Robustness of Topologically Protected Surface States in Layering of Bi₂Te₃ Thin Films

Bulk Bi₂Te₃ is known to be a topological insulator. We investigate surface states of Bi₂Te₃(111) thin films of one to six quintuple layers using density-functional theory including spin-orbit coupling. We construct a method to identify topologically protected surface states of thin film topological insulators. Applying this method to Bi₂Te₃ thin films, we find that the topological nature of the surface states remains robust with the film thickness and that the films of three or more quintuple layers have topologically nontrivial surface states, which agrees with experiments.