Tight-binding Models for Two-dimensional Allotropes of Bismuth based on Wannier Functions

Recently two-dimensional allotropes of bismuth have attracted significant attention in the study of topological materials due to the strong correlation between their crystalline symmetry and electronic band topology. This connection has been studied previously by directly transferring the empirical tight-binding models of semi-metallic bulk bismuth to its two-dimensional counterparts. However, this approach fails to describe the electronic structure of two-dimensional bismuth correctly. Therefore, new physical models are required when considering the two-dimensional forms of bismuth. In this study, we have constructed tight-binding models based on the Wannier representations derived from the Bloch states in first principles calculations. We have successfully reproduced the band features for three types of two-dimensional bismuth allotropes (Bi(111), Bi(110) and bismuthene) with minimal tight-binding parameters. We have verified the accuracy of the model by calculating band representations and topological invariants. We expect these simple but accurate tight-binding models can help to examine the electronic transport in these systems more effectively in the future.