Topological fate of edge states of Bi single bilayer on Bi(111)

We address the topological nature of electronic states of step edges of Bi(111) films by first principles band structure calculations. We confirm that the dispersion of step edge states reflects the topological nature of underlying films. This result unambiguously denies recent claims that the step edge state on the surface of a bulk Bi(111) crystal or a sufficiently thick Bi(111) films represents non-trivial edge states of the two dimensional topologcial insulator phase expected for a very thin Bi(111) film. The trivial step edge states have a gigantic spin splitting of one dimensional Rashba bands and the substantial intermixing with electronic states of the bulk, which might be exploited further.