Transport and particle-hole asymmetry in graphene on boron nitride

All local electronic properties of graphene on a hexagonal boron nitride (hBN) substrate exhibit spatial moire 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 moire pattern, and they exhibit a striking particle-hole asymmetry that we trace to specific features of the effective Hamiltonian that we interpret physically.