Quantum Geometric Origin of Strain-Induced Ferroelectric Phase Transitions

Strain-regulated ferroelectric (FE) materials have long attracted significant attention due to their diverse applications. While soft-phonon theory and the (pseudo) Jahn-Teller effect have achieved considerable success in providing phenomenological descriptions and general understanding, the detailed connection between these perspectives and their microscopic dependence on strain regulation remains unclear. Here, under the framework of density-functional perturbation theory, we demonstrate that the Berry curvature of electron-phonon coupling (EPC) plays a pivotal role in the interatomic force matrix. A subsequent model analysis shows that external strain can reverse the polarity of the EPC Berry curvature in (quasi)degenerate electronic subsystems through band inversion, thereby directly leading to phonon softening. The general theory is then applied to the BiOCl monolayer as a benchmark, which offers an accurate description of the density-functional theory calculations. This mechanism is further observed across a broad range of materials through ab initio calculations, providing an insightful perspective on EPC quantum geometry in lattice dynamics and FE phase transitions.