Accurate effective model Hamiltonian for non-commensurate graphene on hexagonal boron nitride substrate*

High quality hexagonal boron nitride (h-BN) crystals have emerged as a promising substrate and barrier-material for graphene nanoelectronic devices. The influence of the h-BN substrate on graphene's electronic properties is sometimes observable, but often extremely weak. We develop a theory of the h-BN graphene interaction that is based on first-principles electron tunneling amplitudes calculated as a function of horizontal displacement between commensurate honeycomb lattices. The effective Hamiltonian we derive is valid for arbitrary rotation angles between adjacent graphene and h-BN sheets.