Alternative $\nu+\nu$-picture of bosonic fractional Chern insulators at high filling factors in multiple flat-band systems

Abstract

Most fractional quantum Hall states have been traditionally identified within a single energy band, such as the lowest Landau level or topological flat band. As more particles are introduced, they inevitably populate higher energy bands. Whether the inclusion of multiple topological bands leads to new physics remains an open question. Here, we propose a universal picture applicable at higher filling factors $\nu \geq 1$ in bosonic systems: the occupied bands tend to coalesce into an effective single topological band characterized by a total Chern number $\vert C\vert$, the sum of the Chern number of all occupied lower topological flat bands. Using a Kekul\'{e} lattice model with two lower flat bands featuring a total Chern number $C=1$, regardless of their specific configurations, we identify the emergence of a $\frac{1}{2}$ fractional Chern insulator (FCI) state at integer filling factor $\nu=1$, followed by the Jain sequence states $\frac{2}{3}$ and $\frac{3}{4}$ at filling $\nu=\frac{4}{3}$ and $\frac{6}{4}$. That is a $\nu+\nu$ picture, rather than the generally expected $1+\nu^{\prime}$ picture, where $\nu^{\prime}$ is the permitted FCI filling factor in the single second topological flat band. Our findings deepen the understanding of FCI states and open avenues for discovering exotic fractional topological phases in multiband systems.