Quantum anomalous Hall crystal at fractional filling of moiré superlattices

We predict the emergence a state of matter with intertwined ferromagnetism, charge order and topology in fractionally filled moiré 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 ($\nu =1\mathrm{/}2$) at larger twist angles of the twisted semiconductor bilayer $t$MoTe${}_2$