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

With its monoelemental composition, various crystalline forms and an inherently strong spin-orbit coupling, bismuth has been regarded as an ideal prototype material to expand our understanding of topological electronic structures. In particular, two-dimensional bismuth thin films have attracted a growing interest due to potential applications in topological transistors and spintronics. This calls for an effective physical model to give an accurate interpretation of the novel topological phenomena shown by two-dimensional bismuth. However, the conventional semi-empirical approach of adapting bulk bismuth hoppings fails to capture the topological features of two-dimensional bismuth allotropes because the electronic band topology is heavily influenced by crystalline symmetries. Here we provide a new parameterization using localized Wannier functions derived from the Bloch states in first-principles calculations. We construct new tight-binding models for three types of two-dimensional bismuth allotropes: a Bi (111) bilayer, bismuthene and a Bi (110) bilayer. We demonstrate that our tight-binding models can successfully reproduce the electronic and topological features of these two-dimensional allotropes. Moreover, these tight-binding models can be used to explain the physical origin of the occurrence of novel band topology and the perturbation effects in these bismuth allotropes. In addition, these models can serve as a starting point for investigating the electron/spin transport and electromagnetic response in low-dimensional topological devices.