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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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.
The authors declare no competing financial interests.
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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Zibrov, A., Kometter, C., Zhou, H. et al. Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level. Nature 549, 360–364 (2017). https://doi.org/10.1038/nature23893
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