Interference of topologically protected edge states in silicene nanoribbons

Silicene is a graphene-like honeycomb structure made of silicon atoms. It is a two-dimensional quantum spin-Hall insulator due to the spin-orbit interaction. According to the bulk-edge correspondence we expect zero-energy edge channels to appear in silicene nanoribbons. The behaviors of the helical edge channels are completely different between the armchair and the zigzag edges. Zero-energy states disappear in armchair nanoribbons despite the bulk-edge correspondence, while they appear as zigzag nanoribbons even if the width is quite narrow. The difference originates in the penetration depth of the helical edge channel, which is antiproportional to the spin-orbit gap for the armchair edge, while it remains as short as the lattice constant for the zigzag edge. These properties make clear distinctions between silicene and graphene nanoribbons, especially for armchair edges: In silicene edge states emerge as required by its topology, though the zero-energy states disappear from the energy spectrum, whereas in graphene no edge states exist. The emergence of edge states in armchair nanoribbons must be experimentally detectable by scanning tunneling microscopy, and may well serve as an experimental signal that silicene is a topological insulator.