  The spin-orbit interaction affects the electronic structure of solids in
various ways. Topological insulators are one example where the spin-orbit
interaction leads the bulk bands to have a non-trivial topology, observable as
gapless surface or edge states. Another example is the Rashba effect, which
lifts the electron-spin degeneracy as a consequence of spin-orbit interaction
under broken inversion symmetry. It is of particular importance to know how
these two effects, i.e. the non-trivial topology of electronic states and
Rashba spin splitting, interplay with each other. Here we show, through
sophisticated first-principles calculations, that BiTeI, a giant bulk Rashba
semiconductor, turns into a topological insulator under a reasonable pressure.
This material is shown to exhibit several unique features such as, a highly
pressure-tunable giant Rashba spin splitting, an unusual pressure-induced
quantum phase transition, and more importantly the formation of strikingly
different Dirac surface states at opposite sides of the material.
