One-dimensional topological phase and tunable soliton states in atomic nanolines on Si(001) surface

Formation of exotic topological states on technologically important semiconductor substrate is significant from the aspects of both fundamental research and practical implementation. Here, we demonstrate one-dimensional (1D) topological phase and tunable soliton states in atomic nanolines self-assembled on Si(001) surface. By first-principles calculations and tight-binding modeling, we reveal that Bi nanolines provide an ideal system to realize a multi-orbital Su-Schrieffer-Heeger (SSH) model, and the electronic properties can be modulated by substrate-orbital-filtering effect. The topological features are confirmed by nontrivial end states for a finite-length nanoline and (anti-)soliton states at the boundary of two topologically distinct phases. We demonstrate that solitons are highly mobile on the surface, and their formation could be controlled by surface B/N doping. As these nanolines can extend several micrometers long without kinks, and quantum transport simulations suggest clear signatures of topological states characterized by transmission resonance peaks, our work paves an avenue to achieve 1D topological phase compatible with semiconductor technology and to engineer the properties with high tunability and fidelity for quantum information processing.