Emergence of Bulk 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 surface states and the bulk band inversion within the Bi2Se3 family of three-dimensional (3D) TIs via first-principles calculations. Thin films exposing the three lowest-energy surfaces are simulated by two-dimensional (2D) 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 dependence of the bulk gap on the thickness is found consistent for various surface slabs. This relationship is then utilized to predict the required thickness for maintaining the 3D TI phase in the bulk domain of the thin films. Our findings provide a unique understanding of the finite-size effects on various surfaces of the 3D TI materials. 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 nontrivial surface states.