Characterization of Anyons in TMD Moiré Fractional Chern Insulators

Breakthrough experiments have recently realized fractional Chern insulators (FCIs) in moiré materials. As a defining feature of their intrinsic topological orders, FCIs host exotic quasiparticle excitations dubbed anyons with fractional charge and statistics. In this talk, I will present a detailed study of Abelian quasiparticles of FCIs in twisted homobilayer MoTe₂ (tMoTe₂) at hole filling ν_h=2/3. With extra particles and unit cells added to the FCI ground state, quasiparticles of charge e/3 with nontrivial energy dispersion are created. The interaction between two FCI quasiparticles is evaluated by calculating the energy spectrum with a single and two delocalized quasiparticles, which shows a crossover from repulsion to attraction as the gate-to-sample distance decreases. We further localize the FCI quasiparticles by short-range delta impurity potentials. Unlike the fractional quantum Hall (FQH) counterpart in the lowest Landau level (LLL), the density profile around a localized FCI quasiparticle in tMoTe₂ loses continuous rotation invariance and depends on the location of the impurity potential. This feature can be well captured by a trial wave function based on the nearly ideal quantum geometry of the top valence band of tMoTe₂. Despite of the difference in density profiles, the excess charge of the FCI quasiparticle in tMoTe₂ is still similar to that of the FQH quasiparticle 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. We confirm that the excess charge far away from the impurity potential indeed tends to e/3 in tMoTe₂. The braiding phase of two FCI quasiparticles in tMoTe₂ also agrees with the theoretical prediction of fractional statistics. We briefly examine the effect of band mixing, and find it may increase the spatial extent of FCI quasiparticles.