Anomalous Hall metal and fractional Chern insulator in twisted transition metal dichalcogenides

Abstract: We predict robust Ising ferromagnetism driven by Coulomb interaction in the metallic phase of twisted transition metal dichalcogenides homobilayers for a range of small twist angles. Due to the presence of spin-valley locking and Chern band, the completely spin polarized state -- a half metal -- has a spin gap and exhibits anomalous Hall effect. We also find that near a magic angle where the Chern band is predicted to be exceptionally flat, the anomalous Hall metal at $1/3$ filling may become unstable at low temperature to a $\sqrt{3}\times\sqrt{3}$ charge density wave, or a fractional Chern insulator.