The investigation of twisted bilayer graphene has opened a “twistronics era”, providing unprecedented tunability for solid-state systems and an excellent platform for strongly correlated quantum phases and their transitions. While twisted bilayer graphene requires involved multi-band descriptions, twisted bilayer transition metal dichalcogenides can have simpler models partially because of the spin-valley locking induced by spin-orbit couplings. Spin-orbit couplings also promote thermal stability of anomalous (quantum) Hall effects.
We theoretically study two cases of twisted bilayer transition metal dichalcogenides: (1) effective triangular systems and (2) effective honeycomb systems. For triangular systems, we study the magnetic orders and spin liquids could be realized for half-filling; we also study the magnetic orders at the van Hove filling, providing an explanation for the absence of the predicted anomalous quantum Hall effect in experiments. For honeycomb systems, we study integer and fractional quantum anomalous Hall effects, providing theoretical support for the ground-breaking experimental discovery of fractional quantum anomalous Hall effects.