Robust fractional quantum Hall effect and composite fermions in the $N=2$ Landau level in bilayer graphene

TL;DR

This study reports the observation of robust fractional quantum Hall states in the N=2 Landau level of bilayer graphene, consistent with the composite fermion model, and exhibiting large energy gaps and particle-hole symmetry.

Contribution

First demonstration of particle-hole symmetric fractional quantum Hall states in the N=2 Landau level of bilayer graphene, supporting the composite fermion model in higher Landau levels.

Findings

FQH states in N=2 LL form a complete particle-hole symmetric sequence.

Energy gaps of FQH states are a few Kelvin, comparable or larger than in lower LLs.

Highest set of particle-hole symmetric pairs observed in any material system.

Abstract

The fractional quantum Hall (FQH) effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most FQH studies have focused on the lowest Landau level (LL), whose fractional states are successfully explained by the composite fermion (CF) model, in which an even number of magnetic flux quanta are attached to an electron and where states form the sequence of filling factors $\nu = p/(2mp \pm 1)$, with $m$ and $p$ positive integers. In the widely-studied GaAs-based system, the CF picture is thought to become unstable for the $N \geq 2$ LL, where larger residual interactions between CFs are predicted and competing many-body phases have been observed. Here we report transport measurements of FQH states in the $N=2$ LL (filling factors $4 < \nu < 8$) in bilayer graphene, a system with spin and valley degrees of freedom in all LLs, and an additional orbital degeneracy in the 8-fold degenerate $N=0$/$N=1$ LLs. In contrast with recent observations of particle-hole asymmetry in the $N=0$/$N=1$ LLs of bilayer graphene, the FQH states we observe in the $N=2$ LL are consistent with the CF model: within a LL, they form a complete sequence of particle-hole symmetric states whose relative strength is dependent on their denominators. The FQH states in the $N=2$ LL display energy gaps of a few Kelvin, comparable to and in some cases larger than those of fractional states in the $N=0$/$N=1$ LLs. The FQH states we observe form, to the best of our knowledge, the highest set of particle-hole symmetric pairs seen in any material system.