Electric field tunable layer polarization in moiré of moiré graphene-hBN heterostructures*

Ferroelectricity has been discovered in four-layer hexagonal Boron Nitride (hBN) — graphene heterostructures [1], but a microscopic theory of the system is still lacking. The system exhibits incommensurate moiré of moiré patterns due to the coexistence of the twist angle and the lattice constant mismatch. We developed a continuum model for electronic structures of the system, in which a Bernal-stacked graphene bilayer is encapsulated by top and bottom hBN layers with a twist angle. The model we developed is efficient compared to atomistic calculations, and we do not resort to a periodic approximation. We found that the low-energy bands exhibit layer polarization that is tunable via an external displacement field.

[1]  Zheng, Zhiren, et al. “Unconventional ferroelectricity in moiré heterostructures.” Nature 588.7836 (2020): 71-76.