Quasiparticle Excitations in Integer and Fractional Quantum Anomalous Hall insulators

Integer and fractional quantum anomalous Hall insulators (QAHIs) have been realized in moiré systems, such as twisted bilayer MoTe2 (tMoTe2) and moiré rhombohedral graphene. In these systems, QAHIs emerge from spontaneous ferromagnetism driven by electron Coulomb interactions. The ground state is characterized by an insulating topological bulk with a quantized Chern number and gapless chiral edge states. Moreover, QAHIs host a rich variety of quasiparticle excitations, including excitons and magnons, with anyons appearing specifically in the fractional QAHI phase. In this talk, I will present theoretical studies of these quasiparticle excitations in tMoTe2, exploring their deep connections with the topological nature of QAHIs and discussing experimental implications. We first examine the optical response in Chern insulators, deriving a sum rule for the optical conductivity that links excitonic effects to the quantum geometry of the system. Applied to the QAHI in tMoTe2 at hole filling ν=1, the excitonic optical response reveals nearly perfect magnetic circular dichroism, providing a unique probe of topological properties. Next, we investigate magnetic excitations in the same state, where the magnon spectrum features topological magnon bands describable by a magnon version of the Haldane model. Finally, we study anyonic quasiparticles in the fractional QAHIs at ν=2/3. In addition to characterizing their fractional charge and braiding phase, we construct a tight-binding model based on anyon Wannier states to capture their energy dispersion. These findings reveal the diverse and rich quasiparticle landscape in integer and fractional QAHIs, offering new perspectives on the spectroscopy of low-energy excitations in correlated topological states.