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

TL;DR

This paper studies the properties of quasiparticles in fractional Chern insulators within twisted bilayer MoTe2, revealing their charge, braiding statistics, and interactions, and proposing a trial wave function for localized quasiparticles.

Contribution

It introduces a detailed model of FCI quasiparticles in twisted MoTe2, including their localization, charge distribution, and interactions, with comparisons to fractional quantum Hall states.

Findings

Quasiparticle density profiles depend on impurity location and lack rotational symmetry.

Excess charge around impurities approaches e/3, consistent with Laughlin quasiparticles.

Braiding phases match fractional statistics predictions.

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 $\nu_h=2/3$. 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 tMoTe$_2$ depends on the location of the impurity potential and loses the continuous rotation invariance. The FCI quasiparticle localized at moir\'e 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 tMoTe$_2$ is still similar to that of the $\nu=2/3$ FQH state in the LLL if an effective magnetic length on the moir\'e 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.