Topological states inBi2Se3surfaces created by cleavage within a quintuple layer: Analysis in terms of the Shockley criterion

Abstract

In topologically trivial materials, the existence of surface states within the bulk band gap depends on the surface condition. A surface state exists if the system is Shockley inverted, and vice versa; furthermore, this surface condition in a superlattice can be tuned from one case to the other by varying the terminating atomic plane within a superlattice period. By contrast, we demonstrate here based on first-principles calculations for ${\text{Bi}}_{2}$${\text{Se}}_{3}$ cleaved at different atomic planes within a quintuple layer that topological surface states always span the bulk band gap in accordance with the topologically nontrivial nature of ${\text{Bi}}_{2}$${\text{Se}}_{3}$. However, the number of surface bands, the band dispersion relations, and the degree of spin polarization are strongly dependent on the cleavage plane. Multiple Dirac cones can exist at the zone center and/or zone boundary, and a massive but topologically nontrivial Dirac cone is observed for a Se-terminated surface. The results confirm the robustness of the topological nature of the system, but the details of the topological surface states themselves can vary substantially within the broad topological constraint. The persistent existence of topological states within the gap is discussed in terms of the Shockley criterion.