  Spin-orbit coupling is increasingly seen as a rich source of novel phenomena,
as shown by the recent excitement around topological insulators and Rashba
effects. We here show that the addition of ferroelectric degrees of freedom to
a semiconductor featuring topologically-non-trivial properties, such as SnTe,
merges the intriguing field of spin-orbit-driven physics with non-volatile
functionalities appealing for spintronics. By using a variety of modelling
techniques, we show that a strikingly rich sequence of phases can be induced in
SnTe, when going from a room-temperature cubic phase to a low-temperature
ferroelectric structure, ranging from a topological crystalline insulator to a
time-reversal-invariant $Z_2$ topological insulator to a "ferroelectric Rashba
semiconductor", exhibiting a huge electrically-controllable Rashba effect in
the bulk band structure.
