Quantum geometry modulation and pseudo-electric field coupling enabled by dynamic strain

Two-dimensional materials are a fertile ground to explore quantum geometric phenomena, where Berry curvature and its first moment, the Berry curvature dipole, play key roles in electronic transport, manifesting in anomalous and nonlinear Hall effects. While typically tuned via static electric field or strain, real-time control of these quantum geometric quantities remains largely unexplored. In this work, we demonstrate real-time modulation of Berry curvature and its moments, along with generation of a pseudo-electric field. By placing heterostructures onto a flexible silicon nitride membrane, we apply an oscillatory strain and an in-plane AC electric field and detect Hall signals at mixed frequencies of the two drives. Our measurements reveal the dynamic modulation of quantum geometry and also its coupling to strain-induced pseudo-electric field, which generates a distinctive external electric field free anomalous Hall effect. This approach opens up a new pathway for controlling quantum geometry on demand, moving beyond static perturbations. The coupling of 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.