Energy Minimization of Two Dimensional Incommensurate Heterostructures

We derive and analyze a novel approach for modeling and computing the mechanical relaxation of incommensurate two dimensional heterostructures. Our approach parametrizes the relaxation pattern by the compact local configuration space rather than real space, thus bypassing the need for the standard supercell approximation and giving a true aperiodic atomistic configuration. Our model extends the computationally accessible regime of weakly coupled bilayers with similar orientations or lattice spacing, for example materials with a small relative twist where the widely studied large-scale moiré patterns arise (Kim et al. in Proc Natl Acad Sci 114:3364–3369, 2017; Yoo et al. in Atomic and electronic reconstruction at van der Waals interface in twisted bilayer graphene, Nat Mater 18:448–453, 2019). Our model also makes possible the simulation of multi-layers for which no inter-layer empirical atomistic potential exists, such as those composed of MoS ₂ layers, and more generally makes possible the simulation of the relaxation of multi-layer heterostructures for which a planar moiré pattern does not exist.