Moir\'e metrology of energy landscapes in van der Waals heterostructures

The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moir\'e superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moir\'e metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moir\'e domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moir\'e metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked $MoSe_2/WSe_2$. Moir\'e metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.