Robustness of topological insulating phase against vacancy, vacancy cluster, and grain boundary bulk defects

One distinguished property of the topological insulator (TI) is its robust quantized edge conductance against edge defect. However, this robustness, underlined by the topological principle of bulk-boundary correspondence, is conditioned by assuming a perfect bulk. Here, we investigate the robustness of the TI phase against bulk defects, including vacancy (VA), vacancy cluster (VC), and grain boundary (GB), instead of edge defect. Based on a tight-binding model analysis, we show that a two-dimensional (2D) TI phase, as characterized by a nonzero spin Bott index, will vanish beyond a critical VA concentration (nvc). Generally, nvc decreases monotonically with the decreasing topological gap induced by spin-orbit coupling. Interestingly, the nvc to destroy the topological order, namely, the robustness of the TI phase, is shown to be increased by the presence of VCs but decreased by GBs. As a specific example of a large-gap 2D TI, we further show that the surface-supported monolayer Bi can sustain a nontrivial topology up to nvc∼17%, based on a density-functional theory–Wannier-function calculation. Our findings should provide useful guidance for future experimental studies of effects of defects on TIs.