Emergence of Band Inversion in the Nanodomain and Relaxation Effects on the Surface States of the Bi2Se3 Topological Insulator Family

Topological insulators (TIs) hold compelling promise for diverse applications in advanced nanodevices and catalysis, owing to their protected edge and surface states. Under operational conditions, TI materials are typically fabricated into (ultra-)thin films with highly crystalline nanodomains. The exposed facets exhibit distinct surface properties that vary with respect to the size of the nanocrystals. Herein, we investigate the finite-size effects on the topological phase transition within the prototypical Bi2Se3 family of TIs via first-principles calculations. Thin films exposing the three lowest-energy surfaces are simulated by semi-infinite slabs with tunable thicknesses. We propose that the finite-size effects originate from electron confinement in the cutoff direction. The increase in film thickness then counteracts these confinement effects, resulting in a monotonically decreasing band gap evaluated at the spin−orbit decoupled level. The bulk domains of various thin films are found to be inherently related to one another through the band inversion. This allows for the prediction of the required thickness for attaining non-trivial band topology in the bulk domain of TI nanocrystals. A systematic scheme is proposed to determine the required size for the topological phase transition on various facets of TI nanocrystals. Our findings provide a unique understanding of the finite-size effects on various surfaces of TI thin films. In addition, the actual manifestation of topological surface states on the side surfaces is affected significantly by the co-existing dangling bonds produced by surface cuts. Therefore, surface relaxation plays a crucial role in disentangling the trivial and non-trivial surface states.