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Nanoscale electrostatic control in ultraclean van der Waals heterostructures by local anodic oxidation of graphite gates


In an all-van der Waals heterostructure, the active layer, gate dielectrics and gate electrodes are assembled from two-dimensional crystals that have a low density of atomic defects. This design allows two-dimensional electron systems with very low disorder to be created, particularly in heterostructures where the active layer also has intrinsically low disorder, such as crystalline graphene layers or metal dichalcogenide heterobilayers. A key missing ingredient has been nanoscale electrostatic control, with existing methods for fabricated local gates typically introducing unwanted contamination. Here we describe a resist-free local anodic oxidation process for patterning sub-100 nm features in graphite gates, and their subsequent integration into an all-van der Waals heterostructure. We define a quantum point contact in the fractional quantum Hall regime as a benchmark device and observe signatures of chiral Luttinger liquid behaviour, indicating an absence of extrinsic scattering centres in the vicinity of the point contact. In the integer quantum Hall regime, we demonstrate in situ control of the edge confinement potential, a key requirement for the precision control of chiral edge states. This technique may enable the fabrication of devices capable of single anyon control and coherent edge-state interferometry in the fractional quantum Hall regime.

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Fig. 1: Local anodic oxidation and integration of graphite gates into van der Waals heterostructures.
Fig. 2: QPC operation in the integer quantum Hall regime.
Fig. 3: Partitioning of fractional quantum Hall edges and quasiparticle tunnelling.
Fig. 4: Tuning edge sharpness via electrostatic gating.

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Data availability

The data that support the findings of this study are available via Zenodo at Source data are provided with this paper.


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We thank J. Folk and A. Potts for comments on the manuscript, and C. R. Dean and J. Swan for advice on humidity stabilization. We additionally acknowledge Y. Choi for providing the AFM topographs of quantum dot arrays. Work at University of California, Santa Barbara, was primarily supported by the Air Force Office of Scientific Research under award FA9550-20-1-0208 and by the Gordon and Betty Moore Foundation EPIQS program under award GBMF9471. This work used facilities supported via the University of California, Santa Barbara, NSF Quantum Foundry funded via the Q-AMASE-i program under award DMR-1906325. L.A.C. and N.L.S. received additional support from the Army Research Office under award W911NF20-1-0082. T.W. and M.P.Z. were supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the US Department of Energy under contract no. DE-AC02-05-CH11231 (van der Waals heterostructures program, KCWF16). K.K. was supported by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Science Center. C.C.R. was supported by the National Science Foundation through Enabling Quantum Leap: Convergent Accelerated Discovery Foundries for Quantum Materials Science, Engineering and Information (Q-AMASE-i) award no. DMR-1906325. K.W. and T.T. acknowledge support from JSPS KAKENHI (grant nos. 19H05790, 20H00354 and 21H05233).

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Authors and Affiliations



L.A.C. and A.F.Y. conceived the experiment. L.A.C. and N.L.S. fabricated the devices and performed the measurements. L.A.C., N.L.S., M.P.Z., T.W., K.K. and A.F.Y. analysed the data and wrote the paper. M.P.Z. and S.V. proposed the simulation methodology. T.W., K.K. and C.C.R. performed the numerical calculations based on the proposed theoretical modelling. T.T. and K.W. synthesized the hBN crystals

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Correspondence to Andrea F. Young.

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Extended data

Extended Data Fig. 1 Precise determination of α and Hall conductance at B = 6T and B = 13T.

(a) Longitudinal and Hall conductance in the W region of the device for two values of the bottom gate, VB = 1.0V and VB = 2.0V, at B = 10T. All other regions are set to ν = 0. (b) Calculated shift ΔVW applied to the VB = 1.0V trace shows overlap of identical features between the two traces. (c) The region of vanishing longitudinal conductance in ν = − 2/3 was used to numerically determine the shift ΔVW by minimizing the sum of the norm-squared differences between the two traces over a region around ν = − 2/3. (d) σxx and σxy versus VW at B = 13T and VB = 1V. (e) 1/Rxy measured on the west side of the device versus VW while νN = νS = νE = 0 is kept fixed, and VB = − 0.33V. Inset: current measured during 1/Rxy sweep showing ν = 0 gap.

Source data

Extended Data Fig. 2 Possible edge structures in ν = − 5/3.

(a) Hole-conjugate FQH states such as ν = 2/3, 5/3 states can be modeled by a Laughlin- like FQH state of holes within a bulk integer quantum Hall state, leading to a small strip of increased filling factor around the edge of the sample. This is shown schematically in panels a and c by plotting the filling factor of holes νh ≡ − ν at the boundary between a ν = − 5/3 and ν = − 1 state, where the relevant fractional edges measured in the experiment occur. The MacDonald model34 of the resulting edge structure posits a downstream integer mode at the outermost edge of the sample, as well as an upstream (counter-propagating) fractional mode. (b) In real experiments, the two counter-propagating charged modes are rarely observed, but rather mix through the presence of inter-edge interactions, yielding a single effective charge-2e/3 mode propagating downstream, as well as an upstream charge-neutral mode, as explained by the Kane-Fisher-Polchinski model35. (c) A sufficiently soft confining potential may make it energetically favorable to redistribute the charge in the system and create an additional strip of density νh = 4/3, introducing a set of two additional counter-propagating fractional edge modes: the Meir model40. (d) In a real system, where these modes can also mix, the resulting mode structure may contain two downstream fractional-conductance modes as well as two upstream neutral modes. This scenario is consistent with the observation of multiple fractional conductance steps within the ν = − 5/3 state.

Extended Data Fig. 3 Tunneling conductance in an integer vs. fractional edge.

(a) Plot of the tunneling conductance across an integer conductance step, in the ν = 1 state. In the fully reflecting and fully transmitting limits, the conductance is constant for VDC less than about – 1 mV –, and smoothly varies as the edge is transmitted. (b) For a fractional edge state, the conductance remains highly suppressed even when the edge state is partially transmitted, with a sharply nonlinear dI/dV near VDC = 0. Even when the edge state is fully transmitted, and dI/dV (VDC = 0) = 4/3, the tunneling conductance remains nonlinear. (c) and (d) present linecuts of the data in (a) and (b) respectively for comparison.

Source data

Extended Data Fig. 4 Thomas-Fermi simulations of the QPC pinch-off.

(a) The filling at the center of the QPC, νQPC as a function of VB and VNS + αVB, with the bulk filling of the east/west regions fixed at νEW = − 6. The result qualitatively mimics the measured GD shown in Fig. 4a since νQPC determines the number of transmitted modes and therefore the diagonal conductance. Two line cuts which correspond to EV/EC = 2.2 and 4.4 are shown in Fig. 4c. (b-c) Calculated filling factor ν for a realistic device geometry at B = 2 T for (b) EV/EC = 4.4 and (c) EV/EC = 2.2. When EV/EC = 2.2, there exists an incompressible island with νQPC = − 4 at the center of the QPC. Contours of ν = n + 1/2 are shown as white dotted lines, indicating the location of chiral edge modes, two-pairs of which are transmitted through the QPC. This illustrates the rule NQPC = νQPC + 2.

Supplementary information

Supplementary Information

Supplementary Sections 1–5.

Source data

Source Data Fig. 2

Compressed data archive for Fig. 2.

Source Data Fig. 3

Compressed data archive for Fig. 3; the temperature-dependent curves have been collapsed to a single data file for Fig. 3d, simplifying the data format.

Source Data Fig. 4

Compressed data archive for Fig. 4; the simulated data for Fig. 4c have been combined into a single .csv file instead of four .txt files.

Source Data Extended Data Fig. 1

Source data used to generate the linecuts shown in Extended Data Fig. 1, compressed into a single .zip file.

Source Data Extended Data Fig. 3

Source data for Extended Data Fig. 3a,b, from which the linecuts in Extended Data Fig. 3c,d are taken, compressed into a single .zip file.

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Cohen, L.A., Samuelson, N.L., Wang, T. et al. Nanoscale electrostatic control in ultraclean van der Waals heterostructures by local anodic oxidation of graphite gates. Nat. Phys. 19, 1502–1508 (2023).

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