Modulation of quantum geometry and its coupling to pseudo-electric field by dynamic strain.

Two-dimensional materials are a fertile ground for exploring quantum geometric phenomena, with Berry curvature and its first moment, the Berry curvature dipole, playing a central role in their electronic response. These geometric properties influence electronic transport and result in the anomalous and nonlinear Hall effects, and are typically controlled using static electric fields or strain. However, the possibility of modulating quantum geometric quantities in real-time remains unexplored. Here, we demonstrate the dynamic modulation of Berry curvature and its moments, as well as the generation of a pseudo-electric field and their coupling. By placing heterostructures on a membrane, we introduce oscillatory strain together with an in-plane AC electric field and measure Hall signals that are modulated at linear combinations of the frequencies of strain and electric field. We also present direct experimental and theoretical evidence for coupling between pseudo-electric field and quantum geometry that results in an unusual dynamic strain-induced Hall response. This approach opens up a new pathway for controlling quantum geometry on demand, moving beyond conventional static perturbations. The coupling of the pseudo-electric field with Berry curvature provides a framework for external electric field-free anomalous Hall response and opens new avenues for probing the topological properties.