In the presence of a large perpendicular electric field, Bernal-stacked bilayer graphene (BLG) features several broken-symmetry metallic phases [1][2][3] as well as magnetic-field-induced superconductivity 1 . The superconducting state is quite fragile, however, appearing only in a narrow window of density and with a maximum critical temperature T c ≈ 30 mK. Here we show that placing monolayer tungsten diselenide (WSe 2 ) on BLG promotes Cooper pairing to an extraordinary degree: superconductivity appears at zero magnetic field, exhibits an order of magnitude enhancement in T c and occurs over a density range that is wider by a factor of eight. By mapping quantum oscillations in BLG-WSe 2 as a function of electric field and doping, we establish that superconductivity emerges throughout a region for which the normal state is polarized, with two out of four spin-valley flavours predominantly populated. In-plane magnetic field measurements further reveal that superconductivity in BLG-WSe 2 can exhibit striking dependence of the critical field on doping, with the Chandrasekhar-Clogston (Pauli) limit roughly obeyed on one end of the superconducting dome, yet sharply violated on the other. Moreover, the superconductivity arises only for perpendicular electric fields that push BLG hole wavefunctions towards WSe 2 , indicating that proximity-induced (Ising) spin-orbit coupling plays a key role in stabilizing the pairing. Our results pave the way for engineering robust, highly tunable and ultra-clean graphene-based superconductors.

Strong interactions between electrons often lead to a rich competition of symmetry-breaking phases throughout the parameter space. This competition can be substantially altered by external perturbations that lower the energy for one of the phases at the expense of the others. One recent example of such a phase diagram modification occurs in magic-angle twisted bilayer graphene (BLG) 4 aligned with hexagonal boron nitride (hBN), in which sublattice polarization stabilizes a Chern insulating phase near a filling of three electrons per moiré unit cell at the expense of suppressing superconductivity 5,6 . Here we investigate the symmetry-broken phases in Bernal-stacked BLG coupled to a WSe 2 monolayer and show that the phase diagram is altered such that superconductivity is strongly enhanced.

Figure 1a shows the BLG-WSe 2 stack, whereas Fig. 1b displays the corresponding valence bands in the presence of a perpendicular electric displacement field (D), taking into account induced spin-orbit coupling (SOC) by WSe 2 . In a finite D field, BLG features a bandgap at charge neutrality 7,8 , trigonal warping 9 and prominent Van Hove singularities (VHS) near the weakly dispersive band edge. Owing to the large density of states, interactions between electrons are greatly amplified when the chemical potential crosses the VHS. In addition, a finite D field substantially polarizes the low-energy electronic wavefunctions 7,9 (Fig. 1b insets) towards the top or bottom layers and on different sublattices A and B. When combined with WSe 2 placed on one side, BLG becomes an ideal platform for probing the interplay between electronic correlations [1][2][3] and induced SOC [10][11][12][13][14][15][16] .

Longitudinal resistance R xx measured as a function of carrier density n and D at zero magnetic field shows peaks or dips that emerge and separate from each other as |D| is increased (Fig. 1c). These features can be associated with an interplay of Lifshitz transitions and breaking of spin and valley symmetries, similar to the case of hBN-encapsulated BLG 1 . Importantly, the resulting phase diagram is strongly asymmetric with respect to the sign of D field. Focusing on hole doping, for both signs of D, the largest resistance peaks (red diagonal regions in Fig. 1c) correspond to phases that possess a single spin-valley flavour-polarized Fermi surface, which we denote as FP(1) ± (FP(m) denotes a flavour-polarized phase with m degenerate Fermi pockets and ± denotes the sign of D; see Extended Data Fig. 1 for the identification of spin-valley degeneracy). For positive D, this resistive feature spans beyond D/ϵ 0 = +1 V nm -1 , but is suppressed by D/ϵ 0 = -0.75 V nm -1 for negative D, where ϵ 0 is the vacuum permittivity.

The pronounced ±D asymmetry highlights the role of Ising SOC in defining the phase diagram of BLG-WSe 2 . Theoretical calculations 11,12 (Fig. 1b) confirm that Ising SOC is induced only on the top layer proximate to WSe 2 and that, correspondingly, the SOC-induced spin splitting in the valence band is largely restricted to D > 0, consistent with the D-asymmetric experimental data (Fig. 1c; see also Methods). By contrast, Rashba SOC is expected to produce splittings that are largely independent of the sign of D, and thus cannot account for the pronounced ±D asymmetry (see also Supplementary Information section 1).

The most striking difference in the BLG-WSe 2 phase diagram between positive and negative D fields is the emergence of a broad superconducting region at D > 0 (see Extended Data Figs. 234for additional data on other devices). No analogous region has been observed in hBN-encapsulated BLG, in which superconductivity only appears in a finite in-plane magnetic field 1 . The critical current of the zero-magnetic-field superconductivity in BLG-WSe 2 exhibits non-trivial doping dependence (Fig. 1d,e), with two distinct maxima (the larger of which reaches 20 nA). By contrast, at D < 0 a different phase (Fig. 1e,f) exhibiting highly nonlinear current-dependent resistance is observed for similar values of n and |D| (marked by a green arrow in Fig. 1c). This resistive phase is suppressed by small magnetic fields and is similar to the previously reported zero-magnetic-field phase 1 .

The evolution of critical temperature T c with n and D provides further insights into the superconducting phase (Fig. 2a-c). The superconducting dome occupies a wide range of doping (approximately 2 × 10 11 cm -2 ; see also Fig. 1c) and features a maximal T c of approximately 300 mK. Figure 2d shows R xx line cuts at different temperatures; insets show nonlinear current-voltage (I-V) curves at optimal doping, yielding a Berezinskii-Kosterlitz-Thouless (BKT) transition temperature T BKT ≈ 260 mK (estimated by the temperature where V ∝ I 3 ). We emphasize that the superconducting critical temperature observed here is an order of magnitude larger than the T c in hBN-encapsulated BLG. Moreover, the relatively high T c does not appear to be sensitive to minor changes of D field, further substantiating the robustness of the superconducting phase. Figure 2e,f shows the evolution of the superconducting phase in the presence of an out-of-plane magnetic field B ⟂ . The maximal critical field B c⟂ ≈ 15 mT at base temperature yields a corresponding Ginzburg-Landau coherence length ξ Φ B = /(2π ) ≈ 150 nm GL 0 c ⊥ (Φ 0 is the superconductor flux quantum), and the mean free path ℓ mf of BLG-WSe 2 is around 10 µm (see Methods and Extended Data Fig. 5). Superconductivity thus resides deep in the clean limit, ξ GL /ℓ mf < 0.02 similar to the case of hBN-encapsulated BLG and rhombohedral trilayer graphene 1,17 . Another prominent feature of both the T and B ⟂ field dependence (Fig. 2a-c,f) is a resistive peak that intersects the superconducting dome, effectively splitting it into two regions within a certain range of D fields (note the grey arrow in Fig. 1c). This peak signals the presence of another phase that appears to compete with superconductivity. Both the doping range in which this state occurs and its disappearance at relatively low magnetic fields are features shared by the resistive phase observed for D < 0 (see the green arrow in Fig. 1c) and in hBN-encapsulated BLG 1 . Moreover, both the resistive peak and superconductivity feature a broken-symmetry parent state with two large and emerging small Fermi pockets (see discussion below), indicating that transport in this region is highly sensitive to the exact details of the spin-valley ground states (see Extended Data Fig. 6 and Supplementary Information section 5 for possible competition between the ground states).

The D-field asymmetry is further highlighted by low field (B ⟂ < 1 T) quantum oscillations measured at D/ϵ 0 = 1 V nm -1 and -1 V nm -1 , which imply distinct Fermi surface structures within the superconductivity region for D > 0 (Fig. 3a,c,e) and within the resistive phase for D < 0 (Fig. 3b,d,f). Fourier transforms of the oscillations, taken with respect to 1/B ⟂ , reveal the phases in the relevant doping ranges. To resolve the relative sizes of the Fermi pockets of the different flavour-polarized phases, the Fourier transform of R xx (1/B ⟂ ) at low magnetic fields (0.05 T < B ⟂ < 0.6 T) is normalized by the frequency corresponding to the full doping density, f norm = n × h/e, so that the resulting frequency f ν reveals the fraction of the total Fermi surface area enclosed by a cyclotron orbit (Fig. 3c,d). Here, h is Planck's constant and e the electron charge.

At D/ϵ 0 = -1 V nm -1 , the resulting phase diagram is remarkably similar to that reported on hBN-encapsulated BLG without WSe 2 (ref. 1 ; see also Extended Data Fig. 7). In addition to the zero-field resistive phase discussed before (Fig. 1f), at low densities (|n| < 6 × 10 11 cm -2 ) we observe a Fourier transform peak at f ν = 1/12 (along with its higher harmonics) corresponding to a spin-valley symmetric phase with 12 degenerate Fermi pockets produced by trigonal warping (denoted as Sym(12) -). Upon further hole doping, BLG transitions into another phase with two frequency peaks at f ν (1) < 1/2 and f ν

. This phase can be identified as a spin-valley flavour-polarized phase, denoted FP(2, 2) -, with two majority ( f ν (1) < 1/2) and two minority ( f ν (2) < 1/12) flavours. The resemblance between our D < 0 data and hBN-encapsulated BLG 1 indicates that SOC does not play a major role for D < 0.

At D/ϵ 0 = 1 V nm -1 (Fig. 3c,e), at which the wavefunctions are strongly polarized towards WSe 2 , we see a few notable differences (see also Extended Data Fig. 8). First, at low densities, one of the Fourier frequency peaks clearly appears below f ν = 1/12, indicating the existence of Fermi surfaces for which the occupancy is smaller relative to Sym( 12) -. As we can identify two independent frequencies in this region, we denote this phase as FP(6, 6) + , with six bigger and six smaller Fermi pockets. The explicit flavour polarization here probably originates from spin-orbit-induced band splitting. Second, the transition between the FP(6, 6) + phase and the adjacent FP(2, 2) + phase (with two big and two small Fermi pockets) occurs at a lower hole density of |n| = 5 × 10 11 cm -2 . Finally, we observe that superconductivity is established throughout the FP(2, 2) + phase (except a small region where it competes with the resistive phase) ending on the high doping side with the onset of another complex flavour-polarized phase characterized by the occurrence of additional frequency peaks (Fig. 3c,e; see also Supplementary Information section 5). Importantly, in FP(2, 2) + , as for FP(2, 2) -, we find that f f

. Given the non-interacting band structure of Fig. 1b, this observation implies that the carriers in each minority flavour are spontaneously polarized to one of the trigonally warped pockets, pointing towards nematic order 18,19 (Fig. 4d,e).

In-plane magnetic field measurements further illuminate the unconventional nature of superconductivity in BLG-WSe 2 (Fig. 4 and Extended Data Fig. 9). Figure 4a shows R xx as a function of density n and in-plane magnetic field B ∥ for the superconducting region (dark blue) at D/ϵ 0 = 1.1 V nm -1 . When approaching the superconductivity from low densities |n|, the in-plane critical field B c∥ quickly reaches a maximum near the phase boundary separating FP(2, 2) + and FP(6, 6) + , and then slowly decreases with further hole doping. Conversely, the critical temperature measured at zero B ∥ field, T c 0 (red open circles), shows a more symmetric dome shape with a maximum at higher |n|. The interplay between B c∥ and T c 0 indicates that the violation of the Pauli limit

0 for a weak-coupling spin-singlet Bardeen-Cooper-Schrieffer (BCS) superconductor with g-factor g = 2) varies with doping. , strongly violating the Pauli limit. Overall the PVR changes from roughly six to one as the doping is increased (Fig. 4c; see also Extended Data Fig. 9f). Note that the PVR values at the phase boundaries represent a lower limit owing to possible imperfect in-plane alignment of the sample (Methods).

The large PVR of B c∥ /B p ≈ 6 on the low hole doping side of the superconducting dome evokes the phenomenology of Ising superconductivity observed in transition metal dichalcogenides [20][21][22] . Ising superconductivity refers to a scenario in which pairing connects time-reversed states, for example, k, ↑⟩ | and | k -,↓⟩ (with k being the wavevector), with spins oriented along a fixed quantization axis selected by Ising SOC. Here, the Ising SOC strength λ I ≈ 0.7 meV, estimated from quantum Hall measurements at small D (see Methods and Extended Data Fig. 10), far exceeds the superconducting gap Δ = 0.76k B T c ≈ 0.02 meV (k B is the Boltzmann constant) estimated from weak-coupling BCS scaling. The resulting Cooper pairs enjoy resilience against in-plane fields that rotate the spins away from this preferred axis, naturally leading to substantial Pauli-limit violation as measured on the low hole doping side of the dome. The substantial PVR reduction for higher hole doping is more puzzling and implies that the ground state cannot evolve into a predominantly spin or spin-valley polarized (SVP) phase. This reduction could emerge from a doping-dependent change in the flavour polarization of the parent FP(2, 2) + state (see below and Supplementary Information section 7) or in-plane depairing effects (or the interplay between the two). As proof of concept, we consider a simple model that incorporates two depairing mechanisms: Rashba SOC (which favours in-plane spin orientation; see Methods) and orbital in-plane magnetic field effects, both of which compete with the Ising SOC and suppress the PVR (Supplementary Information sections 9 and 10 for details). The solution of a self-consistent superconducting gap equation for this model captures the observed PVR evolution (Fig. 4c inset and Extended Data Fig. 11) provided that the effective Rashba spin splitting increases with hole density, which may be expected if superconductivity arises from minority Fermi pockets that grow with hole doping. 11 and Supplementary Information section 10). d,e, Fermi surfaces of the FP(2, 2) + phase with Ising SOC and nematic order (d), or allowing for IVC order (e). Dashed Fermi pockets correspond to the condition that nematic order is absent. f, Schematics of a proposed scenario in which Ising SOC tilts the energy balance towards IVC order, within which the development of superconductivity is more favoured at the expense of a state which is not conducive to pairing, for example, a valley polarized (VP) state.

The extended superconducting phase space in BLG-WSe 2 clearly contrasts observations in hBN-encapsulated bilayer and trilayer graphene 1,17 , in which superconductivity occurs only within a narrow density range around the symmetry-broken phase boundaries. Moreover, the coincidence of the doping range exhibiting superconductivity with the FP(2, 2) + phase (Fig. 3c,e) at D > 0 strongly hints that (1) superconductivity descends from the latter broken-symmetry parent state and (2) SOC plays a key role in selecting a symmetry-breaking order conducive to pairing. These observations constrain the possible mechanisms that can lead to T c enhancement 23,24 (Methods). Figure 4f depicts a phenomenologically motivated scenario wherein multiple nearly degenerate broken-symmetry orders compete. If the FP(2, 2) + phase is, for example, valley polarized in the absence of SOC, then broken inversion and time-reversal symmetries would heavily disfavour pairing, consistent with the absence of superconductivity in BLG-WSe 2 at D < 0 and hBN-encapsulated BLG at zero magnetic field 1 . Turning on Ising SOC could then tip the balance in favour of orders that facilitate Cooper pairing. One candidate for this parent state is a primarily spin-valley polarized phase arising because of an interaction-enhanced Ising SOC strength (Supplementary Information sections 5 and 7); however, superconductivity emerging from such a state would exhibit a much larger Pauli-limit violation, which would vary far less with doping (Supplementary Information sections 8-10). We suggest instead that Ising SOC can promote inter-valley coherent (IVC) order that is also amenable to pairing while maintaining compatibility with observed trends (Supplementary Information section 7).

The nature of superconductivity in graphene-based systems-both moiré and crystalline [25][26][27][28][29][30][31] -presents an ongoing puzzle. The enticing general similarity between BLG-WSe 2 and moiré graphene superlattices (with WSe 2 32,33 or without [34][35][36][37][38] ) can be noticed, as in both systems superconductivity appears intimately connected to the symmetry-broken state in which two out of four spin-valley flavours are predominately populated. Future efforts are needed to address the origin of apparent striking distinctions between different superconducting phases in graphene systems. Finally, induced SOC 16,39,40 along with other parameters such as virtual tunnelling 24 depends on the relative orientation of WSe 2 (or other transition metal dichalcogenides) and graphene, and is thus tunable-providing a rich landscape for further explorations.

Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-022-05446-x.

All the devices have a dual-graphite gate structure with graphite electrodes and were assembled as follows. First, a thin hBN flake (10-30 nm) is picked up by using a propylene carbonate film previously placed on a polydimethylsiloxane stamp. Then, the hBN flake is used to pick up crystals in the sequence of graphite top gate, top hBN dielectric, an exfoliated monolayer of WSe 2 (commercial source, HQ graphene), BLG, graphite electrodes, bottom hBN dielectric and graphite bottom gate. Care was taken to approach and pick up each flake slowly. In the last step, the whole stack is dropped onto a Si/SiO 2 substrate at 150 °C whereas the propylene carbonate is released at 180 °C. The propylene carbonate is then cleaned off with N-methyl-2-pyrrolidinone. The final geometry is defined by dry etching with a CHF 3 /O 2 plasma and deposition of ohmic edge contacts (Ti/Au, 5 nm/100 nm); see Extended Data Fig. 2.

All measurements were performed in a dilution refrigerator (Oxford Triton) with a base temperature of approximately 30 mK, by using standard low-frequency lock-in amplifier techniques. Unless otherwise specified, measurements were taken at the base temperature. Frequencies of the lock-in amplifiers (Stanford Research, models 865a) were kept in the range of 7-40 Hz to reduce the electronic noise and measure the device's d.c. properties. The a.c. excitation was kept at less than 5 nA (most measurements were taken at 0.5-1 nA to preserve the linearity of the system and avoid disturbing the fragile states at low temperatures). Each of the d.c. fridge lines pass through cold filters, including 4 pi filters that filter out a range from approximately 80 MHz to more than 10 GHz, as well as a two-pole resistor-capacitor low-pass filter. Top-gate voltage (v t ) and bottom-gate voltage (v b ) are swept to adjust doping density n = (c t v t + c b v b )/e and displacement field D = (c t v t - c b v b )/2, where c t and c b are top-and bottom-gate capacitance per area calculated from the Landau fan diagram. Note that following this conversion, we observe a small intrinsic D-field offset (D/ϵ 0 ≈ 0.025 ± 0.005 V nm -1 ; Supplementary Fig. 1), which might be related to WSe 2 being placed on one side or asymmetry in top and bottom hBN thicknesses.

Extended Data Figure 2b,c shows optical images of BLG-WSe 2 devices. We use a dual-graphite gate structure to minimize charge disorder 41 . Superconductivity and symmetry-breaking features are exactly the same between different contacts in one device (Extended Data Fig. 2d,e), owing to the exceptionally high quality of crystalline graphene. Contacts 1-3 of the first device D1 were used for the measurements in the main text. Extended Data Figures 234show enhanced superconductivity from three other devices. We found that superconductivity occasionally onsets at a larger D field (D/ϵ 0 ≳ 1 V nm -1 ) with another flavour-polarized parent state (FP(2, m > 2) + ). Slight differences between the devices could originate from different SOC strengths 16,39,40 induced by WSe 2 ; see below for further discussion. We measured seven BLG-WSe 2 devices in total, and in five we observed zero-magnetic-field superconductivity. The measurements in the other two devices were limited to |D|/ϵ 0 ≤ 1 V nm -1 ; on the basis of the phase diagram obtained in the accessible range of D, we speculate that they would also exhibit superconductivity for larger positive D. Finally, we emphasize that none of the measured devices showed zero-magnetic-field superconductivity for D < 0 down to D/ϵ 0 = -1 V nm -1 (and in some instances to D/ϵ 0 = -1.1 V nm -1 ).

BLG-WSe 2 realizes rather complex spin-valley flavour-polarized phases for both positive and negative D fields (Extended Data Figs. 1, 7 and 8). We argue that the D < 0 phase diagram is similar to that of hBN-encapsulated BLG, whereas the D > 0 phase diagram has essential differences associated with the interplay between SOC and strong correlations.

For D < 0, at low |D| and high |n|, FFT shows a prominent peak at f ν = 1/4 corresponding to a flavour-symmetric phase that preserves the fourfold spin-valley degeneracy (Sym(4) -; Extended Data Fig. 1m). The spin-valley symmetry still holds for high |D| and low |n|, but smaller Fermi pockets are produced by trigonal warping within each flavour, and therefore the system is flavour-symmetric with f ν = 1/12 (Sym(12) -; Extended Data Fig. 1k). As mentioned in the main text, the diagonal largest-resistance region is a single spin-valley flavour-polarized phase (FP(1) -; Extended Data Fig. 1i) that peaks at f ν = 1. The remaining flavourpolarized phases have multiple Fermi pockets with distinct Fermi surface areas. At slightly higher |n| adjacent to FP(1) -, the FFT in the region exhibits peaks around f < 1

. This is a flavour-polarized phase with one majority flavour and one (or more) small Fermi pocket (FP(1, 1) -). At the region we observed the nonlinear resistive phase, the Fermi surface has two frequency peaks near

, and corresponds to a flavour-polarized phase with two majority (

) and two minority (

) flavours (FP(2, 2) -; Extended Data Fig. 1j). At lower |n| next to FP(2, 2) -, a flavoursymmetric phase emerges with 12 trigonally warped pockets (Sym(12) -; Extended Data Fig. 1l).

At D > 0, by contrast, the spin degeneracy in each valley is explicitly lifted by Ising SOC (Fig. 1b). At high D and low |n|, instead of showing frequency at f ν = 1/12, quantum oscillations at the band edge exhibit a peak around f ν = 1/6 (Extended Data Fig. 1f), and this is consistent with Ising-induced spin splitting such that holes are from small trigonally warped Fermi pockets of single spin species in each valley (FP(6) + ). The region next to FP(2, 2) + also shows different frequencies (FP (6, 6) + ; Extended Data Fig. 1g): this can be attributed to Isinginduced band splitting with one spin more filled ( f > 1/12

) and another spin less filled ( f < 1/12

) in each valley. Flavour-polarized phases, such as FP(1) + , FP(1, 1) + and FP(2, 2) + (Extended Data Fig. 1c,d,e), are overall not changed much in terms of FFT frequencies, although spin-valley configurations are most likely different from the D < 0 cases. We note that the ±D asymmetry of the phase diagram is reflected in both D and n for which flavour-polarized phases extend or onset. Focusing on FP(1) ± , besides the asymmetric D extension mentioned in the main text, FP(1) + also onsets at a lower |n| compared with FP(1) - at the same |D|. This is consistent with the picture of Ising SOC. With proximitized Ising SOC at +D, the two spin species in each valley are split in energy: one moves up and the other moves down. Therefore, one spin in each valley is preferentially filled compared with the other, which makes it easier (at lower |n|) to reach the VHS and to trigger flavour polarization.

As discussed in the previous section, at D < 0 the symmetry-broken phases resemble those observed in hBN-encapsulated BLG. In FP(2, 2) -, we observed the resistive phase showing nonlinear critical current behaviour (Fig. 1f) at zero magnetic field. The similarity is also supported by fan diagrams and FFT (Extended Data Figs. 1 and7) as flavour-symmetric and flavour-polarized states observed in hBN-encapsulated BLG are well reproduced at D < 0. However, we did not observe superconductivity with finite in-plane magnetic field at D < 0. The absence of field-induced superconductivity in this regime may reflect a slightly higher electron temperature (approximately 30 mK) and small in-plane-field misalignment. We thus cannot rule out the onset of superconductivity upon more careful characterization. Alternatively, Rashba SOC (which contrary to Ising SOC need not be suppressed at D < 0) is expected to compete against spin polarization favoured by an in-plane field, thus potentially precluding field-induced superconductivity.

The mean free path ℓ mf of BLG-WSe 2 is around 10 µm. Extended Data Figure 5a shows non-local resistance R nl as a function of n and B ⟂ for D/ϵ 0 = 0.6 V nm -1 measured with the configuration shown in Extended Data Fig. 5c. Data at density n = -7 × 10 11 cm -2 show a pronounced feature around B ⟂ ≈ 20 mT, which indicates a transverse magnetic focusing 42 that is comparable with the electrodes separation of 5 µm, and translates to a mean free path ℓ mf ≳ πL/2 ≈ 7.9 µm. The magnetic focusing feature appears over wide density ranges, including the density (approximately -3 × 10 11 cm -2 ) at which superconductivity is observed at this D field.

In-plane field measurements were performed by mounting the sample vertically with a homemade frame. It is inevitable to introduce a small B ⟂ component when the B ∥ field is applied owing to the imperfect vertical sample alignment. Transverse magnetic focusing in B ∥ is a reliable measurement for the angle misalignment as the cyclotron orbits only couple to the B ⟂ component. Extended Data Figure 5b shows R nl as a function of n and B ∥ . The B ∥ plot qualitatively matches the B ⟂ plot (Extended Data Fig. 5a) except for the scaling of the B field axis. The R nl peak feature that appears at B ⟂ ≈ 20 mT roughly matches the same feature in the in-plane field at B ∥ ≈ 7 T. This indicates an in-plane-field misalignment angle θ mis ≈ tan -1 (20 mT/7 T) ≈ 0.16°.

Such angle misalignment results in an underestimation of in-plane critical field at regions where B c⟂ is small, that is, near the phase boundaries. Extended Data Figure 9c shows R xx versus n and B ∥ measured at D/ϵ 0 ≈ 1 V nm -1 . At the phase boundary between FP(6, 6) + and FP(2, 2) + (n ≈ -5 × 10 11 cm -2 ), superconductivity disappears around B ∥ = 0.7 T, which indicates an out-of-plane field component B ⟂ = 0.7 T × tan(0.16°) ≈ 2 mT. The B ⟂ = 2 mT component roughly matches B c⟂ at the same density (Fig. 2f). Therefore, we conclude that the PVR around the phase boundaries in Fig. 4c only serves as a lower limit as B c⟂ is rather low at the relevant densities; hence B ⟂ is a main driver for superconductivity suppression at those regions. By contrast, at the density range at which B c∥ is roughly consistent with the Pauli limit (higher |n|), superconductivity shows much higher B c⟂ (Fig. 2f). The suppression of superconductivity is then mainly caused by B ∥ at higher |n|.

In the main text, we show that the asymmetric n-D phase diagram provides strong evidence of Ising SOC. Quantum oscillations of the noninteracting phases at D > 0 further support the existence of Ising SOC (Extended Data Fig. 1 and10). To quantify WSe 2 -induced Ising SOC, we probe the octet zeroth Landau level (LL) in BLG, as few-meV-scale Ising SOC can rearrange the energies of these states. Note that these LL energies are not sensitive to Rashba SOC 13 . Previous experiments 14,15 have shown that one can quantify the Ising SOC H λτ s = z z I 1 2 I (λ I is the Ising SOC strength, and τ z and s z are Puali matrices in the valley and spin space, respectively) with LLs on opposite graphene layers: the sets of two LLs that cross at ν = ±3 filling factors have opposite layer polarization, such that their energy difference (at zero D) is given by ΔE = E Z ± λ I /2 (E Z is the Zeeman gap between spin-up and spin-down LLs)-only one of the two LLs (with layer polarization close to the WSe 2 ) is affected by the Ising SOC. Therefore, the critical field B* ⊥ that makes ΔE vanish is

I (with μ B being the Bohr magneton). In Extended Data Fig. 10a-e, B* ≈ 3T ⊥ is the magnetic field at which yellow and green arrows level at the same D, yielding λ I ≈ 0.7 meV.

Independently, λ I can also be extracted from the doping-dependent FFT splitting of quantum oscillations. The inset of Extended Data Fig. 10h shows the FFT splitting B split as a function of doping at D/ϵ 0 = 0.2 V nm -1 . Ising-type splitting is suppressed with increasing |n|, in contrast to Rashba-type splitting, which increases with increasing |n|. The observed splitting is consistent with the value of λ I ≈ 0.7 meV extracted from the quantum Hall measurements, as shown in the inset of Extended Data Fig. 10h by comparing it to the band splitting predicted from the band structure calculations at the same D field. This method is, however, less clean than the LL extraction, because Rashba SOC additionally contributes to a spin splitting for both signs of D (see below).

The effect of Rashba SOC is more subtle in the experiment. Quantum oscillations at higher B ⟂ field provide an upper bound on the Rashba SOC parameter λ R ≲ 4 meV, consistent with previous studies reporting λ R ranging from 1 to 15 meV (refs. 10,11,43,44 ). Extended Data Figure 10f-i shows ΔR xx versus 1/B ⟂ and the corresponding FFT measured at D/ϵ 0 = 0.2 V nm -1 and -0.1 V nm -1 , respectively. At D > 0 (Extended Data Fig. 10h), FFT reveals a frequency splitting, whereas at D < 0 the splitting is absent (Extended Data Fig. 10i). These observations are consistent with the interpretation that, at D > 0, the splitting is mainly caused by Ising SOC; however, at D < 0, the Ising effect is strongly diminished and the Rashba SOC strength λ R is not big enough to induce an observable splitting. The FFT peak at D < 0 (Extended Data Fig. 10i) has a full-width at half-maximum around 0.8 T, which translates to an upper bound for the bare Rashba SOC strength λ R ≲ 5 meV by comparing with the spin splitting predicted from band structure calculations at the same density n = -2 × 10 12 cm -2 and displacement field D/ϵ 0 = -0.1 V nm -1 . An upper bound on Rashba SOC can also be extracted from the observed spin splitting at positive D/ϵ 0 = 0.2 V nm -1 , assuming Ising SOC λ I = 0.7 meV (Extended Data Fig. 10h,inset). From this analysis we find an upper bound λ R ≲ 4 meV, roughly consistent with the bound from the negative D-field data.

Extended Data Figures 3 and4 show detailed measurements on two additional superconducting devices D3 and D4. Similar to the one in the main text, the two devices also show zero-magnetic-field enhanced superconductivity (T c ≈ 200 mK) in a wide density range. Key differences are that superconductivity onsets at larger D fields (D/ϵ 0 ≳ 1 V nm -1 ) and the flavour-polarized phase hosting superconductivity appears to have multiple minority Fermi pockets together with two majority pockets (denoted as FP(2, m > 2) + ). The variations of the correlated phases among different devices could originate from ground state selection by Ising SOC of different magnitudes; for example, the two additional devices D3 and D4 have Ising SOC λ I ≳ 1.6 meV, which is stronger than λ I = 0.7 meV for the device shown in the main text. The smaller SOC for device D1 shown in the main text may originate from the alignment between BLG and WSe 2 ; see Supplementary Fig. 2.

Experimentally, we observe enhanced superconductivity that develops at zero magnetic field and only for positive D fields, in which Ising SOC is clearly detected. No superconductivity is observed for the negative sign of D for which experimental signatures of SOC are diminished. Moreover, the magnetic field dependence of the superconducting phase is completely altered in comparison with the previously reported superconductivity in hBN-encapsulated BLG 1 . These observations strongly indicate that SOC plays a key role in the observation of enhanced superconductivity, although other effects are probably still relevant. In the following, we briefly discuss several other possible origins for the T c enhancement.

(1) Possible enhancement of T c due to screening. Screening of Coulomb interactions by WSe 2 would be expected to enhance T c if phonons were the pairing glue. However, this screening should be negligible in the case here for two reasons: (a) WSe 2 is an insulator and acts as a dielectric so no additional screening is expected from it; and (b) the graphene interlayer distance in BLG is less than 1 nm, which is much smaller compared with the typical interparticle distance at hole densities at which superconductivity is observed (approximately 15 nm). In this case, screening would be expected to act in a symmetric way in both layers of BLG (and thus for both signs of the D field), contrary to observations. We note that this line of arguments rules out the simplest case of screening of long-range Coulomb interactions whereas other, short-range terms, could still be possible (see also point (3)). ( 2) Modifications of phonon bands by WSe 2 . A change in the phonon spectrum is indeed to be expected, as was recently experimentally documented in WSe 2 -proximitized monolayer graphene 45 . There, the WSe 2 layer was found to dramatically increase the mobility of graphene at room temperature, which was interpreted to follow from gapping out the acoustic phonon modes. In this case, a simple BCS treatment of superconductivity mediated by acoustic phonons would predict a decrease in T c (assuming the phonon physics is similar for BLG). It may be possible to avoid this reduction if the pairing glue is frequency dependent, but strong constraints are expected in what kind of model can reproduce the data. (3) New types of attractive term mediated by virtual tunnelling to WSe 2 are also possible, as was explored in a recent theoretical work 24 . Such effects can contribute to an enhancement of T c , but do not explain which normal state is selected by interactions in the presence of SOC. (4) When doping WSe 2 , superconductivity originating from a dynamical screening of the Coulomb interaction could be realized with the 'slower' electron gas from WSe 2 acting as a retarded polarizable medium for the electrons in BLG, as was purposed in ref. 23 . Such a mechanism can result in a superconductivity with T c ≈ 100 mK the case of monolayer graphene-WSe 2 structure. However, there is no experimental signature indicating that WSe 2 is doped at the relevant doping range in the experiment.