Non-identical moire twins in bilayer graphene

The superlattice obtained by aligning amonolayer graphene and boron nitride (BN) inherits from the hexagonal lattice a sixty degrees periodicity with the layer alignment. It implies that, in principle, the properties of the heterostructure must be identical for 0 degrees and 60 degrees of layer alignment. Here, we demonstrate, using dynamically rotatable van derWaals heterostructures, that the moire superlattice formed in a bilayer graphene/BN has different electronic properties at 0 degrees and 60 degrees of alignment. Although the existence of these non-identical moire twins is explained by different relaxation of the atomic structures for each alignment, the origin of the observed valley Hall effect remains to be explained. A simple Berry curvature argument is not sufficient to explain the 120 degrees periodicity of this observation. Our results highlight the complexity of the interplay between mechanical and electronic properties in moire structures and the importance of taking into account atomic structure relaxation to understand their electronic properties.