Orbital Magnetization in Correlated States of Twisted Bilayer Transition Metal Dichalcogenides

Abstract: Recent observations of quantum anomalous Hall effects in moir\'e systems have revealed the emergence of interaction-driven ferromagnetism with significant orbital contributions. To capture this physics, we extend the modern theory of orbital magnetization to Hartree-Fock states and show that the standard expression remains valid with Hartree-Fock orbitals and Hamiltonians. We then benchmark our theory against the Kane-Mele-Hubbard model in a weak field, which yields excellent agreement with direct numerical calculations. Applying our theory to twisted MoTe$_2$ bilayers, we find orbital magnetization of order one Bohr magneton per moir\'e cell with a non-monotonic twist-angle dependence. Our work establishes a general theory of orbital magnetization in interacting moir\'e systems and provides quantitative guidance for interpreting recent experiments.