Stable NontrivialZ2Topology in Ultrathin Bi (111) Films: A First-Principles Study

Recently, there have been intense efforts in searching for new topological insulator 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 with the increasing film thickness and associated with the intermediate interbilayer coupling of the 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.