  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 as well as atom spacings. 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 band structures, symmetries and topological
features of these two-dimensional allotropes. We anticipate that these models
can be extended to other similar two-dimensional topological structures such as
antimonene and arsenene. Moreover, these models can serve as a starting point
for investigating the electron/spin transport and electromagnetic response in
low-dimensional topological devices.
