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 $1/3$. 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 $V_{\mathrm{FB}}$ 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 moir\'e 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.