Topological characterization of hierarchical fractional quantum Hall effects in topological flat bands with SU($N$) symmetry

Abstract

We study the many-body ground states of SU($N$) symmetric hardcore bosons on the topological flat-band model by using controlled numerical calculations. By introducing strong intracomponent and intercomponent interactions, we demonstrate that a hierarchy of bosonic SU($N$) fractional quantum Hall (FQH) states emerges at fractional filling factors $\nu =N/(MN+1)$ (odd $M=3$). In order to characterize this series of FQH states, we figure the effective $\mathbf{K}$ matrix from the inverse of the Chern number matrix. The topological characterization of the $\mathbf{K}$ matrix also reveals quantized drag Hall responses and fractional charge pumping that could be detected in future experiments. In addition, we address the general one-to-one correspondence to the spinless FQH states in topological flat bands with Chern number $C=N$ at fillings $\tilde{\nu }=1/(MC+1)$.

arXiv comment7 pages, 6 figures. revised version

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• Recent Developments in Fractional Chern Insulators
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• Chern number matrix of the non-Abelian spin-singlet fractional quantum Hall effect
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