Abstract
Magic-angle twisted bilayer graphene (TBG), with rotational misalignment close to 1.1 degrees, features isolated flat electronic bands that host a rich phase diagram of correlated insulating, superconducting, ferromagnetic and topological phases1,2,3,4,5,6. Correlated insulators and superconductivity have been previously observed only for angles within 0.1 degree of the magic angle and occur in adjacent or overlapping electron-density ranges; nevertheless, the origins of these states and the relation between them remain unclear, owing to their sensitivity to microscopic details. Beyond twist angle and strain, the dependence of the TBG phase diagram on the alignment4,6 and thickness of the insulating hexagonal boron nitride (hBN)7,8 used to encapsulate the graphene sheets indicates the importance of the microscopic dielectric environment. Here we show that adding an insulating tungsten diselenide (WSe2) monolayer between the hBN and the TBG stabilizes superconductivity at twist angles much smaller than the magic angle. For the smallest twist angle of 0.79 degrees, superconductivity is still observed despite the TBG exhibiting metallic behaviour across the whole range of electron densities. Finite-magnetic-field measurements further reveal weak antilocalization signatures as well as breaking of fourfold spin–valley symmetry, consistent with spin–orbit coupling induced in the TBG via its proximity to WSe2. Our results constrain theoretical explanations for the emergence of superconductivity in TBG and open up avenues towards engineering quantum phases in moiré systems.
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The data that support the findings of this study are available from the corresponding authors on reasonable request.
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Acknowledgements
We acknowledge discussions with H. Ren, D. Zhong, Y. Peng, G. Refael, F. von Oppen, Y. Saito, A. Young, D. Efetov, J. Eisenstein and P. Lee. The device nanofabrication was performed at the Kavli Nanoscience Institute (KNI) at Caltech. This work was supported by the National Science Foundation through programme CAREER DMR-1753306 and grant DMR-1723367, the Gist–Caltech memorandum of understanding and the Army Research Office under grant award W911NF-17-1-0323. Nanofabrication performed by Y.Z. was supported by the US Department of Energy DOE-QIS programme (DE-SC0019166). J.A. and S.N.-P. also acknowledge the support of IQIM (an NSF-funded Physics Frontiers Center). A.T. and J.A. are grateful for support from the Walter Burke Institute for Theoretical Physics at Caltech and the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant GBMF8682. The material synthesis at the University of Washington was supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the DOE, Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443 and the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant GBMF6759 to J.-H.C.
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Contributions
H.S.A., R.P., Y.Z. and S.N.-P. designed the experiment. H.S.A. made the TBG–WSe2 devices assisted by Y.Z., H.K. and Y.C. H.S.A. and R.P. performed the measurements. Y.Z. made and measured initial TBG devices and D4. H.S.A., R.P. and S.N.-P. analysed the data. A.T. and J.A. developed the continuum model that includes spin–orbit interactions and performed model calculations. Z.L., I.Z.W., X.X. and J.-H.C. provided WSe2 crystals. K.W. and T.T. provided hBN crystals. H.S.A., R.P., Y.Z., A.T., J.A. and S.N.-P. wrote the manuscript with input from other authors. S.N.-P. supervised the project.
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Extended data figures and tables
Extended Data Fig. 1 Fabrication details.
a–e, Critical steps in the stacking process. f, Optical images of a typical flake and stacks at different stages of the fabrication.
Extended Data Fig. 2 Optical images of devices D1–D4.
a–d, The electrodes that are used in the measurements and the corresponding twisted angles are labelled for each device. The electrodes marked with blue lines were used for measuring the Hall conductance in Fig. 3. The scale bar in each panel corresponds to 15 μm. The bottom hBN thicknesses for D1, D2, D3 and D4 are 62 nm, 40 nm, 48 nm and 56 nm, respectively. D4 differs from the other devices as it features monolayer WSe2 on both the top and bottom of the device. The contact angles for each pair of contacts listed were determined from the Landau-fan diagrams, as described in Methods.
Extended Data Fig. 3 Additional temperature data for device D1 (0.97°).
a, Rxx as a function of ν and temperature, up to 10 K. b, Temperature dependence of Rxx for ν = 2 (red) and ν = 3 (black), showing insulating behaviour. c, At other partial integer filling factors, Rxx increases with temperature, consistent with metallic behaviour.
Extended Data Fig. 4 Additional data for device D3 (1.04°).
a, Rxx as a function of ν and temperature, up to 120 K. In this device, a higher temperature was required for fitting the Arrhenius gaps, owing to the larger gap size. The data in a were therefore measured in a variable-temperature (Quantum Design PPMS) setup, whereas data from other panels were taken in the dilution fridge. b, Line cuts from a, with corresponding fits showing gaps at full filling Δ±4 and partial filling Δ±2. c, Landau-fan diagram showing similar behaviour as for D1 (0.97°). d, Temperature dependence up to 2 K, clearly showing superconductivity on the hole side (for −3 < ν < −2) and with a smaller pocket on the electron side showing signatures of developing superconductivity. e, Fraunhofer-like pattern at ν = −2.78.
Extended Data Fig. 5 Additional data for device D2 (0.83° contacts).
See Extended Data Fig. 2b for the layout of D2. a, Rxx plotted for filling factor ν and temperature up to 2 K, showing the superconducting pocket on the electron side. b, As in a, up to 40 K, showing the reduction of the |ν| = 4 insulating states. c, Arrhenius fits to the gap values of 0.97 meV for ν = −4, and 3.7 meV for ν = +4. d, Rxx versus filling factor and magnetic field (B), forming a Landau-fan diagram, with white dashed lines tracing the dominant ±2, +3, ±4, ±6, ±8, ±10, ±14, ±18, +20, ±22, −26 sequence around charge neutrality. The odd level (+3) is marked with green. e, The Fraunhofer-like pattern for the superconductivity pocket, taken at ν = 2.08. The inset is a magnification of the low-field data, showing that the critical current reaches a local minimum about zero field, indicating “π-junction-like” behaviour3.
Extended Data Fig. 6 Additional data from device D1 (0.97°).
a, Fraunhofer-like pattern for electron doping, at ν = 1.58. b, c, Additional Fraunhofer-like pattern for hole doping, at ν = −2.1 (b), and ν = −2.5 (c).
Extended Data Fig. 7 Additional data for device D4 (0.80°).
D4 was fabricated with monolayer WSe2 on both the top and bottom of the TBG. a, Rxx as a function of ν and temperature, to 2 K, revealing a superconducting pocket over the range 2 < ν < 3.2 and resistance at full filling (|ν| = 4) of less than at the CNP. b, The Landau fan, with dotted lines drawn from the CNP according to the sequence ±2, +3, ±4, ±6, ±8, ±10, −12, ±14, ±18, +22, with the odd level (+3) marked in green. c, Current versus voltage at ν = 2.79, at temperatures from 50 mK to 900 mK in 50 mK steps. The main plot is on a log scale in both axes, revealing a Berezinskii–Kosterlitz–Thouless (BKT) transition temperature near 250 mK. Inset, I–V dependence for the same temperatures. d, Fraunhofer-like pattern for D4 at ν = 2.40.
Extended Data Fig. 8 Weak antilocalization data measured in D4 (θ = 0.80°).
a, Rxx as a function of back-gate voltage, Vbg, for the 0.80° contacts of D4 (see Extended Data Fig. 2). The black (red) line shows the voltage range used in the flat (dispersive) bands, which corresponds to the plots in b–d (e, f). The peak at B = 0 mT is prominent in both ranges, showing the presence of weak antilocalization and, consequently, spin–orbit coupling. b, The change in conductivity Δσ, relative to the 0 mT point, as a function of magnetic field, taken at several gate voltages close to Vbg ≈ −2 V measured at 25 mK; the narrow peak about B = 0 mT, indicative of weak antilocalization, is clearly visible. Universal conductance fluctuations can be averaged out by taking field sweeps at different gate points53. c, d, Averaged data from b for different field ranges. The data taken at 900 mK—where the weak antilocalization peak has disappeared—has been subtracted, and the data points have been symmetrized about 0 mT. The dashed lines are the comparison with the model54 used previously for monolayer graphene/transition metal dichalcogenide heterostructures18,53 with a renormalized Fermi velocity to account for the flatness of the bands. For generating plots at different temperatures, only the dephasing scattering time τϕ is varied. Although the total spin–orbit scattering time τso ≈ 10 ps better reproduces the low-field data in c, τso ≈ 1–3 ps captures the saturation at larger fields (d) with asymmetric and symmetric relaxation-time ratios54 (τasym/τsym) varying in the range 0.3–3. The values of τso obtained here correspond to SOI energies50 in the range 0.5–1 meV. We note that, in the case of TBG, a more detailed analysis with a correct model for describing weak antilocalization in TBG is probably required for quantitative comparison. Regardless, the weak antilocalization peaks are an indication of strong SOI in WSe2–TBG heterostructures. e, f, The data show a weak antilocalization peak in the dispersive bands near Vbg = −6 V (red line in a). Data in e was taken at 25 mK. In f, the data points at each temperature are offset by 0.1 e2/h for clarity.
Extended Data Fig. 9 Theoretical Landau-level spectrum.
a, c, Colour plot of the phenomenologically broadened density of states (see Supplementary Information section 2 for details) as a function of energy squared, in millelectronvolts squared (roughly equivalent to the electron density that is gate-tuned in the experiment), and the magnetic field in tesla. b, d, The spectrum, without taking broadening effects into account. Blue and red lines correspond to levels originating proximate to the +K and −K valleys, respectively. The effective spin–orbit coupling parameters (as distinct from those used in the continuum model) are \(({\tilde{\lambda }}_{{\rm{I}}},{\tilde{\lambda }}_{{\rm{R}}},{\tilde{\lambda }}_{{\rm{KM}}})\) = (3 meV, 4 meV, 0 meV) with a broadening Γ = 0.22 meV (a, b) and \(({\tilde{\lambda }}_{{\rm{I}}},{\tilde{\lambda }}_{{\rm{R}}},{\tilde{\lambda }}_{{\rm{KM}}})\) = (1.5 meV, 2.5 meV, 2 meV) with a broadening Γ = 0.15 meV (c, d). The Fermi velocity in both is vF ≈ 105 m s−1, as is appropriate for θ ≈ 0.8°−0.9°. We note that the Landau-level sequence and energy levels on the hole-doped side are identical to those shown here for a and b. When both \({\tilde{\lambda }}_{{\rm{I}}}\) and \({\tilde{\lambda }}_{{\rm{KM}}}\) are non-zero, as in c and d, a slightly different Landau-level sequence is generically obtained at negative energies relative to the CNP.
Extended Data Fig. 10 SOI dependence of the band structure.
a, c, f, h, Flat-band energies along momentum line cuts defined in the inset of a; dashed lines indicate the chemical potential corresponding to ν = +2. b, d, e, g, i, j, Band structure of the electron-like bands with their ν = +2 Fermi surfaces indicated, for different values of the SOI parameters. We consider the cases in which no SOI is present (a, b), and where only Ising SOI (c–e), only Kane–Mele SOI (f, g), and only Rashba SOI (h–j) are present. In c–j, the non-zero SOI parameter is set to 3 meV; other parameters are provided in Methods. In c, the bands possess an out-of-plane spin polarization, ⟨Sz⟩, which is displayed in colour as per the inset. As indicated in Fig. 4, when both λI and λR are non-zero, the Dirac cones at ±κ generate masses. By contrast, when λI, λR and λKM are individually the only non-zero SOI, only the Kane–Mele term results in a gapped spectrum at charge neutrality. In f, the inset magnifies the −κ point to demonstrate this point. Aside from this feature, the band structure when λKM = 3 meV (f, g) is qualitatively identical to the band structure without SOI (a, b). In i and j, the colour of the Fermi surfaces indicates the expectation value of the in-plane spin according to the wheel above i. All other parameter sets have a zero in-plane spin projection.
Supplementary information
Supplementary Information
Supplementary Methods: The file includes the continuum model details used in Fig. 4 and Extended Data Fig. 10, and Landau level diagram derivations used in Extended Data Fig. 9.
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Arora, H.S., Polski, R., Zhang, Y. et al. Superconductivity in metallic twisted bilayer graphene stabilized by WSe2. Nature 583, 379–384 (2020). https://doi.org/10.1038/s41586-020-2473-8
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DOI: https://doi.org/10.1038/s41586-020-2473-8
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