Unlike conventional two-dimensional (2D) semiconductor superlattices, moir\'{e} 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 moir\'{e} wavelength selection and the formation of wrinkles.
@article{arxiv.2211.02482,
title = {Elastic properties of moir\'e lattices in epitaxial two-dimensional materials},
author = {Alexandre Artaud and Nicolas Rougemaille and Sergio Vlaic and Vincent T. Renard and Nicolae Atodiresei and Johann Coraux},
journal= {arXiv preprint arXiv:2211.02482},
year = {2022}
}