Quantum anomalous Hall crystal at fractional filling of moir\'e superlattices

Abstract

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$_2$