  We determine the electronic structure of a graphene sheet on top of a
lattice-matched hexagonal boron nitride (h-BN) substrate using ab initio
density functional calculations. The most stable configuration has one carbon
atom on top of a boron atom, the other centered above a BN ring. The resulting
inequivalence of the two carbon sites leads to the opening of a gap of 53 meV
at the Dirac points of graphene and to finite masses for the Dirac fermions.
Alternative orientations of the graphene sheet on the BN substrate generate
similar band gaps and masses. The band gap induced by the BN surface can
greatly improve room temperature pinch-off characteristics of graphene-based
field effect transistors.
