Ripples, strain, and misfit dislocations: Structure of graphene-boron nitride superlattice interfaces

In recently synthesized two-dimensional superlattices of graphene and boron nitride, the atomic structure of the interface is complicated by a 2% lattice mismatch between the two materials. Using atomistic and continuum analysis, we show that the mismatch results in a competition between two strain-relieving mechanisms: misfit dislocations and rippling. For flat superlattices, beyond a critical pitch the interface is decorated by strain-relieving misfit dislocations. For superlattices that can deform out-of-plane, optimal ripple wavelengths emerge.