## Abstract

Graphene-based, high-quality, two-dimensional electronic systems have emerged as a highly tunable platform for studying superconductivity^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21}. Specifically, superconductivity has been observed in both electron- and hole-doped twisted graphene moiré systems^{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17}, 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 demonstrated^{20,21} in BBG because of the proximity to a monolayer WSe_{2}. Here we report the observation of superconductivity and a series of flavour-symmetry-breaking phases in electron- and hole-doped BBG/WSe_{2} 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 WSe_{2} layer, underscoring the importance of the WSe_{2} 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.

## Code availability

The codes related to the findings of this study are available from the corresponding authors upon request.

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## 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).

## Author information

### Authors and Affiliations

### Contributions

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.

### Corresponding authors

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The authors declare no competing financial interests.

## Peer review

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*Nature* thanks Sergio de la Barrera, Pierre Pantaleon Peralta and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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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**, *R*_{xx} 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 *E*_{z} compensates the energy split *λ*_{I} due to Ising SOC^{20,21,31}. According to *λ*_{I} = 2*E*_{z} = 2*gµ*_{B}*B*_{SOC}, where *B*_{SOC} is the perpendicular magnetic field where the two fitting lines intersect, the strength of Ising SOC *λ*_{I} in our device is estimated to be about 1.7 meV.

### Extended Data Fig. 2 Estimation of *T*_{BKT}, density dependent *T*_{c} and *I*_{c} at various *D.*

**a**, **c**, d*V*_{xx}/d*I*_{dc} at the optimal doping as a function of *I*_{dc} 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 (*V*_{dc}−*I*_{dc}) curves of **a** and **c**. The dashed line is a power law fit of *V* ∝ *I*^{3}, yielding *T*_{BKT} = 400 mK (**b**) and *T*_{BKT} = 210 mK (**d**) for the hole-doped and electron-doped superconductivity, respectively. **e**–**g**, *R*_{xx} 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**, *R*_{xx} as a function of *n* and *T* for electron-doped superconducting dome at *D* = −1.47 V/nm. **i**-**l**, The measured differential resistance d*V*_{xx}/d*I*_{dc} at *T* = 20 mK as a function of *n* and dc bias current *I*_{dc} 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 previously^{20} 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 WSe_{2} 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/WSe_{2} at negative *D* fields.

**a**, **b**, *R*_{xx} 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 *R*_{xx} (1/*B*_{⊥}) versus *n* and *f*_{ν} 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 *R*_{xx} 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**, *R*_{xx} 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 PIP_{2} 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/WSe_{2} at *D* = 1.19 V/nm.

**a**, *R*_{xx}-*D*-*n* map of hole-doped BBG/WSe_{2} within a narrower *n*, *D* range. Apart from the superconducting region described in the main text, another region with reduced *R*_{xx} 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 *R*_{xx} versus *n* on the hole-doping side at *D* = 1.19 V/nm. The additional resistance dip at about 0.56 × 10^{12 }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**, *R*_{xx} versus *n* and *B*_{⊥} at *D* = 1.19 V/nm on the hole-doping side. **d**, FFT of *R*_{xx} (1/*B*_{⊥}) versus *n* and *f*_{ν} at *D* = 1.19 V/nm on the hole-doping side. The FFT analysis is performed based on the *R*_{xx} data within 0.2 T < *B*_{⊥} < 1.2 T. A spin- and valley-polarized state with *f*_{ν} = 1 emerges at *n* ≈ −0.4 to −0.45 × 10^{12 }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 PIP_{1} phase). Further increasing hole densities, the PIP_{1} phase transits into the trigonal-warping phase with the Ising SOC-induced spin splitting (*f*_{ν}^{(1)} > 1/12 and *f*_{ν}^{(2)} < 1/12) until *n* ≈ −0.75 × 10^{12 }cm^{−2}. The observed additional *R*_{xx} dip locates in between of the PIP_{1} 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 PIP_{2} phase, corresponding to a partial isospin-polarized phase with two major Fermi pockets and multiple minor Fermi pockets. Further increasing hole doping beyond the PIP_{2} phase, the system evolves into a state with four annular Fermi surfaces, which is evident by two FFT frequency peaks satisfying *f*_{ν}^{(1)} - *f*_{ν}^{(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 *f*_{ν} 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 *f*_{ν} is calculated by the fraction *S*_{i}/*S*, where *S*_{i} is area of the ith Fermi pocket and *S* = (2π)^{2}|*n*|. The background colours distinguish different patterns of *f*_{ν}. 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 *λ*_{I} 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) × 10^{12 }cm^{−2}, respectively.

### Extended Data Fig. 7 Fermi surface analysis at *D* = ± 1.1 V/nm on the electron-doping side.

**a**, **b**, *R*_{xx} 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 *R*_{xx} (1/*B*_{⊥}) versus *n* and *f*_{ν} 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 *R*_{xx} 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 PIP_{1} phase is absent, and the electron density range of the PIP_{2} phase become much narrower at *D* = ± 1.1 V/nm. **e**, **f**, *R*_{xx} 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**, *R*_{xx} 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 *R*_{xx} (1/*B*_{⊥}) versus *n* and *f*_{ν} 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 *R*_{xx} 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**, *R*_{xx} 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**, *R*_{xx} as a function of *T* and *B*_{∥} at *n* = −0.53 × 10^{12 }cm^{−2} (**a**), *n* = −0.55 × 10^{12 }cm^{−2} (**b**), and *n* = −0.59 × 10^{12 }cm^{−2} (**c**) for *D* = 0.96 V/nm. **d**–**f**, *R*_{xx} as a function of *T* and *B*_{∥} at *n* = 0.9 × 10^{12 }cm^{−2} (**d**), *n* = 0.89 × 10^{12} cm^{−2} (**e**) and *n* = 0.87 × 10^{12 }cm^{−2} (**f**) for *D* = −1.64 V/nm. The opaque circles in each panel depict the critical in-plane magnetic field *B*_{c∥} as a function of *T*, where the *B*_{c∥} is defined as the field where *R*_{xx} 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−(*B*_{c||}/\({B}_{{c||}}^{0}\))^{2}. The green markers indicate the Pauli-limit field *B*_{P}. Blue lines are plotted based on the formula *T* /\({T}_{c}^{0}\) = 1− (*B*_{c∥}^{2}/*B*_{P} *B*_{SOC}) for an Ising superconductor, where *B*_{SOC} 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 studies^{20,21}. 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**, *R*_{xx} 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 × 10^{12 }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 \({B}_{{c||}}^{0}\)/*B*_{p} 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 \({B}_{{c||}}^{0}\)/*B*_{p} 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/WSe_{2} 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**, *R*_{xx} 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 *B*_{c⊥} 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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