Characterization of fractional Chern insulator quasiparticles in twisted homobilayer MoTe$_2$

TL;DR

This work develops a microscopic framework to characterize Abelian quasiparticles in the $ν_h=2/3$ fractional Chern insulator realized in twisted bilayer MoTe$_2$. By combining a tight-binding description of mobile quasiparticles, delta-impurity pinning, and a geometry-based trial wave function, the authors quantify the quasiparticle charge, size, and fractional statistics, and they map two-quasiparticle interactions, observing a repulsion-to-attraction crossover under enhanced screening. The results show moiré-unit-cell density modulation in the ground state, with localized quasiparticles that nucleate around impurities and carry charge $e/3$, and they report braiding phases close to Laughlin predictions, validating the FCI’s topological order in a moiré platform. The study also connects FCI quasiparticles to an anyon Wannier description and provides practical estimates of quasiparticle spatial extent ($\sim 6\ell_0$) and a variational, geometry-informed wave function, offering a pathway toward interferometric probes in moiré materials.

Abstract

We provide a detailed study of Abelian quasiparticles of valley polarized fractional Chern insulators (FCIs) residing in the top valence band of twisted bilayer MoTe$_2$ (tMoTe$_2$) at hole filling $ν_h=2/3$. 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 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 $ν_h=2/3$ FCIs in tMoTe$_2$ is still similar to that of the $ν=2/3$ 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 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 tMoTe$_2$, we propose a trial wave function for localized FCI quasiparticles, which reproduces the key feature of the density profile around a quasiparticle.

Figures (14)

• Figure 1: (a) The density distribution for a localized single-quasiparticle excitation of the $\nu=2/3$ fermionic FQH state on a square torus with $N=25,N_\phi=37$. (b) The excess charge around the impurity potential. The horizontal reference line indicates $Q=e/3$. The dashed line in (b) is obtained using the first-order Haldane's pseudopotential. Otherwise the interaction is the screened Coulomb potential.
• Figure 2: The fractional statistical phase versus the distance between two quasiparticles for the $\nu=2/3$ fermionic FQH state on a square torus with $N=24, N_\phi=35$. The interaction potentials are screened Coulomb and the first-order Haldane's pseudopotential for the solid and dashed lines, respectively.
• Figure 3: (a) The real-space density of holes for the $\nu_h=2/3$ FCI ground state in tMoTe$_2$. The system size is $N=24, N_s=36$. The white dots indicate the $\mathcal{R}_M^M$ positions. In (b), we show the momentum-space occupation (averaged over the three FCI ground states) for the system in (a). We set $\theta=3.7^\circ$, $d=10 \ {\rm nm}$ and $\epsilon=10$.
• Figure 4: The energy gap (solid lines) and the splitting (dotted lines) of the quasiparticle manifold as a function of the twist angle. We consider the presence of a single delocalized quasiparticle and two delocalized quasiparticles in (a) and (b), respectively. The system sizes are $N=19, N_s=28$ (red), $N=21, N_s=31$ (blue), $N=23, N_s=34$ (green) in (a), and $N=20, N_s=29$ (red), $N=22, N_s=32$ (blue), $N=24, N_s=35$ (green) in (b).
• Figure 5: The low-energy energy spectra in presence of (a) a single delocalized quasiparticle and (b), (c) two delocalized quasiparticles. The system sizes are $N=23, N_s=34$ in (a) and $N=24, N_s=35$ in (b) and (c). $Q$ is a proper folding of the two-dimensional momentum ${\bm Q}$. The definitions of $E_{\rm 1qp}$ and $V_{\rm 2qp}$ are given in the text. Unlike in Ref. goncalves2025spinlessspinfulchargeexcitations, we do not shift the energies in (a) to make the dispersion near zero energy. The subspace of delocalized quasiparticles are highlighted by red. This subspace contains one level per momentum sector in (a), and six levels per momentum sector in (b) and (c). The gray levels are out of this subspace. We set $\theta=3.7^\circ$ and $\epsilon=10$. The sample-to-gate distance is chosen as $d=10 \ {\rm nm}$ in (b) and $d=2 \ {\rm nm}$ in (c).