Crossed nonlinear dynamical Hall effect in twisted bilayers

We propose a nonlinear dynamical Hall effect characteristic of layered materials with chiral symmetry, which is driven by the joint action of in-plane and time variation of out-of-plane ac fields jH∼Ė⊥×E∥. A different band geometric quantity—interlayer Berry connection polarizability, which probes a mixed quantum metric characteristic of layer hybridized electrons by twisted interlayer coupling—underlies this effect. When the two orthogonal fields have a common frequency, their phase difference controls the on/off, direction, and magnitude of the rectified Hall current. We show sizable effects in twisted homobilayer transition metal dichalcogenides and twisted bilayer graphene over a broad range of twist angles. Our work opens the door to discovering mixed quantum metric responses unique to van der Waals stacking and concomitant applications under the nonlinear spotlight. Published by the American Physical Society 2024