Abstract
Graphene-based, high-quality, two-dimensional electronic systems have emerged as a highly tunable platform for studying superconductivity1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21. Specifically, superconductivity has been observed in both electron- and hole-doped twisted graphene moiré systems1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, whereas in crystalline graphene systems, superconductivity has so far been observed only in hole-doped rhombohedral trilayer graphene (RTG)18 and hole-doped Bernal bilayer graphene (BBG)19,20,21. Recently, enhanced superconductivity has been demonstrated20,21 in BBG because of the proximity to a monolayer WSe2. Here we report the observation of superconductivity and a series of flavour-symmetry-breaking phases in electron- and hole-doped BBG/WSe2 devices by electrostatic doping. The strength of the observed superconductivity is tunable by applied vertical electric fields. The maximum Berezinskii–Kosterlitz−Thouless transition temperature for the electron- and hole-doped superconductivity is about 210 mK and 400 mK, respectively. Superconductivities emerge only when the applied electric fields drive the BBG electron or hole wavefunctions towards the WSe2 layer, underscoring the importance of the WSe2 layer in the observed superconductivity. The hole-doped superconductivity violates the Pauli paramagnetic limit, consistent with an Ising-like superconductor. By contrast, the electron-doped superconductivity obeys the Pauli limit, although the proximity-induced Ising spin–orbit coupling is also notable in the conduction band. Our findings highlight the rich physics associated with the conduction band in BBG, paving the way for further studies into the superconducting mechanisms of crystalline graphene and the development of superconductor devices based on BBG.
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Data availability
The data provided in this study are available from the corresponding authors upon request. Source data are provided with this paper.
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The codes related to the findings of this study are available from the corresponding authors upon request.
References
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
Lu, X. B. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).
Saito, Y., Ge, J., Watanabe, K., Taniguchi, T. & Young, A. F. Independent superconductors and correlated insulators in twisted bilayer graphene. Nat. Phys. 16, 926–930 (2020).
Stepanov, P. et al. Untying the insulating and superconducting orders in magic-angle graphene. Nature 583, 375–378 (2020).
Liu, X. et al. Tuning electron correlation in magic-angle twisted bilayer graphene using Coulomb screening. Science 371, 1261–1265 (2021).
Park, J. M., Cao, Y., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Tunable strongly coupled superconductivity in magic-angle twisted trilayer graphene. Nature 590, 249–255 (2021).
Hao, Z. et al. Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene. Science 371, 1133–1138 (2021).
Cao, Y., Park, J. M., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Pauli-limit violation and re-entrant superconductivity in moiré graphene. Nature 595, 526–531 (2021).
Liu, X., Zhang, N. J., Watanabe, K., Taniguchi, T. & Li, J. I. A. Isospin order in superconducting magic-angle twisted trilayer graphene. Nat. Phys. 18, 522–527 (2022).
Zhang, Y. et al. Promotion of superconductivity in magic-angle graphene multilayers. Science 377, 1538–1543 (2022).
Park, J. M. et al. Robust superconductivity in magic-angle multilayer graphene family. Nat. Mater. 21, 877–883 (2022).
Arora, H. S. et al. Superconductivity in metallic twisted bilayer graphene stabilized by WSe2. Nature 583, 379–384 (2020).
Su, R., Kuiri, M., Watanabe, K., Taniguchi, T. & Folk, J. A. Superconductivity in twisted double bilayer graphene stabilized by WSe2. Nat. Mater. 22, 1332–1337 (2023).
Oh, M. et al. Evidence for unconventional superconductivity in twisted bilayer graphene. Nature 600, 240–245 (2021).
Kim, H. et al. Evidence for unconventional superconductivity in twisted trilayer graphene. Nature 606, 494–500 (2022).
Tian, H. et al. Evidence for Dirac flat band superconductivity enabled by quantum geometry. Nature 614, 440–444 (2023).
Zhou, H., Xie, T., Taniguchi, T., Watanabe, K. & Young, A. F. Superconductivity in rhombohedral trilayer graphene. Nature 598, 434–438 (2021).
Zhou, H. et al. Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene. Science 375, 774–778 (2022).
Zhang, Y. et al. Enhanced superconductivity in spin–orbit proximitized bilayer graphene. Nature 613, 268–273 (2023).
Holleis, L. et al. Ising superconductivity and nematicity in Bernal bilayer graphene with strong spin orbit coupling. Preprint at https://arxiv.org/abs/2303.00742 (2023).
Gmitra, M. & Fabian, J. Graphene on transition-metal dichalcogenides: a platform for proximity spin-orbit physics and optospintronics. Phys. Rev. B 92, 155403 (2015).
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. S. On-demand spin-orbit interaction from which-layer tunability in bilayer graphene. Nano Lett. 17, 7003–7008 (2017). 11.
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).
Avsar, A. et al. Spin–orbit proximity effect in graphene. Nat. Commun. 5, 4875 (2014).
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).
Yang, B. W. et al. Tunable spin-orbit coupling and symmetry-protected edge states in graphene/WS2. 2D Mater. 3, 031012 (2016).
Wakamura, T. et al. Strong anisotropic spin-orbit interaction induced in graphene by monolayer WS2. Phys. Rev. Lett. 120, 106802 (2018).
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).
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).
Lin, J.-X. et al. Spin-orbit-driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene. Science 375, 437–441 (2022).
Han, T. et al. Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene. Science 384, 647–651 (2024).
Sha, Y. et al. Observation of a Chern insulator in crystalline ABCA-tetralayer graphene with spin-orbit coupling. Science 384, 414–419 (2024).
Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).
Törmä, P., Peotta, S. & Bernevig, B. A. Superconductivity, superfluidity and quantum geometry in twisted multilayer systems. Nat. Rev. Phys. 4, 528–542 (2022).
Pantaleón, P. A. et al. Superconductivity and correlated phases in non-twisted bilayer and trilayer graphene. Nat. Rev. Phys. 5, 304–315 (2023).
Zhou, H. et al. Half- and quarter-metals in rhombohedral trilayer graphene. Nature 598, 429–433 (2021).
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).
Lin, J. X. et al. Spontaneous momentum polarization and diodicity in Bernal bilayer graphene. Preprint at https://arxiv.org/abs/2302.04261 (2023).
Liu, K. et al. Spontaneous broken-symmetry insulator and metals in tetralayer rhombohedral graphene. Nat. Nanotechnol. 19, 188–195 (2023).
Han, T. et al. Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene. Nat. Nanotechnol. 19, 181–187 (2023).
Han, T. et al. Orbital multiferroicity in pentalayer rhombohedral graphene. Nature 623, 41–47 (2023).
Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).
McCann, E. & Koshino, M. The electronic properties of bilayer graphene. Rep. Prog. Phys. 76, 056503 (2013).
Lu, J. M. et al. Evidence for two-dimensional Ising superconductivity 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).
Xi, X. et al. Ising pairing in superconducting NbSe2 atomic layers. Nat. Phys. 12, 139–143 (2016).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
Tinkham, M. Introduction to Superconductivity 2nd edn (McGraw-Hill, 1975).
Chou, Y.-Z., Wu, F., Sau, J. & Sarma, S. Acoustic-phonon-mediated superconductivity in Bernal bilayer graphene. Phys. Rev. B 105, L100503 (2022).
Chou, Y.-Z., Wu, F., Sau, J. D. & Das Sarma, S. Acoustic-phonon-mediated superconductivity in moiréless graphene multilayers. Phys. Rev. B 106, 024507 (2022).
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).
Boström, E. V. et al. Phonon-mediated unconventional s- and f-wave pairing superconductivity in rhombohedral stacked multilayer graphene. Preprint at https://arxiv.org/abs/2311.02494 (2023).
Jimeno-Pozo, A., Sainz-Cruz, H., Cea, T., Pantaleón, P. A. & Guinea, F. Superconductivity from electronic interactions and spin-orbit enhancement in bilayer and trilayer graphene. Phys. Rev. B 107, L161106 (2023).
Wagner, G., Kwan, Y., Bultinck, N., Simon, S. & Parameswaran, S. Superconductivity from repulsive interactions in Bernal-stacked bilayer graphene. Preprint at https://arxiv.org/abs/2302.00682 (2023).
Li, Z. et al. Charge fluctuations, phonons, and superconductivity in multilayer graphene. Phys. Rev. B 108, 045404 (2023).
Cea, T. Superconductivity induced by the intervalley Coulomb scattering in a few layers of graphene. Phys. Rev. B 107, L041111 (2023).
Szabó, A. L. & Roy, B. Competing orders and cascade of degeneracy lifting in doped Bernal bilayer graphene. Phys. Rev. B 105, L201107 (2022).
Dong, Z., Chubukov, A. V. & Levitov, L. Transformer spin-triplet superconductivity at the onset of isospin order in bilayer graphene. Phys. Rev. B 107, 174512 (2023).
Dong, Z., Levitov, L. & Chubukov, A. V. Superconductivity near spin and valley orders in graphene multilayers. Phys. Rev. B 108, 134503 (2023).
Curtis, J. B. et al. Stabilizing fluctuating spin-triplet superconductivity in graphene via induced spin-orbit coupling. Phys. Rev. Lett. 130, 196001 (2023).
Jung, J. & MacDonald, A. H. Accurate tight-binding models for the π bands of bilayer graphene. Phys. Rev. B 89, 035405 (2014).
Xie, M. & Sarma, S. D. Flavor symmetry breaking in spin-orbit coupled bilayer graphene. Phys. Rev. B 107, L201119 (2023).
Dong, Z., Davydova, M., Ogunnaike, O. & Levitov, L. Isospin- and momentum-polarized orders in bilayer graphene. Phys. Rev. B 107, 075108 (2023).
Wilson, N. R. et al. Determination of band offsets, hybridization, and exciton binding in 2D semiconductor heterostructures. Sci. Adv. 3, e1601832 (2017).
Xu, Y. et al. Creation of moiré bands in a monolayer semiconductor by spatially periodic dielectric screening. Nat. Mater. 20, 645–649 (2021).
Yu, Y. J. et al. Tuning the graphene work function by electric field effect. Nano Lett. 9, 3430–3434 (2009).
Acknowledgements
We thank Y. Chou, J. Liu, Y. Zhang and F. Yuan for their discussions. This work was supported by the National Key R&D Program of China (nos. 2022YFA1405400, 2022YFA1402702, 2022YFA1402404, 2019YFA0308600, 2022YFA1402401 and 2020YFA0309000), the National Natural Science Foundation of China (nos. 12350403, 12174249, 92265102 and 12374045), the Innovation Program for Quantum Science and Technology (grant nos. 2021ZD0302600 and 2021ZD0302500), the Natural Science Foundation of Shanghai (no. 22ZR1430900), the Science and Technology Commission of Shanghai Municipality (nos. 2019SHZDZX01, 19JC1412701 and 20QA1405100), and the Shanghai Jiao Tong University 2030 Initiative (nos. WH510363002/003 and WH510363002/011). X.L. acknowledges the Pujiang Talent Program 22PJ1406700. T.L. acknowledges the Yangyang Development Fund. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant nos. 21H05233 and 23H02052) and the World Premier International Research Center Initiative (WPI), MEXT, Japan. This work was supported by the Synergetic Extreme Condition User Facility (SECUF).
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T.L. and X.L. designed the experiment; C.L. and F.X. fabricated the devices; C.L., F.X. and J.L. performed the measurements with the assistance of G.L. and B.T.; X.L., C.L., T.L. and F.W. analysed the data; B.L. and F.W. performed the theoretical studies; K.W. and T.T. grew the bulk hBN crystals; and T.L., X.L., and F.W. wrote the paper. All authors discussed the results and commented on the paper.
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Extended data figures and tables
Extended Data Fig. 1 Estimation of the strength of Ising SOC from the transition at quantum hall state |ν| = 3.
a–e, Rxx as a function of D and Landau level filling factors ν at B⊥ = 2 T (a), B⊥ = 4 T (b), B⊥ = 5 T (c), B⊥ = 6 T (d) and B⊥ = 8 T (e). The blue and green arrows in each panel mark the orbital transitions of quantum hall state |ν| = 3. f, The D extracted from the transition at |ν| = 3 in a–e as a function of B⊥, and the red and black lines are fits to the data, respectively. The strength of Ising SOC could be estimated from the crossing point of the two fitting lines where the out-of-plane Zeeman energy Ez compensates the energy split λI due to Ising SOC20,21,31. According to λI = 2Ez = 2gµBBSOC, where BSOC is the perpendicular magnetic field where the two fitting lines intersect, the strength of Ising SOC λI in our device is estimated to be about 1.7 meV.
Extended Data Fig. 2 Estimation of TBKT, density dependent Tc and Ic at various D.
a, c, dVxx/dIdc at the optimal doping as a function of Idc measured at various temperatures at D = + 1.1 V/nm (a) and D = −1.64 V/nm (c) for the hole- and electron-doped superconductivity, respectively. An ac modulation current of 2 nA is used for the differential resistance measurements. b, d, The nonlinear voltage-current (Vdc−Idc) curves of a and c. The dashed line is a power law fit of V ∝ I3, yielding TBKT = 400 mK (b) and TBKT = 210 mK (d) for the hole-doped and electron-doped superconductivity, respectively. e–g, Rxx as a function of n and T for hole-doped superconducting domes at D = 0.96 V/nm (e), D = 1.1 V/nm (f) and D = 1.27 V/nm (g), respectively. h, Rxx as a function of n and T for electron-doped superconducting dome at D = −1.47 V/nm. i-l, The measured differential resistance dVxx/dIdc at T = 20 mK as a function of n and dc bias current Idc for superconducting domes at (i) D = 0.96 V/nm, (j) D = 1.1 V/nm, (k) D = 1.27 V/nm and (l) D = −1.47 V/nm, respectively. A competing resistive phase intersecting the hole-doped superconducting dome reported previously20 is evident at D = 0.96 V/nm and eventually diminishes with further increasing D. The data shown in i-l and the data shown in e-h were taken during separate rounds of measurements conducted in different dilution refrigerators. We found that the width of the superconducting dome in density can vary slightly between different rounds of measurements.
Extended Data Fig. 3 DOS calculation.
a–c, Total density of state (DOS) in BBG as a function of doping density n without (a) and with (b,c) the Ising SOC term for different values of the layer potential difference U. At positive (negative) U, hole wavefunctions (electron wavefunctions) concentrate at the top graphene layer which is closer to the WSe2 layer, so the proximity-induced Ising SOC is only notable in the valence band (conduction band).
Extended Data Fig. 4 Fermi surface analysis of the hole-doped BBG/WSe2 at negative D fields.
a, b, Rxx versus n and B⊥ at D = −1.1 V/nm (a) and −1.5 V/nm (b) on the hole-doping side. c, d, FFT of Rxx (1/B⊥) versus n and fν at D = −1.1 V/nm (c) and −1.5 V/nm (d) on the hole-doping side. The FFT analysis in c and d is performed based on the Rxx data within 0.2 T < B⊥ < 1 T in a and b, respectively. No SOC induced FFT peak splitting can be identified at negative D-fields on the hole-doping side. The schematic Fermi surface structures for different phases are also shown in c and d. e, f, Rxx versus n at B = 0 T at D = −1.1 V/nm (e) and −1.5 V/nm (f) on the hole-doping side. In the PIP2 phase at D = −1.1 V/nm, instead of superconductivity, a resistive state emerges.
Extended Data Fig. 5 Fermi surface analysis of the hole-doped BBG/WSe2 at D = 1.19 V/nm.
a, Rxx-D-n map of hole-doped BBG/WSe2 within a narrower n, D range. Apart from the superconducting region described in the main text, another region with reduced Rxx emerges at lower hole doping, within D-field range about 1.1 - 1.3 V/nm (marked by the green arrow). b, Temperature dependence of Rxx versus n on the hole-doping side at D = 1.19 V/nm. The additional resistance dip at about 0.56 × 1012 cm−2 can be observed. Such resistance dip may indicate the developing of another superconducting dome, which may need further studies in higher quality devices or at lower temperatures. c, Rxx versus n and B⊥ at D = 1.19 V/nm on the hole-doping side. d, FFT of Rxx (1/B⊥) versus n and fν at D = 1.19 V/nm on the hole-doping side. The FFT analysis is performed based on the Rxx data within 0.2 T < B⊥ < 1.2 T. A spin- and valley-polarized state with fν = 1 emerges at n ≈ −0.4 to −0.45 × 1012 cm−2. With increasing hole density, the FFT peak becomes less than 1 and new FFT peaks emerge at very low frequencies. These FFT features indicate a partially isospin polarized phase with one majority and multiple minority Fermi pockets (denoted as PIP1 phase). Further increasing hole densities, the PIP1 phase transits into the trigonal-warping phase with the Ising SOC-induced spin splitting (fν(1) > 1/12 and fν(2) < 1/12) until n ≈ −0.75 × 1012 cm−2. The observed additional Rxx dip locates in between of the PIP1 phase and the trigonal warping phase, as indicated by the green arrow. Similar to D = 1.1 V/nm shown in Fig. 2, the superconducting normal state is within the PIP2 phase, corresponding to a partial isospin-polarized phase with two major Fermi pockets and multiple minor Fermi pockets. Further increasing hole doping beyond the PIP2 phase, the system evolves into a state with four annular Fermi surfaces, which is evident by two FFT frequency peaks satisfying fν(1) - fν(2) = 1/4.
Extended Data Fig. 6 The calculation of Fermi surface structure on the electron-doped side.
a–l, Theoretically calculated normalized quantum oscillation frequencies fν as a function of n for different values of U. We first calculate the mean-field ground state (considering both symmetric and symmetry-breaking states) at a given n and U, and then fν is calculated by the fraction Si/S, where Si is area of the ith Fermi pocket and S = (2π)2|n|. The background colours distinguish different patterns of fν. The results are presented for electron doping (n > 0). U is positive in a–f and negative in g–l. The Ising SOC coupling strength λI is taken to be 2 meV in the calculation. m–s, Representative Fermi surfaces for different regimes in l. Electron densities in m–s are n = (0.1, 0.4, 0.5, 0.8, 1.2, 1.6, 3) × 1012 cm−2, respectively.
Extended Data Fig. 7 Fermi surface analysis at D = ± 1.1 V/nm on the electron-doping side.
a, b, Rxx versus n and B⊥ at D = 1.1 V/nm (a) and −1.1 V/nm (b) on the electron-doping side. c, d, FFT of Rxx (1/B⊥) versus n and fν at D = 1.1 V/nm (c) and −1.1 V/nm (d) on the electron-doping side. The FFT analysis in c and d is performed based on the Rxx data within 0.1 T < B⊥ < 1 T in a and b, respectively. The schematic Fermi surface structures for different phases are also shown in c and d. Compared to larger D values (Fig. 3 and Extended Data Fig. 8), the PIP1 phase is absent, and the electron density range of the PIP2 phase become much narrower at D = ± 1.1 V/nm. e, f, Rxx versus n at B = 0 T at D = 1.1 V/nm (e) and −1.1 V/nm (f) on the electron-doping side. Although the flavour-symmetry-breaking phases still exist, the superconductivity is absent at D = −1.1 V/nm.
Extended Data Fig. 8 Fermi surface analysis at D = ± 1.64 V/nm on the electron-doping side.
a, b, Rxx versus n and B⊥ at D = 1.64 V/nm (a) and −1.64 V/nm (b) on the electron-doping side. c, d, FFT of Rxx (1/B⊥) versus n and fν at D = 1.64 V/nm (c) and −1.64 V/nm (d) on the electron-doping side. The FFT analysis in c and d is performed based on the Rxx data within 0.2 T < B⊥ < 1 T in a and b, respectively. The schematic Fermi surface structures for different phases are also shown in c and d. e, f, Rxx versus n at B = 0 T at D = 1.64 V/nm (e) and −1.64 V/nm (f) on the electron-doping side. Electron-doped superconductivity can be only observed at negative D. The main results closely resemble those observed at D = ± 1.55 V/nm, as illustrated in Fig. 3.
Extended Data Fig. 9 Determination of the in-plane critical magnetic field at the zero-temperature limit \({B}_{c\parallel }^{0}\).
a–c, Rxx as a function of T and B∥ at n = −0.53 × 1012 cm−2 (a), n = −0.55 × 1012 cm−2 (b), and n = −0.59 × 1012 cm−2 (c) for D = 0.96 V/nm. d–f, Rxx as a function of T and B∥ at n = 0.9 × 1012 cm−2 (d), n = 0.89 × 1012 cm−2 (e) and n = 0.87 × 1012 cm−2 (f) for D = −1.64 V/nm. The opaque circles in each panel depict the critical in-plane magnetic field Bc∥ as a function of T, where the Bc∥ is defined as the field where Rxx is 50% of the normal state resistance. The data points in each panel are fitted well by the phenomenological relation T /\({T}_{c}^{0}\) = 1−(Bc||/\({B}_{{c||}}^{0}\))2. The green markers indicate the Pauli-limit field BP. Blue lines are plotted based on the formula T /\({T}_{c}^{0}\) = 1− (Bc∥2/BP BSOC) for an Ising superconductor, where BSOC is obtained from our measurement shown in Extended Data Fig. 1. It can be seen that, even for the hole-doped superconductivity, the measured B∥ is still smaller than the values expected for an Ising superconductor. Such discrepancy may depend on multiple details, including the Fermi surface shape, the Rashba SOC, the spin Zeeman effect, and the orbital effect of B∥. As a general trend, the Ising SOC enhances PVR, while additional Rashba SOC and orbital effect from B∥ suppresses PVR. Therefore, the value of PVR becomes a quantitative problem given these competing effects. On the other hand, quantitative estimation of quantities such as Rashba SOC, and orbital g-factor of the in-plane magnetic field is a nontrivial task, since they all have a small energy scale and are all subjected to renormalization by the electron Coulomb interaction. This makes it challenging to theoretically estimate the value of PVR. Nevertheless, the hole-doped superconductivity clearly violates the Pauli paramagnetic limit, consistent with previous studies20,21. However, the limited resilience to B∥ observed in electron-doped superconductivity is more puzzling, as a comparable Ising SOC effect is evident in the conduction band at negative D fields based on the FFT analysis of quantum oscillations.
Extended Data Fig. 10 More data about the in-plane magnetic field dependence of superconducting states.
a–d, Rxx as a function of n and B∥ for hole-doped superconducting domes at D = 1.19 V/nm (a), D = 1.36 V/nm (b), and for electron-doped superconducting domes at D = −1.47 V/nm (c) and D = −1.55 V/nm (d), measured at T = 20 mK. The superconducting dome width in n at D = 1.19 V/nm is almost unchanged under B∥ = 1 T. At D = 1.36 V/nm, the hole-doped superconductivity around −1 × 1012 cm−2 could still survive under B∥ = 1 T. The highest in-plane magnetic field applied is limited to 1 T owing to the magnet limitation of the refrigerator used for the measurement. The Pauli violation ratio \({B}_{{c||}}^{0}\)/Bp at the optimal doping should be much larger than 1.4 in a, and about 2.1 in b. On the contrary, the electron-doped superconductivity in c and d is readily suppressed under a small applied B∥ (about 0.2 – 0.3 T). The \({B}_{{c||}}^{0}\)/Bp at the optimal doping for c and d is about 0.31 and 0.25, respectively, substantially below the Pauli paramagnetic limit.
Extended Data Fig. 11 Device image and the measurement configuration.
a, Optical image of the BBG/WSe2 heterostructure device. The device is shaped into a hall bar geometry and the hall bar channel is fabricated in a bubble-free region. The scale bar is 5 µm. b, Schematic of the hall bar device in a, along with an illustration of the transport measurement configuration.
Extended Data Fig. 12 The perpendicular magnetic field B⊥ dependence of the hole- and electron-doped superconducting states.
a–d, Rxx as a function of n and B⊥ measured at T = 20 mK with D = 1.0 V/nm (a), 1.27 V/nm (b) for hole-doped superconducting domes, and D = −1.47 V/nm (c), and −1.55 V/nm (d) for electron-doped superconducting domes, respectively. The critical perpendicular magnetic fields Bc⊥ for the hole- and electron-doped superconductivity are comparable, which range from about 5 mT to 15 mT.
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Li, C., Xu, F., Li, B. et al. Tunable superconductivity in electron- and hole-doped Bernal bilayer graphene. Nature 631, 300–306 (2024). https://doi.org/10.1038/s41586-024-07584-w
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DOI: https://doi.org/10.1038/s41586-024-07584-w
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