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Marta Perego, Clara Galante Agero, Alexandra Mestre Torà, Elías Portolés, Artem O. Denisov, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Filippo Gaggioli, Vadim Geshkenbein, Gianni Blatter, Thomas Ihn, Klaus Ensslin

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[Experimental detection of vortices in magic-angle graphene](https://mdr.nims.go.jp/datasets/700cf819-cd14-4d7d-945b-fe7b9b48d7f7)

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Experimental detection of vortices in magic-angle grapheneArticle https://doi.org/10.1038/s41467-025-65123-1Experimental detection of vortices in magic-angle grapheneMarta Perego 1 , Clara Galante Agero1, Alexandra Mestre Torà 1,Elías Portolés 1, ArtemO. Denisov 1, Takashi Taniguchi 2, KenjiWatanabe 3,Filippo Gaggioli 4,5, Vadim Geshkenbein 4, Gianni Blatter 4,6,Thomas Ihn 1,6 & Klaus Ensslin 1,6Superconducting magic-angle twisted-layer graphene (MATLG) is a promisingcandidate for superconducting electronics due to its electrical tunability.While the microscopic origins of superconductivity in MATLG have beenintensively studied, many aspects of its phenomenology remain unexploreddue to the challenges associated with studying two-dimensional (2D) materi-als. Here, we report the first direct experimental evidence of superconductingvortices in MATLG, a hallmark of type-II superconductors. Field-dependentcritical current measurements in a gate-tuned Josephson junction revealFraunhofer-like patterns characteristic of ultrathin films with weak transversescreening. These patterns exhibit sudden shifts attributed to spontaneousvortex penetration into the leads. With the leads at the edge of the super-conducting dome, we observe bistable V–I fluctuations linked to rapid vortexdynamics. Time-dependent measurements provide the vortex energy scale,the London penetration depth, and superfluid stiffness, consistent with recentkinetic inductance studies. These findings establish gate-defined Josephsonjunctions as versatile sensors of vortex dynamics in 2D superconductors.Twisted-layer graphene has emerged as a new platform for realizingnon-trivial correlated states1–3, with superconductingbi- andmultilayersystems attracting particular interest recently4–8. Superconductivity inthese two-dimensional (2D) structures can be electrically tuned,enabling the implementation of gate-defined devices. Much researchhas focused onmagic-angle twisted bilayer graphene (MATBG), whichhas become a versatile platform for superconducting electronics9–14.Recently, alternating-twistmagic-anglemultilayer graphene structureshave emerged as a novel family of moiré superconductors8,15–18; in thisconfiguration, each successive layer is rotated by an angle of ± θrelative to the previous one, following an alternating sequence.Superconductivity in these multilayer structures is characterized byhigher critical currents, critical magnetic fields, and critical tempera-tures than inMATBG.Moreover, their band structure canbe tunedby atransverse electrical field, the so-called displacement field19, providingadditional versatility for device operation. As a result, alternating-twistmagic-angle multilayer graphene structures are promising candidatesfor future superconducting electronic devices.Here, we implement a gate-defined Josephson junction (JJ) in four-layer twisted graphene (MAT4G), see ref. 20 for a similar setup in atrilayer film. Exposing the junction to a perpendicularmagnetic field B,we observe a distinct Fraunhofer-like pattern in the junction criticalcurrent Icj(B). Our interference pattern differs markedly from the oneobserved in standard junctions21, a consequenceof the extremelyweaktransverse magnetic screening power of these ultrathin films: i) Theperiodicity of the pattern is given by the flux ΦW = BW2 with W thejunction width, a factor W/2λL larger than the characteristic fluxΦλ = 2BWλL in usual junctions, where λL denotes the LondonReceived: 5 February 2025Accepted: 6 October 2025Check for updates1Laboratory for Solid State Physics, ETH Zurich, Zurich, Switzerland. 2Research Center for Materials Nanoarchitectonics, National Institute for MaterialsScience, Tsukuba, Japan. 3Research Center for Electronic and Optical Materials, National Institute for Materials Science, Tsukuba, Japan. 4Institute forTheoretical Physics, ETH Zurich, Zurich, Switzerland. 5Department of Physics, Massachusetts Institute of Technology, Cambridge, Cambridge, MA, USA.6Quantum Center, ETH Zurich, Zurich, Switzerland. e-mail: mperego@phys.ethz.chNature Communications |        (2025) 16:10259 11234567890():,;1234567890():,;http://orcid.org/0009-0007-4830-4934http://orcid.org/0009-0007-4830-4934http://orcid.org/0009-0007-4830-4934http://orcid.org/0009-0007-4830-4934http://orcid.org/0009-0007-4830-4934http://orcid.org/0009-0000-1010-2922http://orcid.org/0009-0000-1010-2922http://orcid.org/0009-0000-1010-2922http://orcid.org/0009-0000-1010-2922http://orcid.org/0009-0000-1010-2922http://orcid.org/0000-0001-7202-777Xhttp://orcid.org/0000-0001-7202-777Xhttp://orcid.org/0000-0001-7202-777Xhttp://orcid.org/0000-0001-7202-777Xhttp://orcid.org/0000-0001-7202-777Xhttp://orcid.org/0000-0001-9095-1579http://orcid.org/0000-0001-9095-1579http://orcid.org/0000-0001-9095-1579http://orcid.org/0000-0001-9095-1579http://orcid.org/0000-0001-9095-1579http://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/0000-0003-3701-8119http://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/0000-0002-9460-1004http://orcid.org/0000-0002-9460-1004http://orcid.org/0000-0002-9460-1004http://orcid.org/0000-0002-9460-1004http://orcid.org/0000-0002-9460-1004http://orcid.org/0000-0002-1911-5516http://orcid.org/0000-0002-1911-5516http://orcid.org/0000-0002-1911-5516http://orcid.org/0000-0002-1911-5516http://orcid.org/0000-0002-1911-5516http://orcid.org/0000-0003-0521-8028http://orcid.org/0000-0003-0521-8028http://orcid.org/0000-0003-0521-8028http://orcid.org/0000-0003-0521-8028http://orcid.org/0000-0003-0521-8028http://orcid.org/0000-0002-5587-6953http://orcid.org/0000-0002-5587-6953http://orcid.org/0000-0002-5587-6953http://orcid.org/0000-0002-5587-6953http://orcid.org/0000-0002-5587-6953http://orcid.org/0000-0001-7007-6949http://orcid.org/0000-0001-7007-6949http://orcid.org/0000-0001-7007-6949http://orcid.org/0000-0001-7007-6949http://orcid.org/0000-0001-7007-6949http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65123-1&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65123-1&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65123-1&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65123-1&domain=pdfmailto:mperego@phys.ethz.chwww.nature.com/naturecommunicationspenetration depth21. And ii), themaxima in the Fraunhofer-like patterndecay slowly / 1=ffiffiffiBp, rather than the usual decay ∝ 1/B; recognizingthese differences, in the following, we refer to our experimentallyobserved interference pattern as a Fraunhofer pattern (FP). Interest-ingly, our FP exhibits pronounced jumps that we attribute to vorticespenetrating/leaving the superconducting leads. Our JJ then serves as asensor allowing for an indirect detectionof vortices ingated atomicallythin materials. Our observations represent the first experimental evi-dence for superconducting vortices in magic-angle graphene. Using aJJ allows us to detect vortices without using traditional vortex imagingtechniques, which would be extremely challenging in this 2Dsuperconductor22–25. Until now, most research has focused on themicroscopic origin of superconductivity in this correlated material,with a lack of vortex studies26–28. Independently of the microscopicorigin of superconductivity, which is still under debate, we can quan-titatively analyse the observed vortex dynamics thanks to the well-developed phenomenology for these ultrathin materials29–34.ResultsSetup and bulk superconductivityWe have engineered a gate-defined JJ of length Lj = 150 nm in aMAT4Gfilm of width W = 1.1 μm along y, length L = 6W along x, and thicknessd≈ 1 nm35, as illustrated in Fig. 1a, b. A graphite bottomgate (BG), a goldtop gate (TG), and a gold finger gate (FG) are used to independentlycontrol the density nl and the displacement field Dl in the leads and inthe junction (denoted as nj and Dj). Given the nanometer scale thick-ness d of the film d ≪ λL, the device belongs to the class of weaktransverse screeners, with the effective screening power given by thePearl length Λ=2λ2L =d≫ λL36. With the widthW≪ Λ, external magneticfields H penetrate the entire sample and B ≈ H.We first analyse the bulk superconductivity observed in ourMAT4G device. Fig. 1c shows the phase diagram of the film in terms ofthe voltage V (measured at constant probe current I in a 4-terminalconfiguration not crossing the JJ) as a function of nl andDl, see Fig. S3Bfor the same measurement taken across the JJ. Superconductivity isobserved between moiré filling factors ∣ν∣ ≈ ±2 and a value slightlybeyond ∣ν∣ ≈ ±3, as expected8, see the dark blue domes showing zerovoltage. Further characterization of the superconducting domes isdiscussed in the Supplementary Information.The dependence of the bulk critical current Icb on the magneticfield B applied normal to the sample plane is shown in Fig. 1d for thedevice tuned at the green square depicted in Fig. 1c. The critical cur-rent Icb is seen as a peak in the differential resistance R = dV/dIwhich isevaluated numerically from d.c. data (transition between dark blue inFig. 1d, zero resistance, to a finite one, light blue), where the deviceswitches to the resistive state due to vortex motion. The field depen-dence of Icb(B) is governed by the edge- and bulk-pinning ofvortices34,37–40. The lineardrop in Icb(B) at smallfields is characteristicofthe Bean-Livingston barrier37 preventing vortices from entering thesample at the film edges y = ±W/234,39,40, as is typical for such films. Bylinearly fitting Icb versus B, we extract a value for the edge penetrationfield Be ≈ 100mT, see orange dashed line in Fig. 1d. Combining thisresult with the zero-field critical current Icb(0) = 230 nA and using therelation ∂BIcbðBÞ= � dW 2=2μ0λ2L34, we arrive at an estimate for theLondon penetration depth λL of order 10 μm, which compares favor-ably with values of a few μmobtained from other estimates (here, μ0 isthe vacuum permeability). For example, we may use the bulk criticalcurrent Icb(0) ≈ 230nA measured in Fig. 1d, obtain the critical currentdensity jcb ≈ 2.1 × 104 A/cm2, and take this value as a lower bound for thedepairing current density j0 =Φ0=3ffiffiffi3pπμ0λ2Lξ (with Φ0 = h/2eFig. 1 | Device setup and bulk phase diagram. a Schematic cross-section of thethin film JJ device and measurement setup; V is the measured voltage drop and I isthe applied current. The top gate (TG), finger gate (FG), and back gate (BG) areindicated. b Schematic top view of the film with width W (along the y-axis) andoverall lengthL (along the x-axis);Lj is the thickness of the JJ along x. Thedensities inthe leads and junction are denoted by nl and nj, the field B and current I directionsare indicated. Screening currents js (in green) and vortex currents jv (light blue)circulate in opposite directions. c Phase diagram of the film material, with thevoltage V (blue color scale) versus leads' density nl and displacement field Dl,measured in a 4-terminal configuration not crossing the junction at a constantcurrent I = 10nA. The filling factor ν is plottedon the top axis. The blue dark regionsaround ∣ν∣ ≈ 2–3 signal superconductivity. Red dots indicate full filling where thejunction is tuned into the resistive state. d Differential resistance R measured as afunction of I and B with the device tuned to the superconductiong state (greensquare in (c)). The orange dashed line indicates the fit to extract the edge pene-tration field Be, with the inset showing a line trace recorded at the white cir-cle B = 72mT.Article https://doi.org/10.1038/s41467-025-65123-1Nature Communications |        (2025) 16:10259 2www.nature.com/naturecommunicationsdenoting the flux unit). Extracting a value ξ ≈ 40 nm for the coherencelength8,16,17 (Fig. S4), we then find an estimate λL < 3.5 μm. Finally, thelow value in the saturation of Icb at large fields, see Fig. 1d, is testimonyof weak bulk pinning inside the film ∣y∣ < W/234, possibly due to twist-angle variation.Josephson junction (JJ)Keeping the leads in one of the superconducting regimes, we form a JJ inour sample by tuning the junction region into a resistive state. The for-mation of a JJ is confirmed by the observation of a d.c. Josephson criticalcurrent Icj < Icb, as shown in Fig. 2a, and the appearance of theFraunhofer-like interference effect, see Fig. 2b (for details of the devicefabrication and gate control see Supplementary InformationFigs. S1 and S2 andMethods). The high tunability of our device allows usto define a JJ in several ways by exploring the parameter space of densityn and displacement field D in the leads and the junction, see phasediagram inFig. 1c. The formationof a JJ is achievedby tuning the junctiondensity nj at fixed nl = −4.5 × 1012 cm−2 and Dj = 0 (the displacement fieldDl is bound to nj and follows the yellow dashed line within the super-conducting dome in Fig. 1c). The differential resistance R then exhibitstwo steps, i) at lowcurrents Icj when the junction turns resistive, and ii) athigh currents Icb when the leads switch to the resistive state, see orangeline-trace in Fig. 2a. The two critical currents coalescewhen nj enters thesuperconducting state between the white dashed lines in Fig. 2a,resulting in a uniform superconducting device SSS. Away from thisregion, we can implement a JJ with a desired critical current Icj—we referto this weak-link configuration as SJS, with J denoting the resistivejunction region, notwithstanding its nature,metallic, semiconducting, orinsulating. In all of ourmeasurements, the junction region is tuned to thefull-filling peaks (nj = ± 6.2 × 1012 cm−2) as indicated by the red dots inFig. 1c. This tuning is chosen to produce the most resistive state in thejunction region (the junction has been tuned to a magnetically corre-lated state in ref. 20), see Supplementary Information and Fig. S5 and S6for further details on junction tuning. Note that our MAT4G deviceadmits the displacement field Dj as an additional tuning knob for chan-ging Icj as compared to junctions defined in MATBG9,10 (Fig. S5F).Junction in magnetic fieldA typicalmagnetic interferencemeasurement with the device tuned tothe junction regime is presented in Fig. 2b. The current I is swept fromnegative to positive values while measuring the voltage drop acrossthe junction, all at fixed perpendicular applied field B. After each cur-rent sweep, B is stepped and a new trace is recorded. The leads are setto the superconducting state (nl = − 3.5 × 1012 cm−2, Dl/ϵ0 = 0.2 V/nm,light blue rhombus in Fig. 1c) and the junction is gated to full filling(nj = − 6.2 × 1012 cm−2, Dj/ϵ0 = 0.45V/nm, red dot in Fig. 1c); we call thisthe blue-red-blue setting with a corresponding identifier in the top-right corner of Fig. 2b. Note that a SJS device is characterized by a pairof points in the phase diagram Fig. 1c specifying density n and dis-placement field D in the junction and the leads. The critical Josephsoncurrent Icj(B) is suppressed and modulated as B is varied, resulting inthe FP shown in Fig. 2b—the observed pattern is typical for a shortFig. 2 | Josephson junction device and Fraunhofer pattern. a Differential resis-tanceRmeasured as a functionof Iwhile sweepingnj and keepingnlfixed.Dj isfixedat zero whereas Dl is swept as shown on the top axis, following the yellow dashedline in Fig. 1c. By sweeping nj, the junction can be tuned from a resistive to asuperconducting state, resulting in a SJS or SSS configuration, with the criticalcurrents of the bulk and junction denoted by Icb and Icj. A line trace of the differ-ential resistance R is shown with nj fixed at the dotted orange line. b Differentialresistance Rmeasured as a function of I and B for nl = − 3.5 × 1012 cm−2,Dl/ϵ0 = 0.2 V/nm and nj = − 6.3 × 1012 cm−2,Dj/ϵ0 = 0.45V/nm (blue-red-blue setting in Fig. 1c). Theorange and yellow dashed lines show the theoretical predictions for a 2D JJ underweak screening conditions, whereas the dotted yellow line shows the rapid decay∝ 1/B for a standard JJ. c Differential resistance Rmeasured as a function of I and Bwith the entire device tuned to the pink triangle shown in the phase diagram Fig. 1c,implying that no junction is formed.This SSS configuration exhibits no interferencepattern.Article https://doi.org/10.1038/s41467-025-65123-1Nature Communications |        (2025) 16:10259 3www.nature.com/naturecommunicationsjunction41 and exhibits thehallmarks of aweak screeningdevice30,31.Weobserve field-induced oscillations of Icj(B) with the interference periodΔB ≈ 3mT. The FP are symmetric in current and do not show anyskewness. Thanks to the high tunability of our device, we can studythese interference patterns throughout the phase space of bothjunction and leads (see Supplementary Information for further mea-surements with different nl and Dl).To further prove that the measured interference pattern is due tothe JJ rather than sample inhomogeneity, we carry out the same mea-surementwith the JJ tuned into the superconducting lobe (SSS) as shownin Fig. 2c (with nj = nl ≈ − 4.5 × 1012 cm−2 andDj/ϵ0 =Dl/ϵ0 ≈0.2V/nm, pinktriangle in thephasediagramFig. 1c). In thismeasurement, Icj agreeswithIcb up to small oscillations in Icj(B) at low fields; their periodicity closelymatches theoneobserved in thepatternof Fig. 2b andweattribute themto a slight mismatch in the tuning between the leads and the junctionregions. No interference pattern is observed when the device is fullysuperconducting, compare Fig. 2b with Fig. 2c.Fraunhofer interference patternOur JJ shows a Fraunhofer-type pattern Icj(B) that is typical for a weakscreener with Λ ≫ W30,31,42,43; the field B then penetrates the leadscompletely and the gauge-invariant phase-difference ΔγB(y) takes theform30,31ΔγBðyÞ � 1:7ΦW ðBÞΦ0sinðπy=W Þ ð1Þwith the relevant flux determined by the junction width W only,ΦW(B) = BW2, provided that the film leads are longer than the filmwidth, L ≫ W. Furthermore, the usual linear shape21 ΔγB(y) ∝ y/W isreplaced by a sine-function,ΔγBðyÞ / sinðπy=W Þ, a feature that is againdue to the deep penetration of the field into the film, see Supplemen-tary Information. This seemingly minor correction has profound con-sequences for the FP at large B, producing a slow decay of the maxima/ 1=ffiffiffiBpin the pattern instead of the standard 1/B behavior.To relate these insights to our experiment, we find Icj(B) by inte-gration over the junction dimensions: assuming a sinusoidalcurrent–phase relation jjðΔγÞ= jcj sinðΔγ + γ0Þ with γ0 a free shift para-meter, the integral overW can be evaluated exactly30,31 in terms of theBessel function J0,IcjðBÞIcjð0Þ= ∣ J0½1:7ΦW ðBÞ=Φ0�∣, ð2Þwhere the choice γ0 = ± π/2 produces the largest, hence critical, cur-rent. The Bessel function J0 then replaces the sinc-function character-izing the FP in the standard context21. The orange line in Fig. 2b is a fitto the data that makes use of the width W = 1.1 μm of the film in thedetermination of the flux ΦW(B) = BW2. Given that the distancebetween consecutive zeros of the Bessel function J0(s) is Δs ≈ 3.1, werecover the periodicity ΔB ≈ (Δs/1.7)Φ0/W2 ≈ 3mT. Note that the zerosin J0(s) become truly equidistant only at large values of the magneticfield. Furthermore, the maxima are well tracked by the slow decay/ 1=ffiffiffiBp, see the dashed yellow line at B < 0. The good agreementbetween the theoretical prediction and the experimental data holds atfields below ∣B∣ ≈ ± 10mT, i.e., including the first three minima;thereafter, the fit does not work anymore due to the presence of sharpshifts in the pattern of the size of a fraction of Φ0. We attribute theseshifts to vortices that spontaneously penetrate or leave the leadsnearby the junction.Jumps in the Fraunhofer patternThe measured interference patterns show sudden shifts, i.e., jumps inIcj(B), see Figs. 2b, 3a and b. The measurement protocol for the FPdescribed above produces maps Icj(B) over time scales of hours. Thesudden shifts appear in all of our junction tunings, i.e., independent ofgate voltages (Fig. S11).Pronounced jumps in Icj, see black arrows in Fig. 3a, b, areobserved with the leads tuned close to the center of the super-conducting dome (with nl = 4.2 × 1012 cm−2, Dl/ϵ0 = − 0.3V/nm andnj = 6.2 × 1012 cm−2, Dj/ϵ0 = −0.5 V/nm, orange rhombus and red dot inthe phase diagram Fig. 1c, we name it the orange-red-orange, or‘strong-leads’ setting). They are present in both increasing anddecreasing sweeps of the magnetic field, are symmetric in I, and arestable on the time scale of hours.Vortex penetrationWith these shifts present in all of our device configurations,we ruleouta possible origin related to the experimental setup (SupplementaryInformation and Fig. S10). We rather attribute these sudden shifts tovortices penetrating and leaving the superconducting leads in thevicinity (closer than 2W) of the junction32. Similar observations havebeen previously reported32,33,44–47.The presence of a vortex (at the position Rv = (xv, yv) and with aflux parallel to B, see Fig. 1b) changes the phase pattern at the junction,Δγ(y) → Δγ(y; Rv) = ΔγB(y) + Δγv(y; Rv), adding a step-like contribution∣Δγv(y; Rv)∣ < π to the phase difference, see Figs. S14–S16. The phase∣Δγv(y; Rv)∣ as a function of y (see Supplementary Information for anexplicit expression) smoothens and decreases in amplitude withincreasing distance xv of the vortex from the junction, seeFigs. S14 and S15. Since the vortex currents (jv, blue in Fig. 1b) flowopposite to the screening currents (js, green in Fig. 1b), the presence ofa vortex decreases the effect of the B-field and the FP shifts to the rightupon vortex entry at positive B > 0 (the shift is to the left for a vortexwith opposite circularity entering the leadatB <0). This is exactlywhatis seen in the experiment. For example, in Fig. 3c, d, we fit theexperimental traces of Fig. 3a, b, by having 7 (in Fig. 3c) and 4 (inFig. 3d) vortices of ± polarity enter (upon increasing ∣B∣) or leave (upondecreasing ∣B∣) the device leads, see black arrows.Themagnitude of the shift in the FP is primarily determinedby thedistance xv between the vortex and the junction (see Figs. S14 and S15).When changing the yv coordinate, the largest FP-shifts occur when avortex is at the center of the film yv = 0, and theirmagnitude decreasesas the vortex approaches the edges yv = ± W/2, see Fig. S16. Addi-tionally, the yv coordinate modifies the minima in the FP—the sharpminimawith I = 0 become rounded at intermediate values 0 < yv <W/2,see Fig. S16. Inourfit, weplace the vortices at the center of thefilm, i.e.,yv = 0, and tune the pattern’s shifts by choosing vortex positions in therange 0.3( → largeshifts) < ∣xv∣/W < 0.8( → smallshifts), see Fig. 1b(detailed parameters are cited in the Supplementary Information). Theresolution of the FP minima in the experiment is not sufficient todetermine a precise value for the yv coordinate. Note that in Figs. 3aand b, vortices have left the device atB =0 in both cases. Both the localchange in the FP at individual jumps and the accumulated shift atlarger magnetic fields are well reproduced by the fit. When the fieldamplitude ∣B∣ exceeds 10 mT, the patterns become blurred, and theobservation of individual jumps is hampered; however, the JJ is stillsensitive to the presence of vortices.Vortex fluctuationsWe close our discussion with the analysis of another data set with theleads tuned away from the center of the superconducting dome at a‘weak-leads’ setting (nl = 4.8 × 1012 cm−2, Dl/ϵ0 = −0.3 V/nm andnj = 6.2 × 1012 cm−2, Dj/ϵ0 = −0.5 V/nm, see the purple rhombus and reddot in the phase diagramFig. 1c, or ‘weak-leads’ setting). This choice ofparameters reduces the superfluid density ρs of the leads26 and at thesame time the vortex energy ε0d = πρs, where ε0 = ð4π=μ0ÞðΦ0=4πλLÞ2is the vortex line energy. The latter determines the edge barrier Ue forvortex penetration, with Ue smaller than 2ε0d and decreasing withincreasing field B, as follows from the analysis in ref. 29, see Fig. S17A inArticle https://doi.org/10.1038/s41467-025-65123-1Nature Communications |        (2025) 16:10259 4www.nature.com/naturecommunicationsthe Supplementary Information. Combining the reduced edge barrierUe with an increased temperature T, we observe a boost in vortexdynamics, i.e., enhanced vortex fluctuations. Indeed, the FP in Fig. 4a,measured at T = 100mK, exhibits pronounced bi-stability effects in thevoltage–current characteristic, see the grainy white–dark-blue fea-tures in Fig. 4a around B ≈ 1.5mT and B ≈ 2.7mT. We associate thesewith vortices penetrating and leaving the leads, thereby shifting the FPback and forth and switching between two different V(I) curves. Fur-thermore, at these elevated temperatures, the V–I characteristic of thejunction is rounded, with the sharp onset of dissipation at Icj replacedby a smooth non-linear rise; we attribute this rounding in V(I) to phase-slips within the Josephson junction48,49. Figure 4b shows both of theseeffects, phase-slips smoothing the dissipative crossover and sharpsteps due to vortex dynamics at B ≡ B* = 2mT, see black arrows inFig. 4a. The sharp steps in the V–I curve at B* = 2mT manifest aswhite–dark-blue pairs of dots in the differential resistance plotof Fig. 4a.Next, wefix the fieldB* = 2mT and the bias current I* = 4 nA (blackdashed line in Fig. 4b), at a point where the presence (absence) of avortex causes changes in the V(I) characteristic, and measure the vol-tage as a function of time. A typical time-trace exhibiting telegraph-type voltage-noise is shown in Fig. 4c. The timescale t of these fluc-tuations is of order seconds and decreases rapidly with temperature,see Fig. 4d, as typical for a thermally activated process (see Supple-mentary Information, Fig. S8, for the counting statistics of these fluc-tuations). Below 90 mK, the activation process loses its temperaturedependence, which we may attribute to a changeover to a quantumtunneling process of vortices50.Assuming thermal activation of vortices over the edge barriergoverns the voltage fluctuations, we can derive an energy scale for thevortex energy ε0d and hence for the superfluid density ρs = ε0d/π.Given a barrier Ue at temperature T and an attempt time t0, a vortexrequires a time t � t0 exp½Ue=T � to overcome the barrier and pene-trate into the film leads (we set kB to unity). Knowing the typicaldynamical time t of vortex fluctuations, we can derive a quite accurateestimate for Ue � T lnðt=t0Þ. Making use of a typical attempt time51,52t0∼10−11 s, a typical dwell time t∼1 s as observed in our experimentFig. 4c, and the temperature T = 100mK, we find a barrier Ue ≈ 2.5 K.The barrier Ue remains constant upon increasing the temperature toT = 115mK, as supported by the observed decrease in dwell time t. Thisis illustrated in Fig. 4d,where the blackdashed line shows the expectedexponential decayof t. From this result, andusing the relationUe ≈ ε0d,see Fig. S17A,wecan extract a valueρs≈0.8 K for the superfluid densityand a London penetration depth λL∼ 2.8 μm. Furthermore, using therelationTBKT = ε0(TBKT)d/2 and ignoring the reduction in ε0(T) athighertemperatures, we find an upper limit for the Berezinskii-Kosterlitz-Thouless transition temperature TBKT < 1.2 K.Recently, the superfluid density ρs of twisted-layer graphene hasbeen determined using kinetic inductance measurements, both for atrilayer film26 and for a bilayer system27. Given the differences in thevarious systems, the comparison of the results in refs. 26,27 with ourfindings has to remain on a qualitative level, also owing to the fact thatour analysis is done away from the superconducting dome centerwhere ρs is well defined. While for the trilayer film a value ρs between0.1 K and 0.45 K has been reported, a value up to ∼1.2 K has beenmeasured for thebilayer system.Our value ρs ≈0.8 K then iswell withinthis range.DiscussionIn conclusion, we have demonstrated the formation of a gate-definedJosephson junction in MAT4G and its application as a vortex sensor.The measured interference patterns agree excellently with theFig. 3 | Vortex penetration. Differential resistance R measured as a function of Iand B, for a forward magnetic-field sweep in (a) and a backward sweep in (b). Thebottom axes show the corresponding scaled flux ΦW/Φ0 penetrating junction andleads, whereΦW =BW2. The tuning parameters arenl = 4.2 × 1012 cm−2,Dl/ϵ0 = −0.3 V/nm and nj = 6.2 × 1012 cm−2, Dj/ϵ0 = −0.5 V/nm (‘strong-leads’ setting). Sudden shiftsof the interference pattern are highlighted with black arrows. Theoretical fits of themeasuredFraunhofer patterns (a) and (b) on thebasis of the analysis inRef. 32,with7 (in (c)) and 4 (in (d)) vortices leaving/penetrating the leads.Article https://doi.org/10.1038/s41467-025-65123-1Nature Communications |        (2025) 16:10259 5www.nature.com/naturecommunicationspredicted behavior for a weak transverse screener with a Pearl lengthsurpassing the sample dimension, Λ > W. Our data enable us to pre-cisely track the entry and exit of vortices from thedevice leads and findtheir location away from the junction. Our observation of vortices inMAT4G using a Josephson junction sensor opens new avenues forexploring vortex motion in this new class of twisted materials.MethodsFabrication detailsWe fabricated a MAT4G stack using the dry pick-up method53. Gra-phene and hexagonal boron nitride (hBN) flakes were exfoliated on a285 nm p : Si/SiO2 wafer. A graphene flake of around 90 μm by 20 μmwas scratched into four pieces using a tungsten needle with a tip dia-meter of 2 μm controlled by a micromanipulator. We then pickedup each flake using a polydimethylsiloxane/polycarbonate stamp.The top hBN flake, with a thickness of 25 nm, was picked up at 110 °C.Afterwards, the four graphene flakes were picked up at 40 °Cwhile alternatively rotating the stage by ± 1.8°. To pick up the bottomhBN flake, with a thickness of 62 nm, the flake was contacted by thestack at 40 °C and the temperatureof the stagewas raised to95 °C. Thestack was then finished by picking up a graphite flake of thickness23 nm at 100 °C. Afterwards, the stack was deposited on a p : Si/SiO2chip at 170 °C. The polycarbonate stamp was cleaned usingdichloromethane.To contact the MAT4G, we fabricated edge contacts54 made byelectron beam lithography and reactive ion etching. We etched usingCHF3/O2 (40/4 sccm, 60W) and evaporated Cr/Au (10/70 nm). Thefinger gate and the electrode lines were then defined by depositing Cr/Au (10/80 nm). Next, the mesa was defined by etching using CHF3/O2(40/4 sccm, 60W). Afterwards, a layer of 30 nmof aluminumoxidewasdeposited by atomic layer deposition. The top gate and its electrodeline were then fabricated using electron beam lithography and eva-porating Cr/Au (10/80 nm). Optical images after each fabrication stepare shown in Figs. S1, A–D.Measurement setupWe carry out all themeasurements in a dilution refrigerator that uses amixture of 3He and 4He with a base temperature of 55mK (unless sta-ted otherwise). Our measurements are current-biased, i.e., we apply acurrent andmeasure the voltage drop in two (2T), three (3T), and four-terminal (4T) setups, see Figs. S1E–G. In the two and three-terminalconfiguration, we correct for contact resistances. To generate the biascurrent, we use a home-built d.c. source in series with a 10MΩ or100MΩ resistor. The voltage is amplifiedusing ad.c. An amplifier built-in-house (see ref. 55) and its output ismeasuredwith aHewlett-Packard3441A digital multimeter. The bottom, top, and finger gates are con-nected to d.c. voltage sources also built in-house. When performingradio-frequency measurements, the top gate is connected to a Rhodeund Schwarz SMB 100 A signal generator using a bias-tee withR = 10 kΩ and C = 100nF. For the statistical analysis of vortex fluc-tuations, the output voltage is further amplified with a gain amplifier,low-pass filtered at 1.1 kHz, and recorded in time using a NationalInstruments BNC-2110 data acquisition card (DAQ) with a samplingfrequency of 20 kHz.Data availabilityThe data supporting the findings of this study, together with the codefor plotting the figures, is available online through the ETH ResearchCollection at https://doi.org/10.3929/ethz-b-000742291.References1. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).2. Yankowitz, M. et al. Tuning superconductivity in twisted bilayergraphene. Science 363, 1059–1064 (2019).3. Lu, X. et al. Superconductors, orbitalmagnets andcorrelated statesin magic-angle bilayer graphene. Nature 574, 653–657 (2019).4. Cao, Y. et al. Unconventional superconductivity in magic-anglegraphene superlattices. Nature 556, 43–50 (2018).Fig. 4 | Vortexfluctuations. aDifferential resistanceRmeasured atT = 100mKas afunction of I and B with parameters nl = 4.8 × 1012 cm−2, Dl/ϵ0 = −0.3 V/nm andnj = 6.2 × 1012 cm−2,Dj/ϵ0 = −0.5 V/nm (‘weak-leads’ setting). The Fraunhofer patternis smoothed and white—dark-blue speckles mark the presence of bistabilities in theV—I characteristic.bVoltage—current trace atB* = 2.0mT, see arrows in Fig. 4a. TheV—I characteristic is rounded and exhibits pronounced steps; we associate therounding with the presence of phase slips in the junction and the steps with vortexfluctuations in the leads. The stepsmanifest in the speckles visible in Fig. 4a. c Timetraceof the voltageVmeasured atfixedB*= 2.0mTand current I* =4 nA, seedottedline in Fig. 4b.We associate the telegraph-type noise with vortex fluctuations in theleads. 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Universality in the current decayand flux creep of Y-Ba-Cu-O high-temperature superconductors.Phys. Rev. B 42, 6784–6786 (1990).52. Kopylov, V. N. et al. The role of surface effects in magnetization ofhigh-Tc superconductors. Phys. C. 170, 291 (1990).53. Kim, K. et al. van der Waals heterostructures with high accuracyrotational alignment. Nano Lett. 16, 1989–1995 (2016).54. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).55. Märki, P., Braem, B.A. & Ihn, T. Temperature-stabilized differentialamplifier for low-noise DC measurements. Rev. Sci. Instrum.88 (2017).AcknowledgementsWethank PeterMärki and the staff of the ETHcleanroom facility FIRST fortechnical support. We acknowledge fruitful discussions with VladimirKoganandManfredSigrist.We thankGiulia Zheng for her support duringthe project. Financial support was provided by the European GrapheneFlagship Core3 Project, H2020 European Research Council (ERC)Synergy Grant under Grant Agreement 951541, the European Union’sHorizon 2020 research and innovation program under grant agreementnumber 862660/QUANTUM E LEAPS, the European Innovation Councilunder grant agreement number 101046231/FantastiCOF, the EU CostArticle https://doi.org/10.1038/s41467-025-65123-1Nature Communications |        (2025) 16:10259 7www.nature.com/naturecommunicationsAction CA21144 (SUPERQUMAP), and NCCR QSIT (Swiss National Sci-ence Foundation, grant number 51NF40-185902). K.W. and T.T.acknowledge support from the JSPS KAKENHI (Grant numbers21H05233 and 23H02052) and theWorld Premier International ResearchCenter Initiative (WPI), MEXT, Japan. F.G. is grateful for the financialsupport from the Swiss National Science Foundation (Postdoc.MobilityGrant no. 222230).Author contributionsM.P. fabricated the device. T.T. and K.W. supplied the hBN crystals. M.P.and C.G.A. performed the measurements. M.P. and C.G.A. analyzed thedata. F.G., V.G. and G.B. developed the theoretical model. M.P. and G.B.wrote the manuscript, and all authors were involved in the reviewingprocess. M.P., C.G.A., E.P., A.M.T. and A.O.D. discussed the data. M.P.,E.P., K.E. and T.I. conceived and designed the experiment. T.I. and K.E.supervised the work.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-65123-1.Correspondence and requests for materials should be addressed toMarta Perego.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of this work. 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To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-65123-1Nature Communications |        (2025) 16:10259 8https://doi.org/10.1038/s41467-025-65123-1http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Experimental detection of vortices in magic-angle graphene Results Setup and bulk superconductivity Josephson junction (JJ) Junction in magnetic field Fraunhofer interference pattern Jumps in the Fraunhofer pattern Vortex penetration Vortex fluctuations Discussion Methods Fabrication details Measurement setup Data availability References Acknowledgements Author contributions Competing interests Additional information