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Even denominator fractional quantum Hall states in higher Landau levels of graphene

Nature Physics volume 15, pages 154–158 (2019)Cite this article

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Abstract

An important development in the field of the fractional quantum Hall effect was the proposal that the 5/2 state observed in the Landau level with orbital index n = 1 of two-dimensional electrons in a GaAs quantum well1 originates from a chiral p-wave paired state of composite fermions that are topological bound states of electrons and quantized vortices. The excitations of this state, which is theoretically described by a ‘Pfaffian’ wavefunction2 or its hole partner called the anti-Pfaffian3,4, are neither fermions nor bosons but Majorana quasiparticles obeying non-Abelian braid statistics5. This has inspired ideas for fault-tolerant topological quantum computation6 and has also instigated a search for other states with exotic quasiparticles. Here we report experiments on monolayer graphene that show clear evidence for unexpected even denominator fractional quantum Hall physics in the n = 3 Landau level. We numerically investigate the known candidate states for the even denominator fractional quantum Hall effect, including the Pfaffian, the particle–hole symmetric Pfaffian and the 221-parton states, and conclude that, among these, the 221-parton appears a potentially suitable candidate to describe the experimentally observed state. Like the Pfaffian, this state is believed to harbour quasi-particles with non-Abelian braid statistics7.

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Fig. 1: Longitudinal (σxx) and Hall (σxy) conductivity of device D1.
Fig. 2: Hall plateaus at half filling of the n = 3 Landau levels.
Fig. 3: Overlaps and transport gaps at half filling of the n = 3 Landau level.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

The authors acknowledge useful discussions with K. von Klitzing, I. Sodemann, Y.-H. Wu and J. Zhu, and assistance for sample preparation from S. Göres and M. Hagel. The authors thank S. Masubuchi and T. Machida for input on the ELVACITE stamp method for fabrication of the van der Waals heterostructure. J.H.S. is grateful for financial support from the graphene flagship. Y.K. thanks the Humboldt Foundation and A.C.B. the Villum Foundation for support. The Center for Quantum Devices is funded by the Danish National Research Foundation. This project has received funding from the European Research Council under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 1104931001 (TOPDYN)). The work at Penn State was supported by the US Department of Energy under grant no. DE-SC0005042. Some portions of this research were conducted with Advanced CyberInfrastructure computational resources provided by The Institute for CyberScience at The Pennsylvania State University. The authors thank the authors of the DiagHam package, which was used for some of the numerical calculations. The growth of hBN crystals was supported by the Elemental Strategy Initiative conducted by MEXT (Japan) and CREST (JPMJCR15F3, JST).

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Author notes

  1. These authors contributed equally: Youngwook Kim, Ajit C. Balram.

Authors and Affiliations

  1. Solid State Nanophysics, Max Planck Institute for Solid State Research, Stuttgart, Germany

    Youngwook Kim & Jurgen H. Smet

  2. Niels Bohr International Academy and the Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark

    Ajit C. Balram

  3. National Institute for Material Science, Tsukuba, Japan

    Takashi Taniguchi & Kenji Watanabe

  4. Department of Physics, Pennsylvania State University, University Park, Pennsylvania, USA

    Jainendra K. Jain

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  1. Youngwook Kim
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  4. Kenji Watanabe
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Contributions

The experiments were designed by Y.K. and J.H.S., and were carried out in the laboratory by Y.K. The theory was performed by A.C.B. and J.K.J. The calculations were run by A.C.B. The hBN bulk crystal was synthesized by T.T. and K.W. The manuscript was written with contributions from Y.K., A.C.B., J.K.J. and J.H.S.

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Correspondence to Jurgen H. Smet.

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Supplementary Figs. 1–10, supplementary references 1–45

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Kim, Y., Balram, A.C., Taniguchi, T. et al. Even denominator fractional quantum Hall states in higher Landau levels of graphene. Nature Phys 15, 154–158 (2019). https://doi.org/10.1038/s41567-018-0355-x

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