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With its monoelemental composition, various crystalline forms and aninherently strong spin-orbit coupling, bismuth has been regarded as an idealprototype material to expand our understanding of topological electronicstructures. In particular, two-dimensional bismuth thin films have attracted agrowing interest due to potential applications in topological transistors andspintronics. This calls for an effective physical model to give an accurateinterpretation of the novel topological phenomena shown by two-dimensionalbismuth. However, the conventional semi-empirical approach of adapting bulkbismuth hoppings fails to capture the topological features of two-dimensionalbismuth allotropes because the electronic band topology is heavily influencedby crystalline symmetries as well as atom spacings. Here we provide a newparameterization using localized Wannier functions derived from the Blochstates in first-principles calculations. We construct new tight-binding modelsfor three types of two-dimensional bismuth allotropes: a Bi (111) bilayer,bismuthene and a Bi(110) bilayer. We demonstrate that our tight-binding modelscan successfully reproduce the band structures, symmetries and topologicalfeatures of these two-dimensional allotropes. We anticipate that these modelscan be extended to other similar two-dimensional topological structures such asantimonene and arsenene. Moreover, these models can serve as a starting pointfor investigating the electron/spin transport and electromagnetic response inlow-dimensional topological devices.

Localized Wannier function based tight-binding models for two-dimensional allotropes of bismuth