Finite-size-effect-induced topological phase transition in a topological crystalline insulator

We study electronic states and topological invariants of (001)-films of topological crystalline insulator (TCI) Pb_{x}Sn_{1-x}Te. Gapless surface Dirac cones on bulk TCIs become gapped in thin films due to finite-size effect, which is hybridization between those on the top and bottom surfaces. We clarify that the TCI film has the strong finite-size effect as compared to three-dimensional topological insulators such as Bi2Se3. Moreover, the energy gap oscillates with the thickness of film. The oscillation stems from topological phase transitions in two dimensions. The obtained data of the topological invariants and energy gap serve as guide to TCI-device applications.