Double Helix of Atomic Displacements in Ferroelectric PbTiO₃

Recent theoretical work has predicted the existence of a “dipole spiral” structure in strained freestanding membranes of PbTiO 3 , suggesting a potential route to enhanced electromechanical responses [PRL 133, 046802 (2024)]. However, its microscopic nature, energetic landscape, and electronic properties remain largely unexplored from a first-principles perspective. Here, using density function theory on PbTiO 3 under biaxial tensile strain, we identify a novel form of polar order: a chiral, non-collinear ferroelectric double helix. We find that two distinct, intertwined polarization helices are formed by the local Pb-O and Ti-O dipoles, reminiscent of DNA. This topology is stabilized by a collective helical twisting of the encompassing oxygen cages (the polyhedra for both Pb and Ti cations), which gives rise to an electric Dzyaloshinskii-Moriya-like interaction. The resulting structure, which can be canceptualized as a “self-moiré” crystal, exhibits two coupled functionalities. First, it possesses a rotational pseudo-zero-energy mode that underpins a giant piezoelectric response ( e 33 ≈ 16 C/m 2 ). Second, the long-period potential reconstructs the electronic band structure, leading to a multi-valley electronic topology at the valence band edge. Our work establishes a physical route to designing complex chiral order that supports both giant electromechanical coupling and multi-valley electronics.