We provide a detailed study of Abelian quasiparticles of valley polarized fractional Chern insulators (FCIs) residing in the top valence band of twisted bilayer ${\mathrm{MoTe}}_2$ (${\mathrm{tMoTe}}_2$) at hole filling ${\nu }_h=2/3$. We construct a tight-binding model of delocalized quasiparticles to capture the energy dispersion of a single quasiparticle. We then localize quasiparticles by short-range delta impurity potentials. Unlike the fractional quantum Hall (FQH) counterpart in the lowest Landau level (LLL), the density profile around the localized FCI quasiparticle in ${\mathrm{tMoTe}}_2$ depends on the location of the impurity potential and loses the continuous rotation invariance. The FCI quasiparticle localized at moiré lattice center closely follows the anyon Wannier state of the tight-binding model of the mobile quasiparticle. Despite of the difference in density profiles, we find that the excess charge around the impurity potential for the ${\nu }_h=2/3$ FCIs in ${\mathrm{tMoTe}}_2$ is still similar to that of the $\nu =2/3$ FQH state in the LLL if an effective magnetic length on the moiré lattice is chosen as the length unit, which allows a rough estimation of the spatial extent of the FCI quasiparticle. Far away from the impurity potential, this excess charge has the tendency to reach $e/3$, as expected for the Laughlin quasiparticle. The braiding phase of two FCI quasiparticles in ${\mathrm{tMoTe}}_2$ also agrees with the theoretical prediction of fractional statistics. We characterize the interaction between two FCI quasiparticles and find a crossover from repulsive to attractive interaction as gate-to-sample distances decreases. Based on the nearly ideal quantum geometry of the top valence band of ${\mathrm{tMoTe}}_2$, we propose a trial wave function for localized FCI quasiparticles, which reproduces the key feature of the density profile around a quasiparticle.

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• Anyons
• Fractional quantum Hall effect
• Landau levels
• Superlattices
• Transition metal dichalcogenides
• Exact diagonalization