively, but little has been studied on their surface atomic structure.

Fig. 1. The top view (a) and the side view (b) of the optimized surface atomic structure of Bi1BL on a Bi₂Te₃ substrate. The orange circles and the blue circles represent the position of Bi atoms and Te atoms, respectively. In (a), the size of a circle indicate the depth of the atom from the topmost layer. (c) The obtained IV curves (red solid lines) and the calculated ones (blue broken lines). R_p is 0.27, where R_p is Pendry’s reliable factor and indicates the degree of agreement.

Fig. 2. The band structure of a free standing Bi1BL (ab initio calculations) for the lattice constants of bulk Bi (a), and that for Bi which is contracted in-plane and expanded out-of-plane as experimentally determined (b). The inset represents the first Brillouin zone of Bi1BL and the high symmetry points. a is the in-plane lattice constant and d is the out-of-plane lattice constant.

Here we report the surface structures of two topological insulators, Bi₂Te₃ and a single bilayer Bi on Bi₂Te₃ (Bi1BL hereafter), by LEED analysis. There was only a slight relaxation on the Bi₂Te₃ surface, showing that the bulk atomic structure is maintained in the surface topmost layers. On the other hand, we found that Bi1BL was strongly distorted from bulk Bi; contracted in the in-plane direction and expanded in the out-of-plane direction. Figs. 1 (a) and (b) are the optimized surface structure of Bi1BL obtained from the LEED analysis. The red solid lines in Fig. 1 (c) are the measured intensity-voltage curves (IV curves) and the blue broken lines are those calculated from the optimized atomic structure. The in-plane lattice constant of the topmost Bi1BL matches to that of Bi₂Te₃ of 4.38Å which is 3% contracted from the corresponding lattice constant of bulk Bi (4.54Å) [1]. Note that this contraction does not take place on a Si(111) substrate [2]. In contrast, the intralayer distance of 1.71Å was expanded by 7% from the bulk value (1.59Å). The Poisson ratio almost reaches 0.5, the theoretical maximum of an elastic material.

Ab initio calculations revealed the influence of this strong distortion. Fig. 2 shows the band structure of a free standing Bi bilayer with the lattice constants of bulk Bi (a), and that of distorted Bi with the experimentally determined parameters (b). It is found that the energy gap is enlarged from 0.1eV to 0.4eV when the lattice constants are changed.

In summary, we showed that the surface atomic structure relaxation of Bi1BL has a strong impact on its electronic structure. Changing the in-plane lattice constant can be a means to obtain a topological insulator with a wider band gap.

References

• [1] H. Mönig, J. Sun, Yu. M. Koroteev, G. Bihlmayer, J. Wells, E. V. Chulkov, K. Pohl, and Ph. Hofmann, Phys. Rev. B 72, 085410 (2005).
• [2] T. Nagao, J. T. Sadowski, M. Saito, S. Yaginuma, Y. Fujikawa, T. Kogure, T. Ohno, Y. Hasegawa, S. Hasegawa, and T. Sakurai, Phys. Rev. Lett. 93, 105501 (2004).

Authors

• N. Fukui^a, T. Hirahara^a, T. Shirasawa, T. Takahashi, K. Kobayashi^a, and S. Hasegawa^a
• ^aThe University of Tokyo
• ^bOchanomizu University