First-principles study of surface states in topological insulators Bi₂Te₃and 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.