Lattice mismatch induced ripples and wrinkles in planar graphene/boron nitride superlattices

A continuum theory to describe periodic ripple formation in planar graphene/boron nitride superlattices is formulated. Due to the lattice mismatch between the two materials, it is shown that flat superlattices are unstable with respect to ripple formation of appropriate wavelengths. A competition between bending energy and transverse stretching energy gives rise to an optimal ripple wavelength that depends on the superlattice pitch. The optimal wavelengths predicted by the continuum theory are in good agreement with atomic scale total energy calculations previously reported in Nandwana and Ertekin, Nano Lett. 15 1468 (2015).