Moire band model and band gaps of graphene on hexagonal boron nitride

Nearly aligned graphene on hexagonal boron nitride (G/BN) can be accurately modeled by a Dirac Hamiltonian perturbed by smoothly varying moire pattern pseudospin fields. Here, we present the moire-band model of G/BN for arbitrary small twist angles under a framework that combines symmetry considerations with input from ab initio calculations. Our analysis of the band gaps at the primary and secondary Dirac points highlights the role of inversion symmetry breaking contributions of the moire patterns, leading to primary Dirac point gaps when the moire strains give rise to a finite average mass, and to secondary gaps when the moire pseudospin components are mixed appropriately. The pseudomagnetic strain fields, which can reach values of up to similar to 40 T near symmetry points in the moire cell stem almost entirely from virtual hopping and dominate over the contributions arising from bond length distortions due to the moire strains.