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

We predict robust Ising ferromagnetism driven by Coulomb interaction in the metallic phase of twisted transition metal dichalcogenide homobilayers for a range of small twist angles. Due to the presence of spin-valley locking and a Chern band, the completely spin-polarized state—a half metal—has a spin gap and exhibits the 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 and change into a $\sqrt{3}\times \sqrt{3}$ charge density wave or a fractional Chern insulator.