Robust fractional quantum Hall effect in the N=2 Landau level in bilayer graphene.

Georgi Diankov,Jan Jaroszynski,Andrew J Bestwick,François Amet,David Goldhaber-Gordon,Kevin Tharratt,Kenji Watanabe,Takashi Taniguchi,Chi-Te Liang,Patrick Gallagher,William Coniglio,Menyoung Lee

doi:10.1038/ncomms13908

Abstract

The fractional quantum Hall effect is a canonical example of electron–electron interactions producing new ground states in many-body systems. Most fractional quantum Hall studies have focussed on the lowest Landau level, whose fractional states are successfully explained by the composite fermion model. In the widely studied GaAs-based system, the composite fermion picture is thought to become unstable for the N≥2 Landau level, where competing many-body phases have been observed. Here we report magneto-resistance measurements of fractional quantum Hall states in the N=2 Landau level (filling factors 4<|ν|<8) in bilayer graphene. In contrast with recent observations of particle–hole asymmetry in the N=0/N=1 Landau levels of bilayer graphene, the fractional quantum Hall states we observe in the N=2 Landau level obey particle–hole symmetry within the fully symmetry-broken Landau level. Possible alternative ground states other than the composite fermions are discussed.

Highlights

The fractional quantum Hall effect is a canonical example of electron–electron interactions producing new ground states in many-body systems
A fractional quantum Hall (FQH) state was first observed at Landau level (LL) filling factor n 1⁄4 1/3 in a GaAs/AlGaAs two-dimensional electron system[1]
With advances in sample preparation, the FQH effect was recently seen in bilayer graphene, revealing surprising results such as tunability of states with electric field normal to the plane[16], indications of even-denominator FQH states[17] at n 1⁄4 À 1/2 and at n 1⁄4 À 5/2 and, in scanning compressibility measurements, particle–hole asymmetry in the N 1⁄4 0/N 1⁄4 1 LLs and incipient FQH states in the N 1⁄4 2 LL at n 1⁄4 14/3, 17/3, 20/3 and 23/3, not forming a complete composite fermion (CF) sequence[18]

Summary

Introduction

The fractional quantum Hall effect is a canonical example of electron–electron interactions producing new ground states in many-body systems. A fractional quantum Hall (FQH) state was first observed at Landau level (LL) filling factor n 1⁄4 1/3 in a GaAs/AlGaAs two-dimensional electron system[1]. This many-body state was successfully explained by the Laughlin wave-function[2]. In high (NZ2, n44) LLs of GaAs-based two-dimensional electron systems, aside from possible evidence for n 1⁄4 4 þ 1/5 and n 1⁄4 4 þ 4/5 FQH states[20], competing charge-ordered states such as Wigner crystal bubbles and nematic stripes are thought to be the many-body ground states[21,22,23]. A numerical study that does not rely on the mean-field approximation or otherwise assume the CF picture predicts pronounced singlecomponent FQH states at 1/3, 2/3 and 2/5 in the N 1⁄4 2 LL26

Methods

Results

Conclusion