# Two-component quantum Hall effects in topological flat bands

## TL;DR

This paper investigates two-component quantum Hall states in topological flat bands, demonstrating the emergence of fractional quantum Hall states and phase transitions between topological and trivial phases in lattice models.

## Contribution

It introduces a method to realize and characterize two-component fractional quantum Hall states and explores phase transitions in a specific lattice model.

## Key findings

- Two-component fractional quantum Hall states occur at specific fractional fillings.
- A first-order transition from a quantum Hall state to an antiferromagnetic insulator was observed.
- No intermediate topological phase exists at the studied parameters.

## Abstract

We study quantum Hall states for two-component particles (hardcore bosons and fermions) loading in topological lattice models. By tuning the interplay of interspecies and intraspecies interactions, we demonstrate that two-component fractional quantum Hall states emerge at certain fractional filling factors $\nu=1/2$ for fermions ($\nu=2/3$ for bosons) in the lowest Chern band, classified by features from ground states including the unique Chern number matrix (inverse of $\mathbf{K}$-matrix), the fractional charge and spin pumpings, and two parallel propagating edge modes. Moreover, we also apply our strategy to two-component fermions at integer filling factor $\nu=2$, where a possible topological Neel antiferromagnetic phase is under intense debate very recently. For the typical $\pi$-flux checkerboard lattice, by tuning the onsite Hubbard repulsion, we establish a first-order phase transition directly from a two-component fermionic $\nu=2$ quantum Hall state at weak interaction to a topologically trivial antiferromagnetic insulator at strong interaction, and therefore exclude the possibility of an intermediate topological phase for our system.