Topological phase transition in thin-film topological crystalline insulators

Topological crystalline insulator is one of the recent breakthrough ideas [1], in which Dirac fermions on the surface protected by crystalline symmetry, not by time-reversal symmetry. Another direction of the topological expansion is nanofabrication. In this work, we reveal the topological phase diagram of a thin-film topological crystalline insulator Pb$_{x}$Sn$_{1-x}$Te. Odd numbers of layers of Pb$_{x}$Sn$_{1-x}$Te exhibit the topological phase transition between two-dimensional trivial and topological crystalline insulators protected by the mirror-Chern number, which is consistent with the previous work [2]. In addition, we have found a new topological phase in the even numbers of layers, which is protected by the glide symmetry [3]. This glide topological phase can be realized in the thin film not in the bulk system. \\[4pt] [1] L. Fu, Phys. Rev. Lett. 106, 106802 (2011); T. H. Hsieh, et al., Nat. Commun. 3, 982(2012); Y. Tanaka, et al., Nat. Phys. 8, 800 (2012).\\[0pt] [2] J. Liu, et al., Nat. Mater. 13, 178 (2014).\\[0pt] [3] H. Ozawa, A. Yamakage, M. Sato, and Y. Tanaka, Phys. Rev. B 90, 045309 (2014).