Stable nontrivial $Z_2$ topology in ultrathin Bi (111) films: a first-principles study*

Recently, there have been intense efforts in searching for new topological insulator (TI) materials. Based on first-principles calculations, we find that all the ultrathin Bi (111) films are characterized by a nontrivial $Z_2$ number independent of the film thickness, without the odd-even oscillation of topological triviality as commonly perceived. The stable nontrivial $Z_2$ topology is retained by the concurrent band gap inversions at multiple time-reversal-invariant k-points and associated with the intermediate inter-bilayer coupling of the multi-bilayer Bi film. Our calculations further indicate that the presence of metallic surface states in thick Bi(111) films can be effectively removed by surface adsorption.