Itinerant anyons in fractionally filled Chern bands

Fractional Chern insulators are characterized by fractionally charged quasi-particles. In twisted MoTe2​, spontaneous spin polarization leads to multiple low-energy quasi-particle species distinguished by their spin quantum numbers. Using large-scale exact diagonalization (ED), we investigate these excitations, focusing on the θ=3.7∘ ν=−2/3 FCI relevant to recent experiments. We find that the spin-preserving (spinless) charge excitations have a significantly smaller gap than the spin-flipping (spinful) excitations, a result that qualitatively agrees with the measured magnetic field dependence of the transport gaps. Beyond the fundamental gaps, we extract the full quasi-electron and quasi-hole "band structure" and observe significant dispersion with an emergent magnetic translation symmetry. This feature represents a fundamental departure from the immobile excitations characteristic of the quantum Hall fluid. Our findings establish a framework for computing the properties of these novel elementary excitations in Moiré FCIs.