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

In binary compound 2D insulators/semiconductors such as hexagonal boron nitride(h BN), 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° interlayer twisting. Here we show that at a general stacking order where sliding breaks 2π/3-rotational symmetry, the interfacial charge redistribution also leads to an in-plane electric polarization, with a magnitude comparable to that of the out-of-plane ones.The effect is demonstrated in h BN bilayers, as well as in biased graphene bilayers with gate-controlled interlayer charge redistributions. In long wavelength moiré patterns, the in-plane electric polarizations determined by the local interlayer stacking registries constitute topologically nontrivial spatial textures. We show that these textures can be used to distinguish moirépatterns of different origins from twisting, biaxial-and uniaxial-heterostrain, where vector fields of electric polarizations feature Bloch-type merons, Néel-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.