In this study, we have demonstrated novel nonlinear Hall effects in insulating multilayer materials, focusing on hexagonal boron nitride (h-BN) as an example. We surprisingly find that the effect is governed not only by the cumulative Berry curvature dipoles of individual layers, as traditionally anticipated, but by the interlayer interactions mediated by Berry curvatures of neighboring layers. Unlike conventional material systems, our analysis reveals a distinct second-harmonic transverse response in twisted h-BN four-layers, where the overall Berry curvature sum is nullified.
Through rigorous large-scale real-time, time-dependent density functional theory calculations and analytical modeling of various four-layer configurations, we demonstrate that the nonlinear Hall effect in stacked h-BN multilayers is critically influenced by the stacking order and pairwise interactions of the layers. This insight extends beyond four-layer systems, providing a framework to interpret phenomena observed in bilayer, three-layer structures, and bulk materials. Furthermore, we simplify the prediction of nonlinear responses by conducting symmetry analysis on Berry curvatures of stacked layers.
Our results highlight the distinct nonlinear optical behavior enabled by oppositely twisted stacking configurations that can be modulated by applying directional torsion forces to h-BN multilayers. Moreover, these unexpected findings advance our understanding of nonlinear optical response mechanisms and open new avenues for designing innovative multilayer materials with controllable optoelectronic applications that can be modulated by mechanical deformation.