  The coexistence of ferroelectric and topological orders in two-dimensional
(2D) atomic crystals allows non-volatile and switchable quantum spin Hall
states. Here we offer a general design principle for 2D bilayer
heterostructures that can host ferroelectricity and nontrivial band topology
simultaneously using only topologically trivial building blocks. The built-in
electric field arising from the out-of-plane polarization across the
heterostrucuture enables a robust control of the band gap size and band
inversion, which can be utilized to manipulate topological phase transition.
Using first-principles calculations, we demonstrate a series of bilayer
heterostructures are 2D ferroelectric topological insulators (2DFETIs). We
propose a few 2DFETI-based quantum electronics including domain-wall quantum
circuits, bias-free optospintronics, and topological memristor.
