Orbital Chern insulator at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math> in twisted <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>MoTe</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>
Feng‐Ren Fan, Cong Xiao, Wang Yao
Abstract
In twisted ${\mathrm{MoTe}}_{2}$, the latest transport measurement has reported observation of the quantum anomalous Hall effect at hole filling $\ensuremath{\nu}=\ensuremath{-}1$, 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 antiferromagnetic spin background at hole filling $\ensuremath{\nu}=\ensuremath{-}2$. From momentum-space Hartree-Fock calculations, we find this state has a topological phase diagram complementary to that of the $\ensuremath{\nu}=\ensuremath{-}1$ one: by sweeping $D$ from negative to positive, the Chern number of this $\ensuremath{\nu}=\ensuremath{-}2$ state can be switched between $+1$, 0, and $\ensuremath{-}1$, accompanied by a sign change of a sizable orbital magnetization. In the range of $D$ where this antiferromagnet is the ground state, the orbital magnetization allows magnetic field initialization of the spin antiferromagnetic order and the Chern number.