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Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer

Abstract

Helical 1D electronic systems are a promising route towards realizing circuits of topological quantum states that exhibit non-Abelian statistics1,2,3,4. Here, we demonstrate a versatile platform to realize 1D systems made by combining quantum Hall (QH) edge states of opposite chiralities in a graphene electron–hole bilayer at moderate magnetic fields. Using this approach, we engineer helical 1D edge conductors where the counterpropagating modes are localized in separate electron and hole layers by a tunable electric field. These helical conductors exhibit strong non-local transport signals and suppressed backscattering due to the opposite spin polarizations of the counterpropagating modes. Unlike other approaches used for realizing helical states5,6,7, the graphene electron–hole bilayer can be used to build new 1D systems incorporating fractional edge states8,9. Indeed, we are able to tune the bilayer devices into a regime hosting fractional and integer edge states of opposite chiralities, paving the way towards 1D helical conductors with fractional quantum statistics10,11,12,13.

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Figure 1: Quantum Hall effect in twisted bilayer graphene with broken-symmetry states.
Figure 2: Transport in graphene electron–hole bilayers.
Figure 3: Non-local measurements of helical edge states.
Figure 4: Fractional QH effect in twisted bilayer graphene.

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Acknowledgements

We acknowledge helpful discussions with A. Stern, L. Levitov, L. Fu and V. Fatemi. We also acknowledge fabrication help from D. Wei, G. H. Lee, S. H. Choi and Y. Cao. This work has been primarily supported by the National Science Foundation (NSF) (DMR-1405221) for device fabrication, transport and data analysis (J.D.S.-Y., J.Y.L., P.J.-H.), with additional support from the National Science Scholarship Program, Singapore (J.Y.L.). This research has been funded in part by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant GBMF4541 to P.J.-H. The capacitance measurements have been supported in part by the Gordon and Betty Moore Foundation Grant GBMF2931 to R.C.A. and by the Science and Technology Center for Integrated Quantum Materials, NSF Grant (DMR-1231319) (A.F.Y., B.M.H. and R.C.A.). This work made use of the Materials Research Science and Engineering Center Shared Experimental Facilities supported by the NSF (DMR-0819762) and of Harvard's Center for Nanoscale Systems, supported by the NSF (ECS-0335765). Some measurements were performed at the National High Magnetic Field Laboratory, which is supported by NSF Cooperative Agreement DMR-1157490 and the State of Florida.

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J.D.S.-Y. and J.Y.L. fabricated the samples, performed the transport experiments, analysed the data and wrote the paper. A.F.Y. and B.M.H. performed the capacitance measurements and contributed to the discussion of the results. T.T. and K.W. grew the crystals of hexagonal boron nitride. R.C.A. advised on the capacitance measurements and contributed to the discussion of the results. P.J.-H. advised on the transport experiments, data analysis and writing of the paper.

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Correspondence to Pablo Jarillo-Herrero.

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Sanchez-Yamagishi, J., Luo, J., Young, A. et al. Helical edge states and fractional quantum Hall effect in a graphene electron–hole bilayer. Nature Nanotech 12, 118–122 (2017). https://doi.org/10.1038/nnano.2016.214

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