Large-scale mapping of moir\'e superlattices by Raman imaging of interlayer breathing mode and moir\'e phonons

Moir\'e superlattices can induce correlated-electronic phases in twisted van-der-Waals materials. Strongly correlated quantum phenomena emerge, such as superconductivity and the Mott-insulating state. However, moir\'e superlattices produced through artificial stacking can be quite inhomogeneous, which hampers the development of a clear correlation between the moir\'e period and the emerging electrical and optical properties. Here we demonstrate in twisted-bilayer transition-metal dichalcogenides that low-frequency Raman scattering can be utilized not only to detect atomic reconstruction, but also to map out the inhomogeneity of the moir\'e lattice over large areas. The method is established based on the finding that both the interlayer-breathing mode and moir\'e phonons are highly susceptible to the moir\'e period and provide characteristic fingerprints. We visualize microscopic domains with an effective twist-angle resolution of ~0.1{\deg}. This ambient non-invasive methodology can be conveniently implemented to characterize and preselect high-quality areas of samples for subsequent device fabrication, and for transport and optical experiments.