Extracting the Strain Matrix and Twist Angle from the Moiré Superlattice in van der Waals Heterostructures

When two atomic layers are brought into contact at a relative twist angle, a large-scale pattern, called a moiré superlattice, emerges due to the (angular or lattice) mismatch between the layers. This has profound consequences in terms of the Hamiltonian of the system but was also considered in several publications as a means to extract the local strain tensor. While extracting the twist angle based on knowledge of the periodicity of the moiré is trivial in the case of a regular moiré pattern, in many examples in the literature, that is not the case. In particular, extracting the strain tensor and twist angle maps from a spatially varying moiré pattern is not straightforward. This article aims to provide a practical tool to extract the strain tensor and twist angle from an experimentally observable pattern. It further addresses the limitation of any such approach in the absence of additional experimental information beyond the moiré superlattice pattern.