Dynamical stability and electron-phonon interactions in topologically protected conducting channel of atomically thin Bi (111)

Two-dimensional topological insulators possess a single conducting channel embedded inside the insulating bulk surface bandgap, which can be complicated to realize in practical devices due to electron-phonon interactions (EPI) at finite temperatures. Using single bilayer Bi (111) (SBB) and the first-principles method, we find that imaginary phonon modes exist in the native edges, suggesting dynamical instability. We also find that hydrogen passivation-induced sp-hybridization increases spin-orbit coupling (SOC) in the edge atoms. The passivation can entirely remove the imaginary phonon modes of the zigzag edge due to an equal increase of the SOC. In contrast, it cannot entirely remove the imaginary phonon modes of the armchair edge due to the unequal growth of SOC. While the electronic edge states of the native edges don't exhibit a linear dispersion, the passivation can bring linear dispersion. We show that the EPI strongly depend on the edge states dispersion. Particularly, when the dispersion of the topological edge electronic states becomes more linear, the EPI gets negligibly weaker and vice versa. Additionally, we find that the surface phonons have nonzero topological invariant, suggesting the existence of topological phononic edge states in SBB.