Letter | Published:

Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level

Nature volume 549, pages 360364 (21 September 2017) | Download Citation


Non-Abelian anyons are a type of quasiparticle with the potential to encode quantum information in topological qubits protected from decoherence1. Experimental systems that are predicted to harbour non-Abelian anyons include p-wave superfluids, superconducting systems with strong spin–orbit coupling, and paired states of interacting composite fermions that emerge at even denominators in the fractional quantum Hall (FQH) regime. Although even-denominator FQH states have been observed in several two-dimensional systems2,3,4, small energy gaps and limited tunability have stymied definitive experimental probes of their non-Abelian nature. Here we report the observation of robust even-denominator FQH phases at half-integer Landau-level filling in van der Waals heterostructures consisting of dual-gated, hexagonal-boron-nitride-encapsulated bilayer graphene. The measured energy gap is three times larger than observed previously3,4. We compare these FQH phases with numerical and theoretical models while simultaneously controlling the carrier density, layer polarization and magnetic field, and find evidence for the paired Pfaffian phase5 that is predicted to host non-Abelian anyons. Electric-field-controlled level crossings between states with different Landau-level indices reveal a cascade of FQH phase transitions, including a continuous phase transition between the even-denominator FQH state and a compressible composite fermion liquid. Our results establish graphene as a pristine and tunable experimental platform for studying the interplay between topology and quantum criticality, and for detecting non-Abelian qubits.

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  1. 1.

    Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003)

  2. 2.

    et al. Observation of an even-denominator quantum number in the fractional quantum Hall effect. Phys. Rev. Lett. 59, 1776–1779 (1987)

  3. 3.

    , , & Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene. Nano Lett. 14, 2135–2139 (2014)

  4. 4.

    et al. Even-denominator fractional quantum Hall physics in ZnO. Nat. Phys. 11, 347–351 (2015)

  5. 5.

    & Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991)

  6. 6.

    Composite-fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63, 199–202 (1989)

  7. 7.

    , & Theory of the half-filled Landau level. Phys. Rev. B 47, 7312–7343 (1993)

  8. 8.

    , , & Experimental demonstration of a Fermi surface at one-half filling of the lowest Landau level. Phys. Rev. Lett. 71, 3846–3849 (1993)

  9. 9.

    , , , & How real are composite fermions? Phys. Rev. Lett. 71, 3850–3853 (1993)

  10. 10.

    & Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect. Phys. Rev. B 61, 10267–10297 (2000)

  11. 11.

    , , , & Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008)

  12. 12.

    & Topological phases in the zeroth Landau level of bilayer graphene. Phys. Rev. Lett. 112, 046602 (2014)

  13. 13.

    et al. Chemical potential and quantum Hall ferromagnetism in bilayer graphene. Science 345, 58–61 (2014)

  14. 14.

    et al. Tunable fractional quantum Hall phases in bilayer graphene. Science 345, 61–64 (2014)

  15. 15.

    et al. Direct measurement of discrete valley and orbital quantum numbers in bilayer graphene. Nat. Commun. (in the press)

  16. 16.

    , & Compressibility of the two-dimensional electron gas: measurements of the zero-field exchange energy and fractional quantum Hall gap. Phys. Rev. B 50, 1760–1778 (1994)

  17. 17.

    , & Particle-hole symmetry and the Pfaffian state. Phys. Rev. Lett. 99, 236806 (2007)

  18. 18.

    , , & Particle-hole symmetry and the ν = 5/2 quantum Hall state. Phys. Rev. Lett. 99, 236807 (2007)

  19. 19.

    Theory of the quantized Hall conductance. Helv. Phys. Acta 56, 75–102 (1983)

  20. 20.

    , , , & Nonconventional odd-denominator fractional quantum Hall states in the second Landau level. Phys. Rev. Lett. 105, 246808 (2010)

  21. 21.

    & Stable Pfaffian state in bilayer graphene. Phys. Rev. Lett. 107, 186803 (2011)

  22. 22.

    , , & Cooper pairing in non-Fermi liquids. Phys. Rev. B 91, 115111 (2015)

  23. 23.

    & Breaking of particle-hole symmetry by Landau level mixing in the ν = 5/2 quantized Hall State. Phys. Rev. Lett. 106, 116801 (2011)

  24. 24.

    , , & Infinite density matrix renormalization group for multicomponent quantum Hall systems. Phys. Rev. B 91, 045115 (2015)

  25. 25.

    Landau level mixing and the ground state of the ν = 5/2 quantum Hall effect. Phys. Rev. Lett. 119, 026801 (2017)

  26. 26.

    & Collective states of non-Abelian quasiparticles in a magnetic field. Phys. Rev. B 79, 205301 (2009)

  27. 27.

    , & Enhanced bulk-edge Coulomb coupling in fractional Fabry–Perot interferometers. Phys. Rev. Lett. 115, 126807 (2015)

  28. 28.

    Mach–Zehnder interferometry using spin- and valley-polarized quantum Hall edge states in graphene. Sci. Adv. 3, e1700600 (2017)

  29. 29.

    & Observable bulk signatures of non-Abelian quantum Hall states. Phys. Rev. Lett. 102, 176807 (2009)

  30. 30.

    , , , & Fractionalized exciton Fermi surfaces and condensates in two-component quantized Hall states. Preprint at (2016)

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We acknowledge experimental assistance of B. Odegard and J. Island, and discussions with M. Barkeshli, C. Dean, E.-A. Kim, R. Mong, C. Nayak, Z. Papic, S. Simon and A. Stern. Magnetocapacitance measurements were funded by the NSF under DMR-1636607. A portion of the nanofabrication and the transport measurements were funded by the ARO under proposal 69188PHH. A.F.Y. acknowledges the support of the David and Lucile Packard Foundation. Measurements above 14 T were performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation cooperative agreement number DMR-1157490 and the State of Florida. The numerical simulations were performed on computational resources supported by the Princeton Institute for Computational Science and Engineering (PICSciE). E.M.S. acknowledges the support of the Elings Fellowship. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and JSPS KAKENHI grant number JP15K21722.

Author information


  1. Department of Physics, University of California, Santa Barbara, California 93106, USA

    • A. A. Zibrov
    • , C. Kometter
    • , H. Zhou
    •  & A. F. Young
  2. California Nanosystems Institute, University of California at Santa Barbara, Santa Barbara, California 93106, USA

    • E. M. Spanton
  3. Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan

    • T. Taniguchi
    •  & K. Watanabe
  4. Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

    • M. P. Zaletel


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A.A.Z., E.M.S. and H.Z. fabricated devices A, B and C, respectively. T.T. and K.W. synthesized the hexagonal boron nitride crystals. A.F.Y. and C.K. built the measurement electronics. A.A.Z., H.Z., E.M.S. and A.F.Y. acquired and analysed the experimental data. M.P.Z. performed the DMRG calculations. A.A.Z., M.P.Z. and A.F.Y. wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to A. F. Young.

Reviewer Information Nature thanks D. Abanin, K. Park, K. Yang and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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    Supplementary Information

    This file contains methods, figures S1-S17 and tables S1-S3.

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