All local electronic properties of graphene on a hexagonal boron nitride (hBN) substrate exhibit spatial moiré patterns related to lattice constant and orientation differences between shared triangular Bravais lattices. We apply a previously derived effective Hamiltonian for the $\pi$ bands of graphene on hBN to address the carrier dependence of transport properties, concentrating on the conductivity features at four electrons and four holes per unit cell. These transport features measure the strength of Bragg scattering of $\pi$ electrons off the moiré pattern, and they exhibit a striking particle-hole asymmetry that we trace to specific features of the effective Hamiltonian that we interpret physically.

• Received 16 March 2015
• Revised 29 May 2015

DOI:https://doi.org/10.1103/PhysRevB.91.245422