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Dynamic band-structure tuning of graphene moiré superlattices with pressure

Abstract

Heterostructures can be assembled from atomically thin materials by combining a wide range of available van der Waals crystals, providing exciting possibilities for designer electronics1. In many cases, beyond simply realizing new material combinations, interlayer interactions lead to emergent electronic properties that are fundamentally distinct from those of the constituent layers2. A critical parameter in these structures is the interlayer coupling strength, but this is often not easy to determine and is typically considered to be a fixed property of the system. Here we demonstrate that we can controllably tune the interlayer separation in van der Waals heterostructures using hydrostatic pressure, providing a dynamic way to modify their electronic properties. In devices in which graphene is encapsulated in boron nitride and aligned with one of the encapsulating layers, we observe that increasing pressure produces a superlinear increase in the moiré-superlattice-induced bandgap—nearly doubling within the studied range—together with an increase in the capacitive gate coupling to the active channel by as much as 25 per cent. Comparison to theoretical modelling highlights the role of atomic-scale structural deformations and how this can be altered with pressure. Our results demonstrate that combining hydrostatic pressure with controlled rotational order provides opportunities for dynamic band-structure engineering in van der Waals heterostructures.

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Fig. 1: Experiment schematic and transport characterization under pressure.
Fig. 2: Modification of gate capacitance under pressure.
Fig. 3: Bandgaps as a function of pressure.
Fig. 4: Modelling of the bandgaps.

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Acknowledgements

We thank P. San-Jose, J. Song, A. Shytov, L. Levitov, J. Wallbank and P. Moon for theoretical discussions. This work was supported by the National Science Foundation (NSF) (DMR-1462383). C.R.D. acknowledges partial support from the David and Lucille Packard foundation. Development of the device concept and fabrication process was partially supported by the NSF MRSEC program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). We acknowledge S. Tozer for use of his 16 T PPMS which is partially supported as part of the Center for Actinide Science and Technology (CAST), an Energy Frontier Research Center (EFRC) funded by the Department of Energy, Office of Science, Basic Energy Sciences under award no. DE-SC0016568. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by NSF Cooperative Agreement no. DMR-1157490, the State of Florida and the US Department of Energy and additionally provided support for pressure cell development through User Collaboration Grant Program (UCGP) funding. J.J. and N.L. were supported by the Korean NRF through grant NRF-2016R1A2B4010105 and Korean Research Fellowship grant NRF-2016H1D3A1023826, and B.L.C. was supported by grant NRF-2017R1D1A1B03035932. E.L. and S.A. are supported by the National Research Foundation of Singapore under its Fellowship program (NRF-NRFF2012-01) and the Singapore Ministry of Education AcRF Tier 2 (MOE2017-T2-2-140). K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, and JSPS KAKENHI grant no. JP15K21722.

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Contributions

M.Y. and C.R.D. conceived the experiment. M.Y. fabricated the samples and analysed the data. M.Y. and D.G. performed the experiments. J.J., E.L. and S.A. developed the theory. N.L. and B.L.C. calculated the ab initio potentials. K.W. and T.T. grew the hBN crystals. C.R.D. advised on the experiments. All authors participated in writing the paper.

Corresponding author

Correspondence to Cory R. Dean.

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Extended data figures and tables

Extended Data Fig. 1 Pictures of the set-up for pressure experiments.

a, Graphene (outlined in white dashed line) is encapsulated between BN and placed on a graphite back gate. b, The device is shaped into a Hall bar and contacted for electrical measurements. c, The Si wafer is diced to approximate dimensions of 2 mm × 2 mm. d, A new pressure cell stage. e, The stage is threaded with wires which are epoxied in place. f, The sample is glued to the top of the stage. g, Wires are connected to the device electrodes by hand using silver paste. h, A Teflon cup is filled with oil and fitted over the sample and onto the stage. i, The sample is placed into a pressure cell. j, Pressure is loaded using a hydraulic press. k, The loaded pressure cell is attached to a probe for low-temperature magnetotransport measurements. See Methods for complete experimental details. The scale bars for a and b are 25 μm, and the scale bar for c is 2 mm.

Extended Data Fig. 2 Resistivity of device P3 at = 0 T and = 2 K.

For the application of high pressure in this device, we observe virtually no change in the device resistivity for hole carriers, and a decrease in the resistivity for electron carriers.

Extended Data Fig. 3 Arrhenius plot for the SDP in device P1.

The gap exhibits virtually no dependence on pressure.

Extended Data Fig. 4 Bandgaps as a function of pressure for all devices studied.

a, Devices with square markers exhibit thermally activated behaviour over roughly an order of magnitude change in resistance. Devices with triangle markers exhibit thermally activated behaviour over a smaller range. The numbered labels represent the order in which the gaps were acquired. The gap magnitude depends only on the pressure the device is under at the time of measurement, and not on the history of the pressure that has been previously applied. Error bars in the gap fitting arising from the uncertainty identifying the thermally activated regime have been omitted for clarity, but are all less than 2.5 meV. b, Gap dependence in a second aligned device (P6), with misalignment of about 0.1°. This device also exhibits a growing Δp and constant Δs, but is much more disordered than device P1. Inset: Arrhenius plots for the PDP (left) and SDP (right) at 0 GPa and 1 GPa.

Extended Data Fig. 5 Conductivity of the PDP over the full temperature range at various pressures for all devices studied.

a, Device P1 is the aligned device discussed in the main text. Inset, conductivity of the SDP. b, Device P6 is a second aligned device, but is more highly disordered and therefore less resistive at low temperature. Inset, conductivity of the SDP. cf, The remaining devices do not exhibit SDPs, and therefore the alignment to the BN layers is unknown. However, the devices in c and d still exhibit thermally activated behaviour over roughly an order of magnitude change in resistance, suggesting they are nearly aligned to a BN. The devices in e and f have a much smaller thermally activated regime. Pressure tends to have a smaller effect on the PDP conductivity for devices that are less resistive at 0 GPa. The inset in f shows the high-temperature response, demonstrating the weak effect of pressure in the thermally activated regime for the least resistive device. In af, although the PDP generally grows more insulating with higher pressure at low temperatures, this is not universally true, suggesting that the details of the low-temperature resistance depends more critically on the exact nature of disorder in the device. Devices are ordered by decreasing gap size as measured in the thermally activated regime.

Extended Data Fig. 6 Disorder and the quantum Hall effect.

a, Device disorder δn is measured as the n necessary to dope between the maximum and minimum Rxy, averaged over B = 0.25 T to 0.75 T. b, Density fluctuations as a function of pressure across different devices. The error bars denote the uncertainty in picking the peak positions of Rxy. c, ρxx (solid lines, left axis) and σxy (dotted lines, right axis) of device P1 at B = 12.5 T. Symmetry-broken integer quantum Hall states become much more clearly developed with pressure, and fractional quantum Hall states begin to emerge as well. Both are offset for clarity. d, ρxx of device P2 at B = 9 T, similarly showing an improvement in the quantum Hall response. Surprisingly, the improvement persists even after the pressure is released back to vacuum and the device is cleaned in solvents (green curve). Curves are vertically offset for clarity.

Extended Data Fig. 7 Hofstadter butterfly as a function of pressure in device P1.

Magnetotransport data acquired at T = 2 K and a pressure of: a, 0 GPa; b, 2.3 GPa.

Supplementary Information

Supplementary Information

This file contains Supplementary Notes S1-S3, includes Supplementary Figures 1-5 and Supplementary Tables 1-2

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Yankowitz, M., Jung, J., Laksono, E. et al. Dynamic band-structure tuning of graphene moiré superlattices with pressure. Nature 557, 404–408 (2018). https://doi.org/10.1038/s41586-018-0107-1

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