Surface and substrate induced effects on thin films of the topological insulators Bi2Se3 and Bi2Te3

Based on van der Waals density functional calculations, we have studied few-quintuple-layer (QL) films of Bi2Se3 and Bi2Te3. The separation between the QLs near the surface is found to have a large increase after relaxation, whereas, the separation between the inner QLs is smaller and approaches the bulk value as the thickness grows, showing a two-dimensional to three-dimensional structural crossover. Accordingly, the surface Dirac cone of the Bi2Se3 film is evidently gapped for small thicknesses (two to four QLs), and the gap is reduced and, finally, is closed with the increasing thickness, agreeing well with the experiments. We further studied the substrate effect by investigating the Bi2Se3/graphene system. It is found that the underlying graphene induces a giant thickness-dependent Rashba splitting and Dirac point shift. Because Bi2Te3 films have smaller relative inter-QL expansion and stronger spin-orbit coupling, the topological features start to appear in the film as thin as two QLs in good accord with the experiments.