Theory of polar domains in moir? heterostructures

The discovery of ferroelectric behavior in twisted bilayers without inversion symmetry has prompted the consideration of some moire 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 moire heterostructures is needed. In this paper, it is proposed that all moire heterostructures in which there is a local breaking of inversion symmetry exhibit an out-of-plane moire polar domain (MPD) structure, and this is verified using first-principles calculations for several different bilayer systems. In transition-metal dichalcogenide bilayers, a deformation of the charge density on each layer occurs due to the change in stacking arrangements throughout the moire 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 bilayers considered were found to be sensitive to the moire period, it is only in the aligned homobilayers that they can be tuned with an out-of-plane electric field. The misconceptions about ferroelectricity in moire 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 in a homobilayer. Finally, a general theoretical discussion of the polar properties of moire heterostructures without inversion symmetry is provided.