Crossed nonlinear dynamical Hall effect in twisted bilayers

Abstract

<p>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∼̇𝑬⊥×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.<br></p>