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

Journal name:
Nature Nanotechnology
Volume:
12,
Pages:
118–122
Year published:
DOI:
doi:10.1038/nnano.2016.214
Received
Accepted
Published online

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.

At a glance

Figures

  1. Quantum Hall effect in twisted bilayer graphene with broken-symmetry states.
    Figure 1: Quantum Hall effect in twisted bilayer graphene with broken-symmetry states.

    a, Stacking two graphene layers with a relative twist angle θ decouples the Dirac cones from each layer via a large momentum mismatch (K = 4π/3a, where a is the graphene lattice constant). In a magnetic field, each layer will develop monolayer graphene-like Landau levels despite the tiny 0.34-nm interlayer spacing. b, Device schematic of twisted bilayer graphene encapsulated in hexagonal boron nitride (hBN) with dual gates. Contact electrodes are depicted in red. c, Cartoon of twisted bilayer QH edge states when both layers are at filling factor –2. Each layer has a spin degenerate edge state with a hole-like chirality (direction of chirality indicated by horizontal arrows). d, Two-probe conductance of a twisted bilayer graphene device at B = 1T as a function of νtot. The sequence is exactly double the monolayer graphene sequence of (2,6,10,14,…)e2/h (refs 26,27). A contact resistance has been subtracted to fit the νtot = −4 plateau to 4 e2/h. e, Two-probe conductance of the same device at B = 4T showing broken-symmetry states. Contact resistances have been subtracted from the negative and positive νtot sides of the data. Note that this trace is taken with a small interlayer displacement field in order to observe all integer steps (see colour map in Fig. 2e). Cartoons depict proposed edge state configurations in the (0,−1) and (+1,0) states.

  2. Transport in graphene electron–hole bilayers.
    Figure 2: Transport in graphene electron–hole bilayers.

    a, Cartoons depicting edge state configurations with νtop = −νbottom. b, Measured two-probe conductance G for νtot = 0 as a function of displacement field, D, at B = 4T. The (−1,+1) state is conductive while the (−2,+2) state is insulating. c, Magnetic field dependence of νtot = 0 line (white dashed line shows the location of the line trace in b). d, Two-probe conductance map, G, as function of νtot and D. Conductance is given by νtot(e2/h) for all configurations except for the (±1,∓1) states (indicated by the dashed white circles). Contact resistances have been subtracted from the positive and negatives sides of the data to fit the νtot = ±1 plateaus. e, Schematic map of possible filling factor combinations.

  3. Non-local measurements of helical edge states.
    Figure 3: Non-local measurements of helical edge states.

    a, Optical image of four-probe device. Scale bar, 5 µm. Graphite leads are highlighted in orange and the gold top-gate that covers the device is highlighted in yellow. b, Schematics of different measurement configurations for the four-probe device. c, Non-local resistance, RNL, as a function of νtot and displacement field, D, measured at B = 4T. Dashed white circles highlight the (±1,∓1) states that exhibit a strong non-local signal, indicating transport through highly conductive counterpropagating edge modes. Axis ranges are identical to those in Fig. 2d. In the (0,0) insulating state, RNL fluctuates strongly due to low current signals near the noise limit (bright white features). d, RNL (black line, left axis) compared to two-probe resistance, Rtwo-probe, (grey line, right axis) of a constant D line cut through the (+1,−1) state (horizontal dashed line in Fig. 3c). RNL is near zero when Rtwo-probe exhibits a conductance plateau, since the voltage drop along a chiral edge state is zero. During plateau transitions, the bulk becomes conductive, resulting in a small peak that is suppressed by the non-local geometry of the measurement. e, Magnetic field dependence of RNL and Rxx in the (+1,−1) state. Plotted points are determined by averaging the resistance over the region in the νtot and D map corresponding to the (+1,−1) state (error bars represent one standard deviation from the mean).

  4. Fractional QH effect in twisted bilayer graphene.
    Figure 4: Fractional QH effect in twisted bilayer graphene.

    a, Rxx measurements at B = 9 T as a function of νtot and D show clear minima at fractional values of νtot = ±1/3, ±2/3, ±4/3 and ± 5/3 indicating fractional quantum Hall states. Some electron−hole regions are obscured by contact-resistance effects at high fields. b,c, Comparison of Rxx and Rxy line cuts showing the bilayer fractional quantum Hall effect. Rxx minima at fractional values of νtot line up with plateaus in the measurement of 1/Rxy. The plotted lines in b and c are averages of the measured quantities over a range of D field values as indicated respectively by the purple and blue rectangles in the colourmap of a. For the line trace in b, measurements correspond to fractional states in the top layer and an insulating ν = 0 state in the bottom layer. For c, data correspond to electron−hole combinations.

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Author information

  1. These authors contributed equally to this work

    • Javier D. Sanchez-Yamagishi &
    • Jason Y. Luo

Affiliations

  1. Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

    • Javier D. Sanchez-Yamagishi,
    • Jason Y. Luo,
    • Raymond C. Ashoori &
    • Pablo Jarillo-Herrero
  2. Department of Physics, University of California Santa Barbara, Santa Barbara, California 93106, USA

    • Andrea F. Young
  3. Department of Physics, Carnegie Mellon University, Pittsburg, Pennsylvania 15213, USA

    • Benjamin M. Hunt
  4. Advanced Materials Laboratory, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan

    • Kenji Watanabe &
    • Takashi Taniguchi

Contributions

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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The authors declare no competing financial interests.

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