Band gap formation in commensurate twisted bilayer graphene/hBN moiré lattices

We report on the investigation of periodic superstructures in twisted bilayer graphene (tBLG) van der Waals heterostructures, where one of the graphene layers is aligned to hexagonal boron nitride (hBN). Our theoretical simulations reveal that if the ratio of the resulting two moir\'e unit-cell areas is a simple fraction, the graphene/hBN moir\'e lattice acts as a staggered potential, breaking the degeneracy between tBLG AA sites. This leads to additional band gaps at energies where a subset of tBLG AA sites is fully occupied. These gaps manifest as Landau fans in magnetotransport, which we experimentally observe in an aligned tBLG/hBN heterostructure. Our study demonstrates the identification of commensurate tBLG/hBN van der Waals heterostructures by magnetotransport, highlights the persistence of moir\'e effects on length scales of tens of nanometers, and represents an interesting step forward in the ongoing effort to realize designed quantum materials with tailored properties.