First-principles study of surface states in topological insulators Bi₂Te₃ and Bi₂Se₃: film thickness dependence

Abstract

Using first-principles method, we investigated the electronic states of Bi₂Te₃ and Bi₂Se₃. We showed that both Bi₂Te₃ and Bi₂Se₃ are insulators with a bulk band gap. In contrast, the surface states of Bi₂Te₃ and Bi₂Se₃ films have a metallic band connecting the conduction and valence bands. The films have an energy gap at the point when the film thickness is less than four quintuple layers (QLs), or about 30 Å. The energy gaps are closed at six QLs and four QLs for Bi₂Te₃ and Bi₂Se₃, respectively. We confirmed the metallicity up to nine QLs. Furthermore, we investigated the spin structures of nine-QL films at the Fermi energy in momentum space. We found that both the Bi₂Te₃ and Bi₂Se₃ films have Rashba-type spin textures; i.e. the surface states have spin–polarisation. To investigate the spatial distribution of the spin, we decomposed the expected values of the spin for each atom. The expected values of the spin are localised within the third QL from the surface. Our results of nine-QL films clearly show the boundary between the bulk and surface regions.

Keywords::

• topological insulators
• surface state
• Bi₂Te₃
• Bi₂Se₃
• first-principles calculation

Acknowledgements

Computations in this research were performed using supercomputers at ISSP, University of Tokyo, and supercomputers at RIIT, Kyushu University.

Additional information

Funding

The work was partially supported by Grants-in-Aid on Scientific Research [grant number 25104714], [grant number 25790007], [grant number 25390008] from Japan Society for the Promotion of Science, and by the MEXT HPCI Strategic Program.