Abstract
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.
