Tuning the Edge States of Bismuthene via Substrate Effects*

One of the challenges in the field of topological material studies is how to maintain the nontrivial topological behaviour in a practical condition. In this work, we study the robustness of edge states in a two-dimensional topological crystalline insulator (2D TCI) and approaches of modifying them based on a planar bismuthene model. Using first principles calculations and Wannier tight-binding models, we have found that the mirror symmetry protected non-trivial topological phase can be maintained when the thin film has weak interaction with the substrate, or when a sandwich stacking is applied. We have also shown that spin-filtered edge current of 2D TCI can survive strong mirror symmetry breaking field when they have certain edge terminations. Finally we have demonstrated by modulating the interfacial distance, or applying rotation on sandwich structures, bismuthene edge band gap can be opened, which effectively switches off the nontrivial topological states. This research can provide guidelines for methodology to tune or maintain those edge states in the design of TCI-based electronic devices.