  The topological order of single-crystal Bi and its surface states on the
(111) surface are studied in detail based on empirical tight-binding (TB)
calculations. New TB parameters are presented that are used to calculate the
surface states of semi-infinite single-crystal Bi(111), which agree with the
experimental angle-resolved photoelectron spectroscopy results. The influence
of the crystal lattice distortion is surveyed and a topological phase
transition is found that is driven by in-plane expansion. In contrast with the
semi-infinite system, the surface-state dispersions on finite-thickness slabs
are non-trivial irrespective of the bulk topological order. The role of the
interaction between the top and bottom surfaces in the slab is systematically
studied, and it is revealed that a very thick slab is required to properly
obtain the bulk topological order of Bi from the (111) surface state: above 150
biatomic layers in this case.
