Electromechanical response of saddle points in twisted hBN moir\'e superlattices

In twisted layered materials (t-LMs), an inter-layer rotation can break inversion symmetry and create an interfacial array of staggered out-of-plane polarization due to AB/BA stacking registries. This symmetry breaking can also trigger the formation of edge in-plane polarizations localized along the perimeter of AB/BA regions (i.e., saddle point domains). However, a comprehensive experimental investigation of these features is still lacking. Here, we use piezo force microscopy to probe the electromechanical behavior of twisted hexagonal boron nitride (t-hBN). For a parallel stacking alignment of t-hBN, we reveal very narrow (width ~ 20 nm) saddle point polarizations, which we also measure in the anti-parallel configuration. These localized polarizations can still be found on a multiply-stacked t-hBN structure, determining the formation of a double moir\'e. We also visualize a t-hBN moir\'e superlattice in the topography maps with atomic force microscopy, related to the strain accumulated at the saddle point domains. Our findings imply that polarizations in t-hBN do not only point in the out-of-plane direction, but also show an in-plane component, giving rise to a much more complex 3D polarization field.