Exciton-Anyon Binding in Fractional Chern Insulators: Spectral Fingerprints

Abstract

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 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 $0.6$--$1.1$~meV, placing these effects within reach of photoluminescence spectroscopy.

Figures (4)

• Figure 1: The exciton--FCI interacting system. (a) Schematic of an interlayer exciton in proximity to an FCI layer. The exciton dipole orientation induces repulsive interactions with the electronic background while generating a residual attraction to a quasihole. (b) Effective lattice model consisting of superposed kagome lattices for the FCI and exciton layers. Red, green, and blue dots denote sublattices A, B, and C, respectively. Arrows indicate fermionic hopping phases $e^{i\phi}$, with $\phi=\pi/4$. (c) Setup for characterizing exciton--quasihole binding, with binding potential (top) and the quasihole excitation gap (bottom). Excitons and electrons are represented by X symbols and red dots, respectively, while the arrow denotes a flux insertion on the torus that nucleates a quasihole.
• Figure 2: (a) FCI spectra at 1/3 filling for the 3x5 kagome lattice. The fermion-fermion interaction strength is set as constant $V_{\text{FF}}=2.5$. Inset shows the spectral flow of the 3-fold degenerate 1/3 FCI states when varying $\theta_x$. (b) The corresponding quasihole spectrum by adding one flux to the 1/3 FCI system. The aspect ratios chosen here render the lattices as isotropic as possible to avoid strong finite-size artifacts.
• Figure 3: Exciton-quasihole interacting spectra (blue and red circles) on a 4x4 lattice with $V_{\text{FB}}/V_{\text{FF}}=0.4$ and (a) $t_\text{B}/V_{\text{FF}} = 0.12$; (b) $t_\text{B}/V_{\text{FF}} = -0.02$. Red dashed line denotes $\varepsilon_X^0+\Delta_{\text{qh}}$, below which exciton-quasihole states are characterized by negative binding energies (red circles). The quasihole spectrum is plotted in the background for reference (black dashes). Insets show the effect of opposite signs of $t_\text{B}$ on boson single-particle dispersion.
• Figure 4: Characterization of the exciton-quasihole binding. The binding energy $\Delta\varepsilon$ (a) and the total number of bound states (b), versus the fermion-boson interaction strength. Legend denotes the boson hopping strength. Inset shows the change of exciton single-particle dispersion by varying $t_\text{B}$, for positive and negative hopping.