Characterization of quasiholes in two-component fractional quantum Hall states and fractional Chern insulators in $|C|=2$ flat bands

TL;DR

This study characterizes quasiholes in two-component fractional quantum Hall states and fractional Chern insulators with Chern number 2, revealing their size, charge, and braiding properties through exact diagonalization.

Contribution

It provides the first detailed comparison of quasihole properties between continuum Halperin states and lattice fractional Chern insulators with Chern number 2.

Findings

Quasiholes are isotropic with internal structure in Halperin states.

Quasihole charge and statistics match theoretical predictions.

Lattice models show stronger density oscillations but similar quasihole properties.

Abstract

We perform an exact-diagonalization study of quasihole excitations for the two-component Halperin $(221)$ state in the lowest Landau level and for several $\nu=1/3$ bosonic fractional Chern insulators in topological flat bands with Chern number $|C|=2$. Properties including the quasihole size, charge, and braiding statistics are evaluated. For the Halperin $(221)$ model state, we observe isotropic quasiholes with a clear internal structure, and obtain the quasihole charge and statistics matching the theoretical values. Interestingly, we also extract the same quasihole size, charge, and braiding statistics for the continuum model states of $|C|=2$ fractional Chern insulators, although the latter possess a "color-entangled" nature that does not exist in ordinary two-component Halperin states. We also consider two real lattice models with a band having $|C|=2$. There, we find that a quasihole can exhibit much stronger oscillations of the density profile, while having the same charge and statistics as those in the continuum models.