Abstract
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.
Highlights
The discovery of spin-orbit coupling (SOC) induced topological phase transitions in electronic structure have led to a rapidly growing interest in the topological electronics and spintronics applications1,2
To gain physical insights into correlation between crystal symmetry and topological phases of 2D allotropes of bismuth, here we develop effective TB models of Bi (111) and Bi (110) bilayers as well as bismuthene using localized Wannier functions constructed from first-principles calculations20
Several reports have shown that when bismuth films are reduced to only one bilayer thickness, the change of parities occurs between the highest valence band and lowest conduction band, contrary to the data presented in Fig. 1.24,25 This contrasting behavior has been associated with the change of the lattice parameter from its bulk value
Summary
The discovery of spin-orbit coupling (SOC) induced topological phase transitions in electronic structure have led to a rapidly growing interest in the topological electronics and spintronics applications. A notable example is the planar honeycomb structure of bismuthene, which can not be directly related to the bulk bismuth symmetry These issues lead to a poor agreement between the band structure computed from the semiempirical model and first principles density functional theory (DFT). To gain physical insights into correlation between crystal symmetry and topological phases of 2D allotropes of bismuth, here we develop effective TB models of Bi (111) and Bi (110) bilayers as well as bismuthene using localized Wannier functions constructed from first-principles calculations. Wannier functions thereby allow us to construct a model Hamiltonian for each allotrope with relatively few parameters and yet still provide an accurate description of their band structure and its relationship with the crystal symmetry These Wannier function based Hamiltonians can be further employed to investigate charge and spin carrier transport in electronic devices based on low-dimensional topological materials.
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