Abstract
The relative twist angle between layers of near-lattice-matched van der Waals materials is critical for the emergent phenomena associated with moiré flat bands1,2,3. However, the concept of angle rotation control is not exclusive to moiré superlattices in which electrons directly experience a twist-angle-dependent periodic potential. Instead, it can also be used to induce programmable symmetry-breaking perturbations with the goal of stabilizing desired correlated states. Here we experimentally demonstrate ‘moiréless’ twist-tuning of superconductivity together with other correlated orders in Bernal bilayer graphene proximitized by tungsten diselenide. The precise alignment between the two materials systematically controls the strength of induced Ising spin–orbit coupling (SOC), profoundly altering the phase diagram. As Ising SOC is increased, superconductivity onsets at a higher displacement field and features a higher critical temperature, reaching up to 0.5 K. Within the main superconducting dome and in the strong Ising SOC limit, we find an unusual phase transition characterized by a nematic redistribution of holes among trigonally warped Fermi pockets and enhanced resilience to in-plane magnetic fields. The superconducting behaviour is theoretically compatible with the prominent role of interband interactions between symmetry-breaking Fermi pockets. Moreover, we identify two additional superconducting regions, one of which descends from an inter-valley coherent normal state and shows a Pauli-limit violation ratio exceeding 40, among the highest for all known superconductors4,5,6,7. Our results provide insights into ultraclean graphene superconductors and underscore the potential of utilizing moiréless-twist engineering across a wide range of van der Waals heterostructures.
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Data availability
The data shown in the main figures are available from the CaltechDATA (https://doi.org/10.22002/pcm1e-qe565). Other data that support the findings of this study are available from the corresponding authors upon reasonable request.
Code availability
The code that supports the findings of this study is available from the corresponding authors upon reasonable request.
References
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Zhou, H. et al. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 375, 774–778 (2022).
Ran, S. et al. Extreme magnetic field-boosted superconductivity. Nat. Phys. 15, 1250–1254 (2019).
Ran, S. et al. Nearly ferromagnetic spin-triplet superconductivity. Science 365, 684–687 (2019).
Lu, J. et al. Full superconducting dome of strong Ising protection in gated monolayer WS2. Proc. Natl Acad. Sci. USA 115, 3551–3556 (2018).
de la Barrera, S. C. et al. Cascade of isospin phase transitions in Bernal-stacked bilayer graphene at zero magnetic field. Nat. Phys. 18, 771–775 (2022).
Seiler, A. M. et al. Quantum cascade of correlated phases in trigonally warped bilayer graphene. Nature 608, 298–302 (2022).
Wang, Z. et al. Origin and magnitude of ‘designer’ spin–orbit interaction in graphene on semiconducting transition metal dichalcogenides. Phys. Rev. X 6, 041020 (2016).
Gmitra, M. & Fabian, J. Proximity effects in bilayer graphene on monolayer WSe2: field-effect spin valley locking, spin–orbit valve, and spin transistor. Phys. Rev. Lett. 119, 146401 (2017).
Khoo, J. Y., Morpurgo, A. F. & Levitov, L. On-demand spin–orbit interaction from which-layer tunability in bilayer graphene. Nano Lett. 17, 7003–7008 (2017).
Khoo, J. Y. & Levitov, L. Tunable quantum Hall edge conduction in bilayer graphene through spin–orbit interaction. Phys. Rev. B 98, 115307 (2018).
Island, J. O. et al. Spin–orbit-driven band inversion in bilayer graphene by the van der Waals proximity effect. Nature 571, 85–89 (2019).
Wang, D. et al. Quantum Hall effect measurement of spin–orbit coupling strengths in ultraclean bilayer graphene/WSe2 heterostructures. Nano Lett. 19, 7028–7034 (2019).
Li, Y. & Koshino, M. Twist-angle dependence of the proximity spin–orbit coupling in graphene on transition-metal dichalcogenides. Phys. Rev. B 99, 075438 (2019).
Zhang, Y. et al. Enhanced superconductivity in spin–orbit proximitized bilayer graphene. Nature 613, 268–273 (2023).
Holleis, L. et al. Nematicity and orbital depairing in superconducting Bernal bilayer graphene. Nat. Phys. 21, 444–450 (2025).
Li, C. et al. Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene. Nature 631, 300–306 (2024).
Chou, Y.-Z., Wu, F. & Das Sarma, S. Enhanced superconductivity through virtual tunneling in Bernal bilayer graphene coupled to WSe2. Phys. Rev. B 106, L180502 (2022).
David, A., Rakyta, P., Kormányos, A. & Burkard, G. Induced spin–orbit coupling in twisted graphene–transition metal dichalcogenide heterobilayers: twistronics meets spintronics. Phys. Rev. B 100, 085412 (2019).
Naimer, T., Zollner, K., Gmitra, M. & Fabian, J. Twist-angle dependent proximity induced spin-orbit coupling in graphene/transition metal dichalcogenide heterostructures. Phys. Rev. B 104, 195156 (2021).
Zollner, K., João, S. M., Nikolić, B. K. & Fabian, J. Twist- and gate-tunable proximity spin-orbit coupling, spin relaxation anisotropy, and charge-to-spin conversion in heterostructures of graphene and transition metal dichalcogenides. Phys. Rev. B 108, 235166 (2023).
Li, H. et al. Electrode-free anodic oxidation nanolithography of low-dimensional materials. Nano Lett. 18, 8011–8015 (2018).
Masseroni, M. et al. Spin-orbit proximity in MoS2/bilayer graphene heterostructures. Nat. Commun. 15, 9251 (2024).
Seiler, A. M. et al. Layer-selective spin–orbit coupling and strong correlation in bilayer graphene. Preprint at https://arxiv.org/abs/2403.17140 (2024).
Sun, L. et al. Spin-orbit proximity in MoS2/bilayer graphene heterostructures. Nat. Commun. 14, 3771 (2023).
McMillan, W. L. Transition temperature of strong-coupled superconductors. Phys. Rev. 167, 331–344 (1968).
Allen, P. B. & Dynes, R. C. Transition temperature of strong-coupled superconductors reanalyzed. Phys. Rev. B 12, 905–922 (1975).
Tolmachev, V. V. Logarithmic criterion for superconductivity. Dokl. Akad. Nauk SSSR 140, 563–566 (1961).
Morel, P. & Anderson, P. W. Calculation of the superconducting state parameters with retarded electron–phonon interaction. Phys. Rev. 125, 1263–1271 (1962).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
Kedves, M. et al. Stabilizing the inverted phase of a WSe2/BLG/WSe2 heterostructure via hydrostatic pressure. Nano Lett. 23, 9508–9514 (2023).
McCann, E. & Koshino, M. The electronic properties of bilayer graphene. Rep. Prog. Phys. 76, 056503 (2013).
Dong, Z., Davydova, M., Ogunnaike, O. & Levitov, L. Isospin- and momentum-polarized orders in bilayer graphene. Phys. Rev. B 107, 075108 (2023).
Lin, J.-X. et al. Spontaneous momentum polarization and diodicity in Bernal bilayer graphene. Preprint at https://arxiv.org/abs/2302.04261 (2023).
Nuckolls, K. P. et al. Quantum textures of the many-body wavefunctions in magic-angle graphene. Nature 620, 525–532 (2023).
Kim, H. et al. Imaging inter-valley coherent order in magic-angle twisted trilayer graphene. Nature 623, 942–948 (2023).
Arp, T. et al. Intervalley coherence and intrinsic spin–orbit coupling in rhombohedral trilayer graphene. Nat. Phys. 20, 1413–1420 (2024).
Chatterjee, S., Wang, T., Berg, E. & Zaletel, M. P. Inter-valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene. Nat. Commun. 13, 6013 (2022).
Koh, J. M., Thomson, A., Alicea, J. & Lantagne-Hurtubise, É. Symmetry-broken metallic orders in spin–orbit-coupled Bernal bilayer graphene. Phys. Rev. B 110, 245118 (2024).
You, Y.-Z. & Vishwanath, A. Kohn–Luttinger superconductivity and intervalley coherence in rhombohedral trilayer graphene. Phys. Rev. B 105, 134524 (2022).
Xie, M. & Das Sarma, S. Flavor symmetry breaking in spin–orbit coupled bilayer graphene. Phys. Rev. B 107, L201119 (2023).
Thomson, A., Sorensen, I. M., Nadj-Perge, S. & Alicea, J. Gate-defined wires in twisted bilayer graphene: from electrical detection of intervalley coherence to internally engineered Majorana modes. Phys. Rev. B 105, L081405 (2022).
Koh, J. M., Alicea, J. & Lantagne-Hurtubise, É. Correlated phases in spin–orbit-coupled rhombohedral trilayer graphene. Phys. Rev. B 109, 035113 (2024).
Zhumagulov, Y., Kochan, D. & Fabian, J. Swapping exchange and spin-orbit induced correlated phases in proximitized Bernal bilayer graphene. Phys. Rev. B 110, 045427 (2024).
Dong, Z., Lantagne-Hurtubise, É. & Alicea, J. Superconductivity from spin-canting fluctuations in rhombohedral graphene. Preprint at https://arxiv.org/abs/2406.17036 (2024).
Frigeri, P. A., Agterberg, D. F., Koga, A. & Sigrist, M. Superconductivity without inversion symmetry: MnSi versus CePt3Si. Phys. Rev. Lett. 92, 097001 (2004).
Lu, J. M. et al. Evidence for two-dimensional Isuperconductivity in gated MoS2. Science 350, 1353–1357 (2015).
Saito, Y. et al. Superconductivity protected by spin–valley locking in ion-gated MoS2. Nat. Phys. 12, 144–149 (2016).
Seyler, K. L. et al. Electrical control of second-harmonic generation in a WSe2 monolayer transistor. Nat. Nanotechnol. 10, 407–411 (2015).
Szentpéteri, B. et al. Tuning the proximity induced spin–orbit coupling in bilayer graphene/WSe2 heterostructures with pressure. Preprint at https://arxiv.org/abs/2409.20062 (2024).
Cohen, M. H. & Falicov, L. M. Magnetic breakdown in crystals. Phys. Rev. Lett. 7, 231–233 (1961).
Acknowledgements
We thank J. Alicea, É. Lantagne-Hurtubise, Z. Dong, A. Thomson, D. V. Chichinadze, A. Young and E. Berg for discussions. This work has been primarily supported by the Office of Naval Research (grant number N142112635). S.N.-P. and D.H. acknowledge the support of the Institute for Quantum Information and Matter, an NSF Physics Frontiers Center (PHY-2317110). Part of the measurements were supported by the Moore foundation (award 12967). We gratefully acknowledge the critical support and infrastructure provided for this work by The Kavli Nanoscience Institute at Caltech. G.S. acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech, and from the Yad Hanadiv Foundation through the Rothschild fellowship. H.M. and C.L. were supported by start-up funds from Florida State University and the National High Magnetic Field Laboratory. The National High Magnetic Field Laboratory is supported by the National Science Foundation through NSF/DMR-2128556 and the State of Florida. Y.O. and F.v.O. acknowledge suppport by Deutsche Forschungsgemeinschaft through CRC 183 (project C02). F.v.O was further supported by Deutsche Forschungsgemeinschaft through a joint ANR-DFG project (TWISTGRAPH).
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Y.Z. and S.N.-P. designed the experiment. Y.Z. fabricated the devices, performed the measurements and analysed the data. C.W.S. and A.M. helped with the measurements. Y.H. and D.H. performed the second harmonic generation measurements. G.S., H.M., C.L., F.v.O. and Y.O. developed the theoretical models and performed calculations. K.W. and T.T. provided the hexagonal boron nitride crystals. S.N.-P. supervised the project. Y.Z., G.S., C.L., F.v.O., Y.O. and S.N.-P. wrote the paper with the input of other authors.
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Extended data figures and tables
Extended Data Fig. 1 Device fabrication for BLG-WSe2 twisting.
a, Optical image of a WSe2 crystal. b, Second harmonic generation for the WSe2 flake shown in a; the polarization of the incident and reflected beams are selected to lie parallel to the scattering plane. c, Optical image of a large BLG flake. Straight edges form angles 150° that are consistent with the three straight edges being along zigzag- or armchair-edge direction. d, Zoom-in image of the BLG in c, showing small BLG pieces that are separated by atomic-force-microscope-actuated cutting. e-g, Schematics showing the flake transferring processes for the continuous interfacial twisting. The BLG pieces are sequentially picked up with angles relative to WSe2 in increments of 6°, from ~0° to 30°. h, Optical image of the twisting stack, clearly showing that the BLG pieces form different twist angles relative to the WSe2 crystal. i, Optical image of the finished device set D1. All the scale bars correspond to 10μm.
Extended Data Fig. 2 Quantifying Ising SOC strength ∣λI∣ by quantum oscillations.
a, The same data as the one in Fig. 1h, but without the frequency normalization to show Bsplit. b,c, Experimental (dots) doping-dependent frequency splitting around fν = 1/4 measured at different D fields for a large Ising device (b; ∣λI∣ ≈ 1.4 meV) and a small Ising device (c; ∣λI∣ ≈ 0.4 meV). The dashed lines are Bsplit calculated from single-particle band structure using the corresponding Ising SOC values. The gray dashed line in b corresponds to the frequency splitting at zero displacement field.
Extended Data Fig. 3 n-D phase diagrams for devices with various Ising SOC strengths.
a-g, Rxx versus doping density n and displacement field D for devices with Ising SOC strength ∣λI∣ ≈ 0 meV (a), 0.4 meV (b), 0.7 meV (c), 0.9 meV (d), 1.4 meV (e), 1.5 meV (f), and 1.6 meV (g), respectively. See Methods and SI Fig. 4 for detailed discussion and measurement regarding the case at ∣λI∣ ≈ 0 meV. Panel c adapted from ref. 17, Springer Nature Limited.
Extended Data Fig. 4 Characterizations of the three superconducting regions SC1, SC2, and SC3.
a-c, Temperature dependence of the three superconducting domes SC1 (a), SC2 (b), and SC3 (c), respectively. d-f, Critical current versus temperature at the corresponding D and n. g-i, Critical current disappearing with B⊥ at the same D and n as in d-f.
Extended Data Fig. 5 Quantum oscillations and FFT measured at D/ϵ0 = 1.265 V/nm.
a, Rxx versus out-of-plane magnetic field B⊥ and doping density n measured at D/ϵ0 = 1.265 V/nm for a device with ∣λI∣ ≈ 1.5 meV. b, Frequency-normalized Fourier transform of Rxx(1/B⊥) (using data within 0.05 < B⊥ < 0.8 T to resolve \({f}_{\nu }^{(3)}\)) over the same doping density range as in a. c, Intensity peaks in fν from b.
Extended Data Fig. 6 Quantum oscillations and FFT measured at D/ϵ0 = 1.2 V/nm.
a, Rxx versus out-of-plane magnetic field B⊥ and doping density n measured at D/ϵ0 = 1.2 V/nm for a device with ∣λI∣ ≈ 1.5 meV. b, Frequency-normalized Fourier transform of Rxx(1/B⊥) (using data within 0.05 < B⊥ < 0.8 T to resolve \({f}_{\nu }^{(3)}\)) over the same density range as in a. c, Intensity peaks in fν from b. d, zoom-in image at low frequencies from b.
Extended Data Fig. 7 Identifying FP(2, 2, 2) and FP(1, 3, 1) frequencies from the raw data.
a, Rxx versus out-of-plane magnetic field B⊥ and doping density n measured at D/ϵ0 = 1.2 V/nm for a device with ∣λI∣ ≈ 1.5 meV. b, The same data as in a, but plotted as a function of 1/B⊥. The corresponding frequencies are marked by colored arrows and lines. c, Intensity peaks in fν extracted from the FFT data.
Extended Data Fig. 8 FP(1, 3) and FP(1, 3, 1) at D/ϵ0 = 0.85 V/nm and 1 V/nm, respectively.
a,b, Rxx versus out-of-plane magnetic field B⊥ and doping density n measured at D/ϵ0 = 0.85 V/nm (a) and 1 V/nm (b), respectively. c,d, Frequency-normalized Fourier transform of Rxx(1/B⊥) (using data within 0.05 < B⊥ < 0.45 T) at D/ϵ0 = 0.85 V/nm (c) and 1 V/nm (d), respectively. e,f, Intensity peaks in fν extracted from the FFT data in c and d.
Extended Data Fig. 9 FP(1, 3, 1) at D/ϵ0 = 1.2 V/nm and 1.265 V/nm.
a,b, Rxx versus out-of-plane magnetic field B⊥ and doping density n measured at D/ϵ0 = 1.2 V/nm (a) and 1.265 V/nm (b), respectively. c,d, Frequency-normalized Fourier transform of Rxx(1/B⊥) (using data within 0.05 < B⊥ < 0.45 T) at D/ϵ0 = 1.2 V/nm (c) and 1.265 V/nm (d), respectively. e,f, Intensity peaks in fν extracted from the FFT data in c and d.
Extended Data Fig. 10 FFT of FP(1, 3) and FP(1, 3, 1) with data at lower magnetic field.
a,c, Frequency-normalized Fourier transform of Rxx(1/B⊥) at D/ϵ0 = 0.85 V/nm (a) and 1.2 V/nm (c), respectively. The Rxx data are used up to 0.23 T and 0.26 T respectively. b,d, Rxx variation ΔRxx as a function 1/B⊥ measured at n = −3.3 × 1011 cm−2, D/ϵ0 = 0.85 V/nm (b) and n = −6 × 1011 cm−2, D/ϵ0 = 1.2 V/nm (d), respectively.
Extended Data Fig. 11 Evolution of phase boundaries as a function of B⊥.
a, Rxx versus out-of-plane magnetic field B⊥ and doping density n measured at D/ϵ0 = 1.2 V/nm for a device with ∣λI∣ ≈ 1.5 meV. Phase boundaries are marked out in b. The black arrows and dashed lines mark the phase boundaries that are not sensitive to B⊥, suggestive of inter-valley coherence with little or no net orbital moments. The red line draws the phase boundary of the spin-valley polarized FP(1); the boundary grows (orange arrow) with B⊥ due to large orbital moments.
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Zhang, Y., Shavit, G., Ma, H. et al. Twist-programmable superconductivity in spin–orbit-coupled bilayer graphene. Nature 641, 625–631 (2025). https://doi.org/10.1038/s41586-025-08959-3
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DOI: https://doi.org/10.1038/s41586-025-08959-3
