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J. Díez-Mérida, A. Díez-Carlón, S. Y. Yang, Y.-M. Xie, X.-J. Gao, J. Senior, [K. Watanabe](https://orcid.org/0000-0003-3701-8119), [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), X. Lu, A. P. Higginbotham, K. T. Law, Dmitri K. Efetov

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[Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene](https://mdr.nims.go.jp/datasets/4196236e-390e-4d7d-a6ed-4cfc7872383d)

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Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer grapheneArticle https://doi.org/10.1038/s41467-023-38005-7Symmetry-broken Josephson junctions andsuperconducting diodes in magic-angletwisted bilayer grapheneJ. Díez-Mérida 1, A. Díez-Carlón 1, S. Y. Yang1, Y.-M. Xie 2, X.-J. Gao2,J. Senior 3, K. Watanabe 4, T. Taniguchi 4, X. Lu 1, A. P. Higginbotham 3,K. T. Law 2 & Dmitri K. Efetov 1The coexistence of gate-tunable superconducting, magnetic and topologicalorders in magic-angle twisted bilayer graphene provides opportunities for thecreation of hybrid Josephson junctions. Here we report the fabrication of gate-defined symmetry-broken Josephson junctions in magic-angle twisted bilayergraphene, where the weak link is gate-tuned close to the correlated insulatorstate with a moiré filling factor of υ = −2. We observe a phase-shifted andasymmetric Fraunhofer pattern with a pronounced magnetic hysteresis. Ourtheoretical calculations of the junction weak link—with valley polarization andorbital magnetization—explain most of these unconventional features. Theeffects persist up to the critical temperature of 3.5 K, with magnetic hysteresisobserved below 800mK.We showhow the combination ofmagnetization andits current-induced magnetization switching allows us to realise a program-mable zero-field superconducting diode. Our results represent a majoradvance towards the creation of future superconducting quantumelectronic devices.Electronic coupling between materials with competing ground statescan lead to the creation of exotic electronic phases. Of particularinterest are hetero-junctions between superconductors, magnets, andtopological insulators, where especially Josephson junctions (JJ)thereof have attracted formidable attention. Magnetic JJs allow spin-tronic applications through the creation of spin-filters1–5, spin-tripletsupercurrent6–8, and π junctions9–12, whereas topological JJs allowapplications in quantum information processing and in lossless elec-tronics, through the creation of 4π junctions13–15, superconductingdiodes16–18, and Majorana bounds states19. One major difficulty in thecreation of such JJs lies in the engineering of ultra-clean interfacesbetween the different material species, which is needed for efficientcoupling between different phases.A single, two-dimensional material that would host all of theseemergent phases at once, would overcome these issues. It wouldpermit to induce gate-defined, ultra-clean homojunction between allthe different phases, and so open up a new avenue for the creation of anew generation of superconducting electronics. The recently dis-covered quantum phases in the flat bands of θm~1.1° magic-angletwisted bilayer graphene (MATBG) include correlated insulators(CI)20–24, superconductors (SC)22,23,25–27, orbital magnets (OM)23,28,29, andinteraction induced correlated Chern insulators (CCI)30–34.Here, we demonstrate the creation of a symmetry-broken JJ in alocally gated MATBG device, when the weak link is set close to half-filling of the hole band. Remarkably, due to MATBG’s two-dimensionality and ultra-low carrier density, it is possible to use anelectrostatic gate to tune between the different phases, and inducereversible transitions between the SC, CCI, and OMphases35. Althoughthere have already been reports on the creation of MATBG JJs throughthe use of local gates36,37, JJs with the supercurrent mediated by theReceived: 16 January 2023Accepted: 6 April 2023Check for updates1ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Castelldefels, Barcelona 08860, Spain. 2Department of Physics,Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China. 3IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria. 4NationalInstitute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. e-mail: dmitri.efetov@physik.lmu.deNature Communications |         (2023) 14:2396 11234567890():,;1234567890():,;http://orcid.org/0000-0002-9811-4318http://orcid.org/0000-0002-9811-4318http://orcid.org/0000-0002-9811-4318http://orcid.org/0000-0002-9811-4318http://orcid.org/0000-0002-9811-4318http://orcid.org/0000-0001-8124-4549http://orcid.org/0000-0001-8124-4549http://orcid.org/0000-0001-8124-4549http://orcid.org/0000-0001-8124-4549http://orcid.org/0000-0001-8124-4549http://orcid.org/0000-0002-2902-4896http://orcid.org/0000-0002-2902-4896http://orcid.org/0000-0002-2902-4896http://orcid.org/0000-0002-2902-4896http://orcid.org/0000-0002-2902-4896http://orcid.org/0000-0002-0672-9295http://orcid.org/0000-0002-0672-9295http://orcid.org/0000-0002-0672-9295http://orcid.org/0000-0002-0672-9295http://orcid.org/0000-0002-0672-9295http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-3149-4755http://orcid.org/0000-0003-3149-4755http://orcid.org/0000-0003-3149-4755http://orcid.org/0000-0003-3149-4755http://orcid.org/0000-0003-3149-4755http://orcid.org/0000-0003-2607-2363http://orcid.org/0000-0003-2607-2363http://orcid.org/0000-0003-2607-2363http://orcid.org/0000-0003-2607-2363http://orcid.org/0000-0003-2607-2363http://orcid.org/0000-0003-0501-6290http://orcid.org/0000-0003-0501-6290http://orcid.org/0000-0003-0501-6290http://orcid.org/0000-0003-0501-6290http://orcid.org/0000-0003-0501-6290http://orcid.org/0000-0001-5862-0462http://orcid.org/0000-0001-5862-0462http://orcid.org/0000-0001-5862-0462http://orcid.org/0000-0001-5862-0462http://orcid.org/0000-0001-5862-0462http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-38005-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-38005-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-38005-7&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-38005-7&domain=pdfmailto:dmitri.efetov@physik.lmu.destrongly correlated magnetic or topological weak links have so far notbeen achieved.ResultsGate-defined JJThe device consists of a van der Waals (vdW) hetero-structure of gra-phite/hBN/MATBG/hBN/graphite, as shown in Fig. 1a.Metallic graphitelayers are capacitively coupled to the MATBG, through the insulatinghexagonal boron nitride layers (hBN) of ~10 nm thickness. The carrierdensity in theMATBG sheetn is electrostatically tunedby both top andbottom gates n =CBGVBG +CTGVTG where (CBG, CTG) are the respectivecapacitances and (VBG, VTG) gate voltages. In the center of the device,the top graphite layer is separated by a narrow channel of lengthd = 150nm, which creates a region in the MATBG that is almost notcoupled to the top gate, and whose carrier density is mainly set by theback gate voltage nJ ~ CBGVBG. Hence, by applying different values ofVBG and VTG, it is possible to locally vary the carrier concentration inthe channel region, which allows creating gate-defined junctions oflength dJ ~ 100 nm in the MATBG, as is confirmed by electrostaticsimulations and is highlighted in Fig. 1b.Figure 1c shows the 4-terminal longitudinal resistance Rxx as afunction of VBG (VTG = 0V) at base temperature T = 35mK, and fordifferent perpendicular magnetic fields B. From Hall and quantummagneto-oscillation measurements (see Methods) we extract a twist-angle of θ = 1.11° ± 0.02°. We observe well-pronounced CI states, whichgive rise to peaks of high resistance at integer electron and hole fillingsof themoiréunit cell, υ = +1, ±2, and +3, aswell as a SC state on thehole-doped side of υ = −2, with a critical temperature Tc ~ 3.5 K (see Supple-mentary Fig. 3). Overall the device shows a phasediagramwhich is verysimilar to previous reports of hBN non-alignedMATBG devices22,23,25,26,which is confirmed by examining the crystallographic edges (seeSupplementary Fig. 1).In order to create a JJ in the device, we control both (VBG, VTG) totune the n to nsc = −1.72 × 1012cm−2, where the SC state is at optimaldoping. By further changing (VBG, VTG) following the relationΔVBG = −(CTG/CBG)/ΔVTG, n can be kept constant, while the carrierdensity in the junction nJ is continuously tuned (see SupplementaryInformation for detailed dual-gate maps). This allows to tune thejunction region from a metallic (N) to a SC and into a CI state. Asthe length of the junction is in theorder ofmagnitude of the coherencelength of the SC dJ ~ ξ ~ 100 nm (see Supplementary Fig. 3), it is possibleto proximitize the junction and to create a JJ38.Figure 1d shows the differential longitudinal resistance dVxx/dIvs. source-drain current I and as a function of nJ, for a range of fillingswhich is centered around the SC state −3 < υ < −2. The upper panelshows the corresponding Rxx vs. nJ measurement which demon-strates the density ranges of the N, SC and CI states. For nJ = nsc, thedevice is uniformly in the SC state, and forms a SC/SC/SC junction,with an Ic > 200 nA. However, when nJ is tuned away from this point aSC/SC’/SC junction is created, where we observe a second setof coherence peaks with reduced Ic. For density ranges close toυ = −3, −2.2 × 1012cm−2≲ nJ≲ −1.86 × 1012cm−2, and close to υ = −2,−1.58 × 1012cm−2 ≳ nJ ≳−1.5 × 1012cm−2, the junction region is notintrinsically superconducting, but we still observe a supercurrent,which hints at the creation of a JJ. While close to υ = −3 the junction ismetallic and a SC/N/SC is formed, close to υ = −2 the junction is in thevicinity of the correlated insulator state making a SC/CI’/SC. Beyondthese density ranges we do not observe a supercurrent, however,distinct superconducting non-linearities remain, which are in-linewith Andreev reflections at the SC interfaces39.Fig. 1 | Gate-tunable JJ in MATBG. a Schematic of the measured device and mea-suring circuit, where Vbias is the source voltage, I is the current through the device,Vxx the voltage drop between the measurement probes, and VBG (VTG) correspondto the back (top) gate voltage. The top graphite gates are separated by 150nm.b Electrostatic simulation profile of carrier density n vs. position x, setting n andcarrier density in the junction nJ at different values with a junction length dJ of100nm. The inset shows a schematic of the MATBG JJ with two distinct regionscreated by the gating structure. c Four terminal longitudinal resistanceRxx vs.fillingfactor υ at different out-of-plane magnetic fields B from 0mT (black curve) to300mT (red curve). d (Top) Magnification of c around the superconducting state−3 < υ < −1.8, where we define three distinct regions with metallic (N),superconducting (SC), and correlated insulator (CI) behavior. (Bottom) dVxx=dI vs.I at different nJ, keeping n = −1.72 × 1012cm−2 in the SC state. Dashed green verticallines mark the position where nJ is no longer in the SC state. e Fraunhofer patternsmeasured at (left) nJ = −2 × 1012cm−2 (SC/N/SC), (center) −1.72 × 1012cm−2 (SC/SC/SC), and (right) −1.56 × 1012cm−2 (close to SC/CI/SC), respectively. The color dotsshow the corresponding nJ positions in the dVxx/dI vs. Imap in d bottom. f Positivecritical current Ic+ vs. B with B sweeping up (blue) and down (red). g dVxx/dI vs. I atB =0mT after applying a pre-magnetizing field BM= + 50 and −50mT for the redand blue curve. The shaded gray regions mark the values of current at which thediode behavior is observed.Article https://doi.org/10.1038/s41467-023-38005-7Nature Communications |         (2023) 14:2396 2Unconventional Fraunhofer pattern and superconducting diodeWe further analyze the various gate-induced junctions by applying anout-of-plane magnetic field B, where Fig. 1e shows the color maps ofdVxx/dI vs. I vs.B. For theuniformSC/SC/SC junction (center)weobservea diamond-shaped dependence, which is symmetric with the inversionof the current Ic+(B+)= Ic−(B+) and the B-field directions Ic+(B+)= Ic+(B−),where Ic+(Ic−) and B+(B−) correspond to the positive (negative) criticalcurrent and field. This behavior is in-line with previous reports on SCstates in MATBG22,23,25–27, with a critical magnetic field Bc2 ∼ 120mT. Theabsence of Fraunhofer oscillations confirms the uniformity of the junc-tion and the absence of a JJ. For both, the SC/N/SC (left) and SC/CI’/SC(right) junctions (taken at nJ as marked in Fig. 1d) we observe clearFraunhofer oscillations with oscillation periods that are consistent withexpectations for one flux quantum through the junction (see Supple-mentary Information) which unambiguously prove the formation of agate-defined JJ37,40. Here the SC/N/SC JJ displays a typical Fraunhoferpattern, which obeys the same symmetries along the I and B directionsas the pristine SC state. In stark contrast to this, the SC/CI’/SC JJ shows avery unusual Fraunhofer pattern, which is not symmetric with inversionof the current Ic+(B+)≠ Ic−(B+) and the B-field directions Ic+(B+)≠ Ic+(B−),which indicates time-reversal symmetry breaking. These asymmetriesare well seen in the line cuts in Fig. 1f, g which show Ic+ vs. B and dVxx/dIvs. Imeasurements respectively.Most strikingly, for bothmeasurementswe observe a hysteresis as a function of B-field direction. A direct con-sequence of the hysteresis in the dVxx/dI vs. I is its non-reciprocaltransport. This is demonstrated in Fig. 1g, where for a fixed current value|I|∼10–50nA the device can be superconducting in one current direc-tion, while highly resistive in the other. This behavior enables the crea-tion of a superconducting diode,which is the superconducting analog ofa p-n junction, and is highly sought after as a building block for super-conducting electronics. Since the magnetization direction can be swit-ched by a small field BM (red and blue lines in Fig. 1g), the polarity of thecurrent asymmetry can be switched, and the direction of the diodereversed, making it so programmable (see Supplementary Fig. 11). Wenow focus on the Fraunhofer pattern at the SC/CI’/SC position. First, westudy the behavior to highermagnetic fields, where we observe a revivalof the oscillations and the SC after a field of ±30mT (Fig. 2a), where theoscillations have completely decay and then reappear again. The doubleperiodicity suggests the presence of edge states giving rise to a SQUID-like type of behavior41. In order to better understand the origin of thesignal, we calculate a Fraunhofer pattern corresponding to a givencurrent density distribution in real space Ic(β)= ∣R1�1dx Js(x) eiβx| whereβ(B) is a normalized field along the length of the JJ and Js(x) is the realspace current density distribution42 (see Supplementary Information fordetails). By having a Js(x) combining edge and bulk states we can obtain apattern similar to the one observed in experiment (Fig. 2b, c). Startingfrom this combined bulk and edge supercurrent, we can also simulatethe other features of the pattern, mainly that the central lobes do notreach zero at the oscillation period and the asymmetries with respect tothefield and current directions. The fact that the lobes donot reach zerocan be understood by having asymmetric edges, which we can simplysimulate by attributing a different critical current to each edge. Theasymmetries in the field direction (Ic+(B+)≠ Ic+(B−)), however, require thatthe edges carry an extra phase different from the bulk. This phase acts asan effective magnetic field in the β parameter, substituting the field B asB=Bext+φ, where Bext is the externally applied field and φ the extraphase acquired by the sample (see Supplementary Information fordetails). Finally, in order to obtain themeasured current-field asymmetry(Ic+(B+)≠ Ic−(B+)) these phases have to change sign for opposite currentdirections. The final pattern plotted in Fig. 2b is obtained by makingφedge1≠φedge2 and sgn(φ(I +))= −sgn(φ(I−)). A second sample with twist-angle 1.04±0.02° has also been measured (device B). The Ic(B) behaviorof the new sample at the SC/CI’/SC position is shown in Fig. 2d. In thiscase we do not observe any asymmetries or hysteretic behavior, butthe sample displays clear SQUID-like oscillations. We can again modelthe pattern, in this case having a supercurrent which is purely carried byFig. 2 | Fraunhofer patterns emerging fromedge state supercurrent of device Aand B. a Fraunhofer pattern at the SC/CI’/SC position of sample A up to higher out-of-plane magnetic field B. A revival of the oscillations is observed after 30mT.b Calculated Ic(B) behavior based on the current density distribution shown in c. Acombination of edge and bulk supercurrent with non-symmetric edges havingdifferent phases φedge,n, where n = 1, 2 for the top and bottom edge respectively,such that φedge1(I >0) = −π/4, φedge1(I <0) =π/4 and φedge2 = −φedge1 give rise to aqualitatively similar pattern as measured in the experiment. c Current densitydistribution combining edge and bulk supercurrent. The inset shows a cartoondisplaying the superconducting TBG forming the JJ (SCTBG) in light green and theweak link with bulk and edge contribution in purple and violet, as well as thedifferent phases carried by the edges to calculate the pattern in b. d Fraunhoferpattern at the SC/CI’/SC position of sample B. The pattern resembles a patterncoming from purely edge supercurrent. e Calculated Ic(B) behavior based on thecurrent density distribution shown in f, in which all the supercurrent is carried bythe edges. f Current density distribution with only edge conduction. The insetshows a cartoon in which the current is only carried by edge states, withoutacquiring any extra phase.Article https://doi.org/10.1038/s41467-023-38005-7Nature Communications |         (2023) 14:2396 3the edge states, hinting that in device B theCI state has amore insulatingbulk than for device A. For both devicesweobserve how in the SC/CI’/SCconfiguration edge states play an important role carrying thesupercurrent.Magnetic JJNext, we analyze themagnetic signatures of device A.We first examinethe Fraunhofer pattern with the parameters of Fig. 1e (right) at anelevated temperature of T = 800mK, where the hysteretic behavior atweak magnetic field has not yet developed (Fig. 3a–c). In this regime,the Fraunhofer pattern has the following highly unconventional fea-tures: 1. The central peakof theFraunhofer pattern is shifted fromB = 0to a value of B ~2.5mT; 2. The Fraunhofer pattern is highly asymmetricwith respect to the central peak; 3. The critical current I +c does notvanish as a function of B; 4. Even more strikingly, when the currentdirection is reversed, a different Fraunhofer pattern is observed, andthe central peak is shifted as shown in Fig. 3d. AtB =0, for example, thecritical current is dramatically different for currents flowing in oppo-site directions. 5. The critical current shows a hysteresis and thedirectional dependence of the critical current appears only when thesystem is pre-magnetized by an external magnetic field larger than acoercive field of ~300mT (purple and orange lines in Fig. 3a). As noneof these features are observed in the SC/SC/SC and the SC/N/SCjunctions, we suggest that the CI state in the middle of the JJ is anunconventional insulating state responsible for the observed Fraun-hofer pattern. Qualitatively, the shift of the central peak, the breakingof the time-reversal symmetry condition Ic+(B+) = Ic+(B−) and the hys-teresis behavior all suggest that time-reversal symmetry is broken andthere is a spontaneous net magnetic flux which is responsible to movethe position of the central peak away from the B = 0 position. Fur-thermore, the observed behavior in Fig. 2 indicates that edge statesplay an important role in carrying the supercurrent. It is important tonote that the observed unconventional Fraunhofer patterns are highlyreproducible, i.e. we do not observe significant changes in the patternsafter several thermodynamic cycles of warming up and cooling downthe sample.The question is: Which microscopic state of MATBG near υ = −2can explain these? We propose below that the observed experimentalfeatures are consistentwith the assumption that theCI is an interactioninduced valley-polarized state with net orbital magnetization.This state has been previously identified at slightly elevatedmagnetic fields B > 300mT26, which is in good agreement with theobserved coercive field of the JJ. Moreover, the orbital magneticmoment of this state is huge ~6 µB (Bohr magneton)43 and produces anout-of-plane magnetic field of B ~ 3mT (see Supplementary Informa-tion for derivation). This is consistent with the experimentallyobtained phase shift of ΔB ~ 2.5mT. The phase shift of the Fraunhoferpattern survives up to the critical temperature of the JJ of Tc ~ 1 K, and iscomparable to the Curie temperature of previously observed orbitalmagnetic states in hBN aligned28,29 and non-aligned MATBG23,26 as wellas in twisted mono-bi graphene44,45. Finally, the valley-polarized statewith orbital magnetization is characterized by the presence of edgestates, which would arise as observed in the Fraunhofer patternsof Fig. 2.To further support this hypothesis, we construct a MATBG-basedJJ model by assuming the CI in the central region to be aFig. 3 | JJ with orbital magnetism. a dVxx/dI vs. I measured at B =0mT andT = 800mK right after cooldown (black) and after the samplehas been subjected totwo opposing pre-magnetizing fields BM. The curves are vertically shifted by 2.5 kΩeach for clarity. The inset shows a schematic of magnetizationM vs. B. The coloreddots correspond to the magnetic states in which the different dVxx/dI vs. I curveswere taken and the arrows describe the direction in which the field is swept.b Fraunhofer pattern with nJ = −1.56 × 1012cm−2 measured at 800mK. The whitedashed lines mark the 0 current and 0 field positions. c (Top) Positive criticalcurrent Ic+ vs. B at 800mK. The vertical dashed lines remark the shift of the Ic+maximumfromzerofield. (Bottom)Theoretical Ic+ vs.magneticflux (Φ) normalizedby the flux quantum (Φ0) calculated for a MATBG JJ with a valley-polarizedυ = −2 state as the weak link. The pattern has been shifted by +Φ0 to compare withthe experiment. d Experimental Ic+ and |Ic−| vs. B, extracted from b. Reversing thecurrent direction inverts the line-shape of the curve and changes the shift inmagnetic field. e Theoretical Ic+ and |Ic−| vs.Φ for aMATBG JJ with a valley-polarizedυ = −2 state as the weak link. To compare with the experiment, a shift of +Φ0 and+0.2Φ0 was added to Ic+ and |Ic−|, respectively.Article https://doi.org/10.1038/s41467-023-38005-7Nature Communications |         (2023) 14:2396 4valley-polarized state with net Chern number C = −2 at filling factorυ = −2, while the Chern bands are partially filled (see SupplementaryInformation for details). The superconducting part of the JJ is assumedto be a fully gapped superconductor with s-wave pairing. The theoryclearly reproduces the asymmetry with respect to the central peak ofthe unconventional Fraunhofer pattern (Fig. 3c). Unlike in the case of aconventional Fraunhofer pattern, it is asymmetric with respect to theB-field direction, where Ic(B+) > Ic(B−). We found that removing the C2Tbreaking terms will make the bands topologically trivial with no Berrycurvatures nor net orbital magnetic moments. In this case, a standardFraunhofer pattern is obtained (see Supplementary Information). Thissuggests that this behavior is a direct consequence of the electronicground state near υ = −2 carrying orbital magnetization. We can thensimulate the behavior of deviceBby setting the chemical potential intothe gap of the CI, equivalent to having a more insulating bulk (seeSupplementary Information), inwhich case the current is solely carriedby edge states, consistent with the results shown in Fig. 2. Therefore,the main features of both devices can be captured within thesame model.To explain the directional dependence of the critical current inFig. 3d, one extra assumption is needed. Namely, the current I ~ 10 nAcan induce orbital magnetization switching similar to the current-inducedorbitalmagnetization switching,which is observedat afillingofυ = 3 in MATBG28,29,44,46–48. In other words, a small current can overcomethe free energy barrier between two degenerate orbital magnetizationstates of the CI.With this assumption, which is furthermotivated by themodel of Fig. 2, the directional dependence of the critical current is wellexplained (Fig. 3e). In the case of device B, the fact that there is no bulkcurrent and the Ic is an order of magnitude smaller (∼5 nA vs. 80nA),could be the reason why no asymmetry is observed. However, furthertheoretical study is needed to understand the current-induced orbitalmagnetization switching in this C = −2 state.The Fraunhofer pattern of device A at low temperatures is evenmore intriguing. Figure 4a, b shows it for T = 500mK, where it ismeasured by sweeping the B-field up (a) and down (b). Strikingly, bothFraunhofer patterns show a phase jump (marked by an arrow), whichwas not observed at higher temperatures. Comparing the two Fraun-hofer patterns, one notices that they are phase-shifted, and overallsymmetric with respect to the reversal of the current and B-fielddirections, Ic+(B+,→) ~ Ic−(B−,←). Its phase jump is hysteretic and occurs atdifferent B-fields for the up (B→) and down(B←) sweeps. Such B-fieldhysteresis is better seen in the line cuts in Fig. 4c, which shows the Ic+(B)for both field sweeping directions at T = 800, 500, and 35mK. Here wedefineΔB as the difference between themaximaof the Ic+(B+) and Ic+(B−)sweeps. If we understand this hysteresis as the magnetization of thesample and plot its temperature dependence, we can fit it with a Curie-Bloch equation49ΔB∼ (1–T/Tc)α (Fig. 4d) obtaining a Curie temperatureTc ~750± 25mK and α ∼ 0.4 ±0.05.DiscussionBoth the hysteresis of Ic(B) and the phase jumps are prominent char-acteristics of ferromagnetic JJs3–5. The hysteresis is induced by aswitching of the magnetic orientation and the phase jumps are due tothe presence of domains switching at different field values. While theI-B asymmetry, indicative of orbital magnetism, continues to be pre-sent in the Fraunhofer pattern, the low T hysteretic features cannot befully explained by it. These appear at a lower temperature and requiretwo orders of magnitude lower switching field |BM| ≥ 3mT thanobserved for the valley-polarized state. Therefore, a further theoreticalexplanation is needed to explain these lower T features which have aclear distinct behavior.For now, we can just propose possible scenarios based on thedata. A first scenario would be to have both spin and valley polariza-tion, for example, by having a partially valley-polarized state, in whichboth the spin and valley flavors have a population imbalance. Suchstates have been studied recently as possibilities to explain magneticsignals observed at υ = −2 and had been previously discussed inliterature50,51. In this case, the valley and spin polarization could havedifferent energy scales, being responsible for the observed signals.Another alternative would be to have domains of different magneticbehavior ashasbeen recently observed in a SQUIDon tip experiment52.In this case, there could be domains all of orbital origin or a combi-nation of domains of orbital and spin origin. In the latter case the spinand orbital domains could behave differently while, in the former case,thedifferent behavior couldbe coming fromdomains of different sizesor domains having a different type of magnetic behavior as wasobserved in ref. 52. Considering the phase jumps in the data at lowT and the modeling of the current density with opposing phases onboth edges, the domain picture might be a more likely scenario.However, a definite proof of the origin of these signals cannot bedrawn from the present study.To summarize, we have proved that time-reversal symmetry-broken states can coexist with superconductivity in a single MATBGdevice. The zero-field coexistence and gate tunability of the magneticand topological phases with superconductors in MATBG presents aremarkable opportunity to electronically hybridize these phasesthrough engineering of complex gate-induced junctions. This will leadto the creation of ever more complex quantum phases based on theMATBG platform. Also, the so-created JJs can shed new light on theunderlying ground states of MATBG, as the JJ probes much smallerareas than traditional transport experiments and are highly sensitive tomagnetic fields.MethodsDevice fabricationTheMATBGdevices are fabricated using a cut-and-stack technique. Allflakes were first exfoliated in a Si/SiO2 (285 nm) substrate and laterFig. 4 | Evolution of magnetic hysteresis with temperature. a, b Fraunhoferpatterns measured at 500mK with field sweeping up (a) and down (b) as markedwith the black arrows. The white dashed lines mark the 0 current and 0 fieldpositions. The colored arrows highlight a period change in the pattern and the factthatby rotating aby 180°onewouldget theperiodicity ofb. c Ic+ extracted from theFraunhofer patterns with the magnetic field sweeping up (blue) and down (red) at800, 500, and 35mK. The curves are vertically shifted by 60 nA each for clarity.d Extracted ΔB vs. temperature T for Ic+. The red curve is a fit to the Curie–Blochequation (1–T/Tc)α with fitting parameters Tc ~750± 25mK and α ~0.4 ±0.05. Theerror bars are defined as the standard deviation of the extracted Ic values asexplained in the SI.Article https://doi.org/10.1038/s41467-023-38005-7Nature Communications |         (2023) 14:2396 5picked up using a polycarbonate (PC)/polydimethylsiloxane (PDMS)stamp. All the layers were picked up at a temperature of ~100 °C. Thegraphene is initially cutwith anAFM tip, to avoid strain during thepick-up process. The PC/PDMS stamp was used to pick-up first the topgraphite layer, the first hBN, and the first graphene layer. Beforepicking up the second graphene layer, the stage is rotated by an angleof 1.1–1.2°. Finally, the bottom hBN and bottom graphite gates werepicked up. The finalized stack is dropped on a Si/SiO2 substrate bymelting the PC at 180 °C. The resulting stack is etched into a Hall barwith CHF3/O2 and a 1D contact is formed by evaporating Cr (5 nm)/Au(50nm). The narrow channel of ~150nm in the top gate is etched withO2. Before etching the top gate, the device was characterized atT = 35mK to identify the pair of contacts closest to the magic-angle(θ ~ 1.1°). The junction was made in between this pair of contacts.MeasurementsTransport measurements were carried out in a dilution refrigerator(Bluefors SD250) with a base temperature of 20mK. Standard low-frequency lock-in techniques (Stanford Research SR860 amplifiers)were used to measure Rxx with an excitation current of 10 nA at afrequency of 13.11 Hz. For the dVxx/dI measurements the excitationcurrent was reduced to 1 nA. The d. c. bias current was applied througha 1/100 divider and a 1MΩ resistor before combining it with the a.c.excitation. Keithley 2400 Source-meters were used to control thegates as well as serve as the source for the DC current. The measureddVxx=dI signals were filtered and amplified by voltage-preamplifiersSR560 before entering the lock-in amplifiers.Twist-angle extractionThe twist angle is extracted from the phase diagrams shown in Sup-plementary Fig. 2. The carrier density corresponding to a fully filledsuperlattice unit cell is extracted to be ns = (2.88 ±0.1) ×1012cm−2. Byapplying the relation ns =8θ2=p3a2, where a = 0.246 nm is the gra-phene lattice constant, we extract a twist angle θ = 1.11° ± 0.02°.Data availabilityThe data that support the findings of this study are available at thepublic repository Zenodo under accession code: https://zenodo.org/record/7774670. Other data which might be relevant is available fromthe corresponding author upon request.Code availabilityThe code that supports the findings of this study is available from thecorresponding author upon request.References1. Linder, J. & Robinson, J. W. A. Superconducting spintronics. Nat.Phys. 11, 307–315 (2015).2. Senapati, K., Blamire, M. 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D.K.E. acknowledges support from the Ministry ofEconomy and Competitiveness of Spain through the “Severo Ochoa”program for Centers of Excellence in R&D (SE5-0522), Fundació PrivadaCellex, Fundació PrivadaMir-Puig, the Generalitat de Catalunya throughtheCERCAprogram, funding from theEuropeanResearchCouncil (ERC)under the European Union’s Horizon 2020 research and innovationprogram (grant agreement no. 852927)” and the La Caixa Foundation.K.T.L. acknowledges the support of the Ministry of Science and Tech-nology of China and the HKRGC through grants MOST20SC04, C6025-19G, 16310219, 16309718, and 16310520. J.D.M. acknowledges supportfrom the INPhINIT ‘la Caixa’ Foundation (ID 100010434) fellowship pro-gram (LCF/BQ/DI19/11730021). Y.M.X. acknowledges the support ofHKRGC through Grant No. PDFS2223-6S01.Author contributionsD.K.E. and X.L. conceived and designed the experiments; J.D.M., A.D.C.,and X.L. fabricated the devices and performed the measurements;J.D.M., A.D.C., S.Y.Y., D.K.E., Y.M.X, X.G., and K.T.L. analyzed the data;Y.M.X., X.J.G., and K.T.L. performed the theoretical analysis; T.T. andK.W. contributed materials; J.S., A.P.H., and D.K.E. supported theexperiments: J.D.M., A.D.C., S.Y.Y., D.K.E., Y.M.X., and K.T.L. wrotethe paper.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-38005-7.Correspondence and requests for materials should be addressed toDmitri K. Efetov.Peer review information Nature Communications thanks Chung-TingKe, Shi-Zeng Lin, and the anonymous reviewer(s) for their contribution tothe peer review of this work. Peer reviewer reports are available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard tojurisdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons license, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons license and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-38005-7Nature Communications |         (2023) 14:2396 7https://doi.org/10.1038/s41467-023-38005-7http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Symmetry-broken Josephson junctions and superconducting diodes in magic-angle twisted bilayer graphene Results Gate-defined JJ Unconventional Fraunhofer pattern and superconducting diode Magnetic JJ Discussion Methods Device fabrication Measurements Twist-angle extraction Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information