Effect of surface relaxation on the Dirac surface states of the topological crystalline insulator Bi

Recent theoretical studies revealed that bulk bismuth is a higher-order topological insulator and also a first-order crystalline topological insulator [1,2]. As a crystalline topological insulator, Bi exhibits two gapless Dirac states on (1-10)-type surfaces. Since the position of either of these Dirac cones in the surface Brillouin zone is not fixed by symmetry, the Dirac cone can be found at a general location within the zone, with the only constraint being that the two Dirac cones are related to each other by a twofold rotational symmetry. Here, using first-principles calculations, we study how surface relaxation changes the (1-10) topological surface states. We found that as the atoms move to their equilibrium positions, the locations of the Dirac cones shift significantly, and the surface band structure changes drastically. The possible physical reasons behind these phenomena are discussed.

1. F. Schindler et al., Nature Physics, 14, 918 (2018).

2. C-H. Hsu et al., PNAS, 116, 13255 (2019).