The existence of Bloch flat bands of electrons provides a facile pathway to obtain exotic quantum phases owing to strong correlation. Despite the established magic angle mechanism for twisted bilayer graphene, understanding of the emergence of flat bands in twisted bilayers of two-dimensional polar crystals remains elusive. Here, we show that due to the polarity between constituent elements in the monolayer, the formation of complete flat bands in twisted bilayers is triggered as long as the twist angle is less than a certain critical value. Using the twisted bilayer of hexagonal boron nitride ($h\mathrm{BN}$) as an example, our simulations using the density-functional tight-binding method reveal that the flat band originates from the stacking-induced decoupling of the highest occupied (lowest unoccupied) states, which predominantly reside in the regions of the moiré superlattice where the anion (cation) atoms in both layers are overlaid. Our findings have important implications for the future search for and study of flat bands in polar materials.

• Received 6 October 2019
• Revised 23 December 2019
• Accepted 5 February 2020

DOI:https://doi.org/10.1103/PhysRevLett.124.086401