Abstract
The quantum spin Hall effect is characterized by spin-polarized counter-propagating edge states1,2,3. It has been predicted that this edge state configuration could occur in graphene when spin-split electron- and hole-like Landau levels are forced to cross at the edge of the sample4,5,6. In particular, a quantum-spin-Hall analogue has been predicted in bilayer graphene with a Landau level filling factor ν = 0 if the ground state is a spin ferromagnet7. Previous studies have demonstrated that the bilayer ν = 0 state is an insulator in a perpendicular magnetic field8,9,10,11,12,13,14, although the exact nature of this state has not been identified. Here we present measurements of the ν = 0 state in a dual-gated bilayer graphene device in a tilted magnetic field. We map out a full phase diagram of the ν = 0 state as a function of experimentally tunable in-plane magnetic field and perpendicular electric field. At large in-plane magnetic field we observe a quantum phase transition to a metallic state with conductance of the order of 4e2/h, consistent with predictions for the ferromagnet.
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Acknowledgements
The authors thank M. Kharitonov for useful discussions. Portions of this experiment were conducted at the National High Magnetic Field Laboratory, which is supported by National Science Foundation Cooperative Agreement No. DMR-0654118, the State of Florida and the US Department of Energy. We thank S. Hannahs, T. Murphy and A. Suslov for experimental assistance at NHMFL. This work is supported by AFOSR MURI. P.M. acknowledges support from ONR MURI and FENA. A.F.Y. and P.K. acknowledge support from DOE (DE-FG02-05ER46215) for carrying out experiments and INDEX for sample fabrication.
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P.M., C.R.D. and A.F.Y. designed and conceived the experiment. T.T. and K.W. synthesized hBN samples, P.M. fabricated the samples. P.M., C.R.D. and A.F.Y. performed the measurements. P.M., C.R.D. and P.K. analysed the data and wrote the paper. J.H., K.L.S. and P.K. advised on experiments.
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Maher, P., Dean, C., Young, A. et al. Evidence for a spin phase transition at charge neutrality in bilayer graphene. Nature Phys 9, 154–158 (2013). https://doi.org/10.1038/nphys2528
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DOI: https://doi.org/10.1038/nphys2528
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