  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 Z2 number
independent of the film thickness, without the odd-even oscillation of
topological triviality as commonly perceived. The stable nontrivial Z2 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.
