Distinct moiré textures of in-plane electric polarizations for distinguishing moiré origins in homobilayers

Abstract: In binary compound 2D insulators/semiconductors such as hexagonal boron nitride (hBN), the different electron affinities of atoms can give rise to out-of-plane electric polarizations across inversion asymmetric van der Waals interface of near 0-degree twist angles. Here we show that at a general stacking order where sliding breaks the in-plane C3 rotational symmetry, the interfacial charge redistribution also leads to an in-plane electric polarization, with a comparable magnitude to that of the out-of-plane ones. The effect is demonstrated in hBN bilayers, as well as in biased graphene bilayers with the gate-controlled interlayer charge redistribution. In long wavelength moir\'e patterns, the in-plane electric polarizations determined by the local interlayer stacking registries constitute topologically nontrivial spatial textures. We show that these textures can distinguish moir\'e patterns of different origins from twisting, biaxial- and uniaxial-heterostrain, where vector fields of the electric polarizations feature Bloch-type merons, N\'eel-type merons, and anti-merons, respectively. Combinations of twisting and heterostrain can further be exploited for engineering various electric polarization textures including 1D quasiperiodic lattices.