Bifurcation of the edge-state width in a two-dimensional topological insulator

We examine the properties of edge states in a two-dimensional topological insulator. Based on the Kane-Mele model, we derive coupled equations for the energy and the effective width of the edge states at a given crystal momentum in a semi-infinite honeycomb lattice with a zigzag boundary. It is revealed that, in a one-dimensional Brillouin zone, the edge states merge into continuous bands of the bulk states through a bifurcation of the edge-state width. We discuss the implications of the results for experiments in monolayer or thin-film topological insulators.