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

## TL;DR

This paper investigates SU(N) symmetric hardcore bosons on topological flat bands, revealing a hierarchy of fractional quantum Hall states characterized by a K matrix, with potential experimental signatures like quantized drag Hall responses.

## Contribution

It introduces a new hierarchy of SU(N) fractional quantum Hall states in topological flat bands and characterizes them using an effective K matrix derived from the Chern number matrix.

## Key findings

- Hierarchy of SU(N) FQH states at fractional fillings
- Quantized drag Hall responses and fractional charge pumping
- Correspondence to spinless FQH states with Chern number N

## 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 $\widetilde{\nu}=1/(MC+1)$.