Title: Moiré alchemy: artificial atoms, Wigner molecules, and emergent Kagome lattice

Abstract: Semiconductor moir\'e superlattices comprise an array of artificial atoms and provide a highly tunable platform for exploring novel electronic phases. We introduce a theoretical framework for studying moir\'e quantum matter, which treats intra-moir\'e-atom interactions exactly and is controlled in the limit of large moir\'e period. We reveal an abundance of new physics arising from strong electron interactions when multiple occupancy of moir\'e atoms is involved. In particular, Coulomb interaction in three-electron moir\'e atoms leads to a three-lobed ``Wigner molecule'', which forms an emergent Kagome lattice at filling factor $n=3$. Our work identifies two universal length scales characterizing the kinetic and interaction energies in moir\'e materials and demonstrates a rich phase diagram due to their interplay.