Bosonic fractional Chern insulating state at integer fillings in multi-band system

TL;DR

This paper reports the discovery of fractional Chern insulating states of hard-core bosons in a multi-band lattice model with high Chern number, revealing new fractional quantum Hall states at integer fillings.

Contribution

The study demonstrates the existence of bosonic fractional Chern insulators at integer fillings in a multi-band system with high Chern number, using numerical methods to identify novel fractional states.

Findings

Identification of a bosonic 1/2-Laughlin-like fractional Chern insulator.

Two lower topological flat bands form an effective C=1 band at half-filling.

Discovery of a particle-hole symmetry between filling fractions.

Abstract

The integer quantum Hall state occurs when the Landau levels are fully occupied by the fermions, while the fractional quantum Hall state usually emerges when the Landau level is partially filled by the strongly correlated fermions or bosons. Here, we report two fractional Chern insulating states of the hard-core bosons in a multi-band lattice model hosting topological flat bands with high Chern number. The previously proposed $\nu=1/3$ fractional Chern insulating state inherited from the high Chern number $C=2$ of the lowest topological flat band is revisited by the infinite density matrix renormalization group algorithm. In particular, we numerically identify a bosonic $1/2$-Laughlin-like fractional Chern insulating state at the integer fillings. We show two lower topological flat bands jointly generate an effective $C=1$ Chern band with half-filling. Furthermore, we find a strictly particle-hole-like symmetry between the $\nu$ and $3-\nu$ filling in our model. These findings extend our understanding of quantum Hall states and offer a new route to realize the novel fractional states in the system with multi-bands and high-Chern numbers.