  We study the possibility of pressure-induced transitions from a normal
semiconductor to a topological insulator (TI) in bismuth tellurohalides using
density functional theory and tight-binding method. In BiTeI this transition is
realized through the formation of an intermediate phase, a Weyl semimetal, that
leads to modification of surface state dispersions. In the topologically
trivial phase, the surface states exhibit a Bychkov-Rashba type dispersion. The
Weyl semimetal phase exists in a narrow pressure interval of 0.2 GPa. After the
Weyl semimetal--TI transition occurs, the surface electronic structure is
characterized by gapless states with linear dispersion. The peculiarities of
the surface states modification under pressure depend on the band-bending
effect. We have also calculated the frequencies of Raman active modes for BiTeI
in the proposed high-pressure crystal phases in order to compare them with
available experimental data. Unlike BiTeI, in BiTeBr and BiTeCl the topological
phase transition does not occur. In BiTeBr, the crystal structure changes with
pressure but the phase remains a trivial one. However, the transition appears
to be possible if the low-pressure crystal structure is retained. In BiTeCl
under pressure, the topological phase does not appear up to 18 GPa due to a
relatively large band gap width in this compound.
