Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints

Transition–metal dichalcogenides (TMDs) uniquely combine topological electronic states realized without external magnetic fields with a strong optical response arising from long–lived excitons. Motivated by this confluence, we investigate an interacting fermion–boson system formed by coupling an exciton to a quasihole of a fractional Chern insulator (FCI) at filling fraction $1\mathrm{/}3$. We introduce a kagome–lattice fermion–boson model hosting an electronic FCI and a mobile exciton whose dispersion is tunable from a parabolic band to a flatband. Using exact diagonalization, we demonstrate the emergence of exciton–quasihole bound states controlled by the repulsive electron–exciton interaction $V_{\mathrm{F}\mathrm{B}}$ and the exciton kinetic energy $t_{\mathrm{B}}$. These states appear as low–lying levels in the fermion–boson spectrum, well separated from the scattering continuum, and arise despite repulsive interactions due to a residual attraction to the local charge depletion associated with a quasihole. Reducing $t_{\mathrm{B}}$ enhances this effect by favoring interaction–dominated binding. Our results provide a model description of moiré TMD heterostructures, including fractional Chern insulating twisted bilayer MoTe${}_2$ proximitized by excitonic TMD heterobilayers, where we estimate exciton–quasihole binding energy scales of $0.8$–$1.2$~meV, placing these effects within reach of photoluminescence spectroscopy.