  The unoccupied states in topological insulators Bi_2Se_3, PbSb_2Te_4, and
Pb_2Bi_2Te_2S_3 are studied by the density functional theory methods. It is
shown that a surface state with linear dispersion emerges in the inverted
conduction band energy gap at the center of the surface Brillouin zone on the
(0001) surface of these insulators. The alternative expression of Z_2 invariant
allowed us to show that a necessary condition for the existence of the second
Gamma Dirac cone is the presence of local gaps at the time reversal invariant
momentum points of the bulk spectrum and change of parity in one of these
points.
