Edge states and topological properties of electrons on the bismuth on silicon surface with giant spin-orbit coupling

We derive a model of localized edge states in the finite width strip for two-dimensional electron gas formed in the hybrid system of bismuth monolayer deposited on the silicon interface and described by the nearly-free electron model with giant spin-orbit splitting. The edge states have the energy dispersion in the bulk energy gap with the Dirac-like linear dependence on the quasimomentum and the spin polarization coupled to the direction of propagation, demonstrating the properties of topological insulator. The topological stability of edge states is confirmed by the calculations of the $Z_2$ invariant taken from the structure of the Pfaffian for the time reversal operator for the filled bulk bands in the surface Brillouin zone which is shown to have a stable number of zeros with the variations of material parameters. The proposed properties of the edge states may support future advances in experimental and technological applications of this new material in nanoelectronics and spintronics.