Engineering relativistic effects in ferroelectric SnTe

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.