Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number

TL;DR

This paper explores fractional quantum Hall states in Harper-Hofstadter bands with higher Chern numbers, predicting new series of states and providing numerical evidence for their realization as incompressible quantum liquids.

Contribution

It extends the understanding of fractional quantum Hall states to bands with higher Chern numbers, including predictions and numerical validation of new series of states.

Findings

Predicts fractional quantum Hall states with specific filling factors for higher Chern bands

Identifies a bosonic integer quantum Hall state in |C|=2 bands

Provides numerical evidence for incompressible quantum liquids in Harper-Hofstadter bands

Abstract

The Harper-Hofstadter model provides a fractal spectrum containing topological bands of any integer Chern number, $C$. We study the many-body physics that is realized by interacting particles occupying Harper-Hofstadter bands with $|C|>1$. We formulate the predictions of Chern-Simons or composite fermion theory in terms of the filling factor, $\nu$, defined as the ratio of particle density to the number of single-particle states per unit area. We show that this theory predicts a series of fractional quantum Hall states with filling factors $\nu = r/(r|C| +1)$ for bosons, or $\nu = r/(2r|C| +1)$ for fermions. This series includes a bosonic integer quantum Hall state (bIQHE) in $|C|=2$ bands. We construct specific cases where a single band of the Harper-Hofstadter model is occupied. For these cases, we provide numerical evidence that several states in this series are realized as incompressible quantum liquids for bosons with contact interactions.