  The electronic states of a single Bi(111) bilayer and its edges, suggested as
a two dimensional topological insulator, are investigated by scanning tunneling
spectroscopy (STS) and first-principles calculations. Well-ordered bilayer
films and islands with zigzag edges are grown epitaxially on a cleaved
Bi$_{2}$Te$_{2}$Se crystal. The calculation shows that the band gap of the Bi
bilayer closes with a formation of a new but small hybridization gap due to the
strong interaction between Bi and Bi$_{2}$Te$_{2}$Se. Nevertheless, the
topological nature of the Bi bilayer and the topological edge state are
preserved only with an energy shift. The edge-enhanced local density of states
are identified and visualized clearly by STS in good agreement with the
calculation. This can be the sign of the topological edge state, which
corresponds to the quantum spin Hall state. The interfacial state between Bi
and Bi$_{2}$Te$_{2}$Se is also identified inside the band gap region. This
state also exhibits the edge modulation, which was previously interpreted as
the evidence of the topological edge state [F. Yang et al., Phys. Rev. Lett.
109, 016801 (2012)].
