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, has revolutionized quantum materials research. The twist angle induced superlattice offers means to control topology and strong correlations -- topics of great interest in contemporary quantum physics. 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. In this work 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$_{\mathrm{2}}$/WSe$_{\mathrm{2}}$. Moir\'{e} metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.