Polar and quasicrystal vortex observed in twisted-bilayer molybdenum disulfide.

We report the observation of an electric field in twisted-bilayer molybdenum disulfide (MoS) and elucidate its correlation with local polar domains using four-dimensional scanning transmission electron microscopy (4D-STEM) and first-principles calculations. We reveal the emergence of in-plane topological vortices within the periodic moiré patterns for both commensurate structures at small twist angles and the incommensurate quasicrystal structure that occurs at a 30° twist. The large-angle twist leads to mosaic chiral vortex patterns with tunable characteristics. A twisted quasicrystal bilayer, characterized by its 12-fold rotational symmetry, hosts complex vortex patterns and can be manipulated by picometer-scale interlayer displacement. Our findings highlight that twisting 2D bilayers is a versatile strategy for tailoring local electric polar vortices.