Theory of polar domains in moir\'e heterostructures

The discovery of unconventional ferroelectric behavior in twisted bilayers has prompted the consideration of moir\'e heterostructures as polar materials. However, misconceptions about the nature and origin of the observed ferroelectricity indicate that a better theoretical understanding of the polar properties of moir\'e heterostructures is needed. In this paper, it is proposed, and verified with first-principles calculations, that all moir\'e heterostructures exhibit an out-of-plane moir\'e polar domain (MPD) structure. In transition metal dichalcogenide bilayers, an interlayer charge transfer occurs due to the change in stacking arrangements throughout the moir\'e superlattice, leading to a local out-of-plane dipole moment, with the magnitude and shape of the MPDs being dominated by the chalcogen atoms. While the MPDs in all heterostructures are sensitive to the moir\'e period, it is only in the homo-bilayers that they can be tuned with an out-of-plane electric field. The misconceptions about ferroelectricity in moir\'e heterostructures are addressed, and it is proposed that the only scenario in which the MPDs can be considered ferroelectric domains is via a global van der Waals sliding by one third of a unit cell in a homo-bilayer. Finally, a general theoretical discussion of the polar properties of moir\'e heterostructures is provided.