Giant piezoelectric effects of topological structures in stretched ferroelectric membranes

Freestanding ferroelectric oxide membranes emerge as a promising platform for exploring the interplay between topological polar ordering and dipolar interactions that are continuously tunable by strain. Our investigations combining density functional theory (DFT) and deep-learning-assisted molecular dynamics simulations demonstrate that DFT-predicted strain-driven morphotropic phase boundary involving monoclinic phases manifest as diverse domain structures at room temperatures, featuring continuous distributions of dipole orientations and mobile domain walls. Detailed analysis of dynamic structures reveals that the enhanced piezoelectric response observed in stretched PbTiO$_3$ membranes results from small-angle rotations of dipoles at domain walls, distinct from conventional polarization rotation mechanism and adaptive phase theory inferred from static structures. We identify a ferroelectric topological structure, termed "dipole spiral," which exhibits a giant intrinsic piezoelectric response ($>$320 pC/N). This helical structure, primarily stabilized by entropy and possessing a rotational zero-energy mode, unlocks new possibilities for exploring chiral phonon dynamics and dipolar Dzyaloshinskii-Moriya-like interactions.