Abstract
Extensive efforts have been undertaken to combine superconductivity and the quantum Hall effect so that Cooper-pair transport between superconducting electrodes in Josephson junctions is mediated by one-dimensional edge states1,2,3,4,5,6. This interest has been motivated by prospects of finding new physics, including topologically protected quasiparticles7,8,9, but also extends into metrology and device applications10,11,12,13. So far it has proven challenging to achieve detectable supercurrents through quantum Hall conductors2,3,6. Here we show that domain walls in minimally twisted bilayer graphene14,15,16,17,18 support exceptionally robust proximity superconductivity in the quantum Hall regime, allowing Josephson junctions to operate in fields close to the upper critical field of superconducting electrodes. The critical current is found to be non-oscillatory and practically unchanging over the entire range of quantizing fields, with its value being limited by the quantum conductance of ballistic, strictly one-dimensional, electronic channels residing within the domain walls. The system described is unique in its ability to support Andreev bound states at quantizing fields and offers many interesting directions for further exploration.
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Data availability
The original data files that support the findings of this study are available at https://doi.org/10.5281/zenodo.10698874 (ref. 52) and from J.B.
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Acknowledgements
We acknowledge financial support from the European Research Council (Grant VANDER), the Lloyd’s Register Foundation, Horizon 2020 Graphene Flagship Core3 Project and the Engineering and Physical Sciences Research Council (EPSRC; Grant Nos EP/V007033/1 and EP/S030719/1). J.B. acknowledges support from the EPSRC (Doctoral Prize fellowship). R.K.K. acknowledges the EU Horizon programme (Grants 754510, 893030) and the FLAG-ERA programme (PhotoTBG). L.I.G. was supported by the National Science Foundation (Grant DMR-2002275) and the Office of Naval Research (Award N00014-22-1-2764).
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Contributions
A.K.G. and J.B. initiated and led the project. N.X. and P.K. fabricated the devices with help from L.H. Domain walls in MTGBs were imaged by R.K.K., F.H.L.K. and R.V.G. J.B. carried out the electrical measurements with help from M.K., E.N., A.I.B. and J.R.P. J.B. and A.K.G. analysed the data with help from I.V.G., L.I.G., J.R.P. and V.I.F. C.M., V.V.E., L.I.G. and V.I.F. provided theoretical support. K.W. and T.T. supplied quality hBN crystals. J.B., I.V.G. and A.K.G. wrote the manuscript with contributions from N.X. and V.I.F. All authors contributed to discussions.
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Extended data figures and tables
Extended Data Fig. 1 Josephson junctions with AB/BA domain walls.
(a) Piezo-force micrograph showing domains in an MTGB before its encapsulation in hBN. The blue and green triangles indicate two neighboring regions with AB and BA stacking. (b) Photocurrent map for one of our fully encapsulated MTGB stacks that was used to make the studied Josephson junctions (photoexcitation energy of 188 meV, n ≈ 1012 cm−2). Negative photocurrents are shown in blue, positive in red, and the white stripes in between reveal domain walls40. (c) Photocurrent map of a chosen domain walls with an overlaid design for superconducting electrodes, which is shown by the shaded red areas. (d) Optical micrograph of the same region as in panel c after depositing the electrodes. (e) Atomic-force microscopy (AFM) image of one of the studied Josephson junctions. The darker areas correspond to superconducting electrodes. (f) Schematic of our ‘edgeless’ devices where MTGBs extended beyond the width W of Josephson junctions to avoid the presence of graphene edges in between the electrodes (compare with our ‘edged’ devices in Fig. 1a of the main text). The greenish triangles represent different AB and BA domains.
Extended Data Fig. 2 Normal-state transport.
(a) Typical Landau fan diagram for our MTGB devices. This particular junction contained a single domain wall and had L ≈ 150 nm. The filling factors ν indicated by the dashed lines were calculated using the known capacitance to the back gate; T = 10 K. (b) Two-probe conductance at the neutrality point as a function of B for different NDW. For all the plotted junctions, L was between 150 and 200 nm; T = 10 K. (c) Resistance as a function of gate-induced n at different T for two representative junctions with 0 and 1 domain walls at 14 T (L ≈ 200 and 150 nm, respectively). Both junctions were ‘edged’. (d) Corresponding conductance at ν = 0 (after subtracting relatively small contact resistances).
Extended Data Fig. 3 Supercurrent carried by AB/BA domain walls.
(a) Fraunhofer pattern typical for MTGB junctions. The shown Josephson junction was edgeless and contained 15 ± 3 domain walls. Measurements were done using steps in B of 60 µT. White curve: standard Fraunhofer dependence Ic(B) calculated using the critical current at zero B and the apparent period for the first few oscillations. The deviations from the standard behavior are caused by ballistic transport of electrons and holes forming Andreev bound states20,25. (b) Differential resistance of the same junction in quantizing fields. For both (a) and (b): T ≈ 50 mK, n ≈ 2 × 1012 cm−2, Iac = 5 nA. (c) Critical current for different NDW (B = 3 T, electron doping of ≈3 × 1012 cm−2, T ≈ 50 mK in all cases). Blue symbols, edged junctions; orange, edgeless ones. The dashed line is the best linear fit. The horizontal error bars are caused by uncertainty in estimating the number of domain walls within the Josephson junctions. The vertical bars appear because Ic rapidly fluctuated with changing B and oscillated with n (Extended Data Figs. 4, 7; Fig. 3b of the main text) so that we plotted its rms values. (d) Same as in panel c but normalized by the number of domain walls.
Extended Data Fig. 4 Superconductivity in Josephson junctions with multiple domain walls.
(a and b) Differential resistance for junctions with a few (estimated as 2 or 3) and many (16 ± 3) domain walls, respectively. Iac = 5 and 2 nA; n ≈ 2 and 3 × 1012 cm−2, respectively. T ≈ 50 mK. Both junctions were edgeless. The white curves in the bottom halves mark the boundaries of the zero-resistance state. The red curves in the top halves, the critical current. The step size in B was 10 mT.
Extended Data Fig. 5 No supercurrent in the quantum Hall regime in reference devices.
Left column, schematics of Josephson junctions. Right column, corresponding differential resistance maps at high electron doping n ≈ 3 × 1012cm−2 and L ≈ 200 nm for all the panels. Red curves, critical current. (a) Junction made from Bernal bilayer graphene. W ≈ 1 μm, Iac = 5 nA, T ≈ 50 mK, ΔIdc = 1 nA. (b) Junction with a wrinkle formed in monolayer graphene. The wrinkle’s full width was ≲100 nm as measured by AFM. W ≈ 1 µm, Iac = 7 nA, T ≈ 50 mK, ΔIdc = 15 nA. (c) Monolayer graphene with a very narrow slit. Its width estimated by AFM was <10 nm. W ≈ 4 µm, Iac = 5 nA, T ≈ 1 K, ΔIdc = 1 nA. The junction in panel b was edgeless; panels a and c show edged Josephson junctions.
Extended Data Fig. 6 Differential resistance maps for another junction with a single domain wall.
(a) Map over a large interval of B (composed of two parts where the white gap indicates no data taken). Shown is an edged junction with L ≈ 150 nm and W ≈ 0.5 µm. Red curve, critical current. The digital noise is caused by finite steps in current: ΔIdc = 3.3 and 1.3 nA below and above 3 T, respectively. Step size in B, 5 mT. (b and c) Detailed maps around 3 and 5 T, respectively. Step size in B, 0.5 mT. ΔIdc = 0.6 and 0.3 nA for panels b and c, respectively. For all the panels, T ≈ 50 mK, n ≈ 1.7 × 1012cm−2, Iac = 2 nA. Same color scales for panels a and b.
Extended Data Fig. 8 Temperature dependence of proximity superconductivity in zero and quantizing fields.
(a and c) Differential resistance maps dV/dI(Idc, T) at 0 and 3 T, respectively. (b and d) Examples of dV/dI for selected temperatures (cross-sections from the corresponding maps). White dashed curve in panel a: fit to eq. S1 above 2 K. Data are for a Josephson junction with a single domain wall, L ≈ 200 nm, n ≈ 2 × 1012 cm−2, Iac = 5 nA.
Extended Data Fig. 9 Shapiro steps in the quantum Hall regime.
(a) Voltage vs current characteristics as a function of RF power. For clarity, the curves are shifted horizontally by 10 nA each. The power P was increased in steps that corresponded to Vrf increasing from 0 to 26 µV. Shown is the same one-domain wall junction as in Fig. 1 of the main text; frf = 3.3 GHz, B = 3 T, no Iac applied; n ≈ 1.8 × 1012 cm−2 which corresponds to a maximum in Ic (Fig. 3b of the main text). Inset: ΔV as a function of the RF frequency. Green line: ΔV= ϕ0frf as per eq. S2. (b) dV/dI(Idc) with varying Vrf. The same junction and conditions as for panel a; Iac = 5 nA. Color scale: indigo to yellow is 0 to 480 Ω. (c) Same as in panel b but for n ≈ 1.7 × 1012 cm−2 which corresponds to a minimum in Ic(n); frf = 3.52 GHz. Color scale: indigo to yellow is 70 to 440 Ω. (d) Similar map for a Josephson junction with many domain walls at B = 5 T. NDW = 9 ± 2, L ≈ 200 nm, W ≈ 3.5 µm, n ≈ 2.7 × 1012 cm−2, frf = 3.0 GHz, Iac = 2 nA. Color scale: indigo to yellow is 0 to 70 Ω. (e) Width of Shapiro steps extracted from the map of panel d. The pink curves in panels b-d and the black curves in panel e are the fits by the corresponding Bessel functions as per eq. S3. For all panels, T ≈ 50 mK.
Extended Data Fig. 10 Fabry-Pérot oscillations in the supercurrent provided by 1D states inside domain walls.
(a and b) Differential resistance maps at high and low dc biases, respectively. In both cases, Iac = 5 nA. The white dashed lines indicate the filling factors ν = 4, 8, 12,… expected for Bernal bilayer graphene. The dotted curve in panel b indicates the quantum Hall regime boundary, 2rc = L. (c) Oscillations in the critical current. Values of Ic are obtained from IV curves that were recorded in small steps of ~3 × 1010 cm−2 in electron density and steps in B of 0.5 T. All the measurements were carried out at T ≈ 50 mK using junctions with a single domain wall and L ≈ 200 nm.
Supplementary information
Supplementary Information
This file contains details regarding the theory of one-dimensional electronic states inside AB/BA domain walls, additional references and Supplementary Fig. 1.
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Barrier, J., Kim, M., Kumar, R.K. et al. One-dimensional proximity superconductivity in the quantum Hall regime. Nature 628, 741–745 (2024). https://doi.org/10.1038/s41586-024-07271-w
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DOI: https://doi.org/10.1038/s41586-024-07271-w
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