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 strength, which can be utilized to manipulate topological phase transitions. Using first-principles calculations, we demonstrate a series of bilayer heterostructures are 2D ferroelectric topological insulators (2DFETIs) characterized with a direct coupling between band topology and polarization state. We propose a few 2DFETI-based quantum electronics including domain-wall quantum circuits and topological memristor.
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