Spontaneous strains and gap in graphene on boron nitride

The interaction between a graphene layer and a hexagonal boron nitride (hBN) substrate induces lateral displacements and strains in the graphene layer. The displacements lead to the appearance of commensurate regions and the existence of an average gap in the electronic spectrum of graphene. We present a simple, but realistic, model, with which the displacements, strains, and spectral gap can be derived analytically from the adhesion forces between hBN and graphene. When the lattice axes of graphene and the substrate are aligned, strains reach a value of the order of 2%, leading to effective magnetic fields above 100 T. The combination of strains and induced scalar potential gives a sizable contribution to the electronic gap. Commensuration effects are negligible due to the large stiffness of graphene.