Robustness of two-dimensional topological insulator states in bilayer bismuth against strain and electrical field

Using first-principles and Wannier function methods, we systematically calculate the electronic band structure and topological edge states of single bilayer Bi (111) film (BL-Bi) as a function of strain and perpendicular electric field to investigate the effects induced by lattice mismatch and interfacial charge transfer when BL-Bi is epitaxially grown on a substrate. We found that the BL-Bi remains with a finite band gap and a nontrivial band topology for strains up to ±{}6$%$ and electric fields up to 0.8 eV/{}. This indicates that the BL-Bi is a robust two-dimensional topological insulator against strain and electrical field on a substrate.