SU(N) fractional quantum Hall effects in topological flat bands

Abstract

We study $N$-component interacting particles (hardcore bosons and fermions) loaded in topological lattice models with SU$(N)$-invariant interactions based on density matrix renormalization group method. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that a class of SU$(N)$ fractional quantum Hall states can emerge at fractional filling factors $\nu =N/(N+1)$ for bosons ($\nu =N/(2N+1)$ for fermions) in the lowest Chern band, characterized by the nontrivial fractional Hall responses and the fractional charge pumping. Moreover, we establish a topological characterization based on the $\mathbf{K}$ matrix, and discuss the close relationship to the fractional quantum Hall physics in topological flat bands with Chern number $N$.

9 pages, 12 figures

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• Recent Developments in Fractional Chern Insulators
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Fractional Chern Insulators in Twisted Bilayer MoTe${}_2$: A Composite Fermion Perspective
• Quantum Hall effects of exciton condensate in topological flat bands
• Halperin $(m^{\prime },m,n)$ fractional quantum Hall effect in topological flat bands
• Optical Signature of Flat Bands in Topological Hourglass Semimetal Nb3SiTe6
• Integer quantum Hall effect of two-component hardcore bosons in a topological triangular lattice
• Three-component fractional quantum Hall effect in topological flat bands