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We predict the emergence a state of matter with intertwined ferromagnetism, charge order and topology in fractionally filled moir\'e superlattice bands. Remarkably, these quantum anomalous Hall crystals exhibit a quantized integer Hall conductance that is different than expected from the filling and Chern number of the band. Microscopic calculations show that this phase is robustly favored at half-filling ($\nu=1/2$) at larger twist angles of the twisted semiconductor bilayer $t$MoTe$_2$, Comment: 5 + 5 pages, PRL Editors' Suggestion

Semiconductor moir\'e superlattices provide a versatile platform to engineer new quantum solids composed of artificial atoms on moir\'e sites. Previous studies have mostly focused on the simplest correlated quantum solid - the Fermi-Hubbard model - where intra-atom interactions are simplified to a single onsite repulsion energy U. These studies have revealed novel quantum phases ranging from Mott insulators to quantum anomalous Hall insulators at a filling of one electron per moir\'e unit cell. New types of quantum solids should arise at even higher filling factors where the multi-electron configuration of moir\'e artificial atoms provides new degrees of freedom. Here we report the experimental observation of Wigner molecular crystals emerging from multi-electron artificial atoms in twisted bilayer WS2 moir\'e superlattices. Moir\'e artificial atoms, unlike natural atoms, can host qualitatively different electron states due to the interplay between quantized energy levels and Coulomb interactions. Using scanning tunneling microscopy (STM), we demonstrate that Wigner molecules appear in multi-electron artificial atoms when Coulomb interactions dominate. Three-electron Wigner molecules, for example, are seen to exhibit a characteristic trimer pattern. The array of Wigner molecules observed in a moir\'e superlattice comprises a new crystalline phase of electrons: the Wigner molecular crystal. We show that these Wigner molecular crystals are highly tunable through mechanical strain, moir\'e period, and carrier charge type. Our study presents new opportunities for exploring quantum phenomena in moir\'e quantum solids composed of multi-electron artificial atoms.

Remarkable recent experiments have observed fractional quantum anomalous Hall (FQAH) effects at zero field and unusually high temperatures in twisted semiconductor bilayer $t$MoTe$_2$. Intriguing observations in these experiments such as the absence of integer Hall effects at twist angles where a fractional Hall effect is observed, do however remain unexplained. The experimental phase diagram as a function of twist angle remains to be established. By comprehensive numerical study, we show that band mixing has large qualitative and quantitative effects on the energetics of competing states and their energy gaps throughout the twist angle range $\theta\leq 4^\circ$. This lays the ground for the detailed realistic study of a rich variety of strongly correlated twisted semiconductor multilayers and an understanding of the phase diagram of these fascinating systems., Comment: 5 + 2 pages, 7 Figures