Elastic properties of moir? lattices in epitaxial two-dimensional materials

Unlike conventional two-dimensional (2D) semiconductor superlattices, moire patterns in 2D materials are flexible and their electronic, magnetic, optical, and mechanical properties depend on their topography. Within a continuous+atomistic theory treating 2D materials as crystalline elastic membranes, we abandon the flat -membrane scenario usually assumed for these materials and address out-of-plane deformations. We confront our predictions to experimental analyses on model systems, epitaxial graphene, and MoS2 on metals and reveal that compression/expansion and bending energies stored in the membrane can compete with adhesion energy, leading to a subtle moire wavelength selection and the formation of wrinkles.