Assuming any site-potential dependent on two-point correlations, we rigorously derive a new model for an interlayer potential for incommensurate bilayer heterostructures such as twisted bilayer graphene. We use the ergodic property of the local configuration in incommensurate bilayer heterostructures to prove convergence of an atomistic model to its thermodynamic limit without a rate for minimal conditions on the lattice displacements. We provide an explicit error control with a rate of convergence for sufficiently smooth lattice displacements. For that, we introduce the notion of Diophantine 2D rotations, a two-dimensional analogue of Diophantine numbers, and give a quantitative ergodic theorem for Diophantine 2D rotations.
Published in: "arXiv Material Science".