Orbital Chern Insulator at ν=-2 in Twisted MoTe_2

In twisted MoTe_2, latest transport measurement has reported observation of quantum anomalous Hall effect at hole filling ν=-1, which undergoes a topological phase transition to a trivial ferromagnet as layer hybridization gets suppressed by interlayer bias D. Here we show that this underlies the existence of an orbital Chern insulating state with gate (D) switchable sign in an antiferromagtic spin background at hole filling ν=-2. From momentum-space Hartree Fock calculations, we find this state has a topological phase diagram complementary to that of the ν=-1 one: by sweeping D from negative to positive, the Chern number of this ν=-2 state can be switched between +1, 0, and -1, accompanied by a sign change of a sizable orbital magnetization. In range of D where this antiferronagnet is the ground state, the orbital magnetization allows magnetic field initialization of the spin antiferromagnetic order and the Chern number.