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Einav Grynszpan, Ayelet Zalic, Pradheesh Ramachandran, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Anna Keselman, Hadar Steinberg

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[Ballistic graphene-NbSe                    <sub>2</sub>                    Josephson junction in high parallel magnetic field](https://mdr.nims.go.jp/datasets/27e70fc4-c99d-4d32-b128-b466ed2d9207)

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Ballistic graphene-NbSe2 Josephson junction in high parallel magnetic field2D Materials     LETTER • OPEN ACCESSBallistic graphene-NbSe2 Josephson junction inhigh parallel magnetic fieldTo cite this article: Einav Grynszpan et al 2025 2D Mater. 12 041004 View the article online for updates and enhancements.You may also likeInvestigation of Layer Structured NbSe2 asan Intercalation Anode Material forSodium-Ion Hybrid CapacitorsYuvaraj Subramanian, Ganesh KumarVeerasubramani, Myung-Soo Park et al.-Synthesis and tribological properties ofNbSe2/CeNbO4 nanocompositeFeixia Zhang, Jie Sun, Yuan Lu et al.-On the nature of superconductivity in theanisotropic dichalcogenideNbSe2{CoCp2}xE-W Scheidt, M Herzinger, A Fischer et al.-This content was downloaded from IP address 144.213.253.16 on 23/10/2025 at 05:50https://doi.org/10.1088/2053-1583/ae07fa/article/10.1149/2.0641904jes/article/10.1149/2.0641904jes/article/10.1149/2.0641904jes/article/10.1149/2.0641904jes/article/10.1149/2.0641904jes/article/10.1088/2053-1591/ab2f59/article/10.1088/2053-1591/ab2f59/article/10.1088/2053-1591/ab2f59/article/10.1088/2053-1591/ab2f59/article/10.1088/2053-1591/ab2f59/article/10.1088/0953-8984/27/15/155701/article/10.1088/0953-8984/27/15/155701/article/10.1088/0953-8984/27/15/155701/article/10.1088/0953-8984/27/15/155701/article/10.1088/0953-8984/27/15/1557012D Mater. 12 (2025) 041004 https://doi.org/10.1088/2053-1583/ae07faOPEN ACCESSRECEIVED6 April 2025REVISED1 September 2025ACCEPTED FOR PUBLICATION17 September 2025PUBLISHED22 October 2025Original Content fromthis work may be usedunder the terms of theCreative CommonsAttribution 4.0 licence.Any further distributionof this work mustmaintain attribution tothe author(s) and the titleof the work, journalcitation and DOI.LETTERBallistic graphene-NbSe2 Josephson junction in high parallelmagnetic fieldEinav Grynszpan1, Ayelet Zalic1, Pradheesh Ramachandran1, Takashi Taniguchi2, Kenji Watanabe3,Anna Keselman4,5 and Hadar Steinberg1,6,∗1 The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel2 International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan3 Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan4 Physics Department, Technion—Israel Institute of Technology, Haifa 32000, Israel5 The Helen Diller Quantum Center, Technion, Haifa 32000, Israel6 The Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Jerusalem 91904, Israel∗ Author to whom any correspondence should be addressed.E-mail: hadar@phys.huji.ac.ilKeywords: superconductivity, graphene, NbSe2, TMD, Josephson effect, ballistic, Josephson junctionSupplementary material for this article is available onlineAbstractPlanar graphene-NbSe2 Josephson junctions can support supercurrents at high in-plane magneticfields (B∥) due to the robust superconductivity in thin NbSe2, protected from both orbital andspin-driven decay by a combination of atomic thickness and Ising spin orbit coupling. We fabricateand characterize a clean, flat graphene-NbSe2 junction encapsulated in hBN. The junction isballistic, exhibiting Fabry–Pérot oscillations of the critical current, and supports very high criticalcurrent densities. The junction is remarkably robust to both in-plane and out-of-plane magneticfields, and exhibits a clear ballistic Josephson effect up to the maximally available in-plane field of8 T. We model the suppression of the critical current using a tight-binding model, accounting forthe large overlap area between the NbSe2 and graphene. We find that the suppression is governedby both the Zeeman splitting of Andreev bound states and by the flux threading the van-der-Waalsgap that separates graphene from the NbSe2 leads.In recent years, there has been growing interestin lateral Josephson junctions (JJs) configured ina planar geometry. These junctions serve as plat-forms for exploiting material transport propertiesthat arise from geometry and proximity effects, toinduce phenomena that are not inherent to the super-conductor alone. Like in JJs based on ferromag-netic weak links [1], junction weak links can gen-erate Cooper pairs with a non-zero center-of-massmomentum when a parallel magnetic field, B∥, isapplied in the junction plane [2–5]. When materialsthat permit the presence of spin–orbit coupling in theweak link are used in the JJ architecture, the systemcan be driven to non-trivial topological states [2, 6].An example of such systems are graphene-basedJJs, which came to prominence in 2007 [7] andprovide a promising new platform to study surface-addressable high-quality 2D systems coupled tosuperconductors [8]. The first ballistic graphene JJsutilized suspended graphene [9], while today theyaremore readily constructed from graphene encapsu-lated by hexagonal boron nitride (hBN), with super-conducting side contacts [10–12]. A hallmark of thesejunctions are the observed Fabry-Pérot oscillations inthe critical current (IC), which serve as evidence ofballistic superconductivity [11, 13].Owing to its low-disorder interface withgraphene, NbSe2 presents itself as a compellingmaterial choice for integration into graphene-baseddevices, especially those designed to function inhigh magnetic fields. This is bolstered by the factthat thin layers of NbSe2 remain superconductingat very high fields due to a combination of Isingprotection [14] and suppressed orbital depairing[15–17]. Recently, devices of this kind have beenrealized with the successful fabrication of van der© 2025 The Author(s). Published by IOP Publishing Ltdhttps://doi.org/10.1088/2053-1583/ae07fahttps://crossmark.crossref.org/dialog/?doi=10.1088/2053-1583/ae07fa&domain=pdf&date_stamp=2025-10-22https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://orcid.org/0000-0002-9420-0315https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-5226-8522https://orcid.org/0000-0002-7409-5087mailto:hadar@phys.huji.ac.ilhttps://doi.org/10.1088/2053-1583/ae07fa2D Mater. 12 (2025) 041004Figure 1. Device characterization. (a) Schematic of NbSe2-graphene Josephson junction device, encapsulated in hBN. The devicehas four contact electrodes and a top gate electrode. (b) Microscope image of the cracked NbSe2, with the outlines of top hBN(graphene) flakes shown in black (white) and the contact electrodes shown in false color. (c) AFMmeasurement of graphene flakeafter transfer to hBN substrate, heat cleaning and tip cleaning. The location of the subsequently transferred NbSe2 crack is shownbetween yellow lines, while the in-plane orientation of B∥ is shown by the white arrow. (d) Critical current IC, normal resistanceRN and calculated ICRN product as a function of gate voltage. All traces exhibit Fabry Perot oscillations on the electron side. (e)Current densities for graphene JJs, based on the compilation in [22] (Nb side contacts) with data taken from [9] (suspendedgraphene with NbN contacts) [10], (MoRe side contacts) [13] (Al contacts). The device reported here is marked by a star. (f)Normalized ICRN as a function of temperature. The solid line is the result of a tight-binding calculation, assuming a value of∆∗ = 0.6 meV for the induced gap in graphene.Waals Josephson devices that incorporate grapheneweak links and NbSe2 contacts, which we will referto as two-dimensional Josephson junctions (2DJJs)[18, 19]. In previous experiments involving thesedevices, we have explored diffusive 2DJJs and SQUIDdevices at high B||, observing possible signaturesof field-driven finite-momentum Cooper pairing,as well as current density redistribution within thegraphene weak link [19, 20].In this letter we present evidence of an all-vdWlateral ballistic 2DJJ. The device exhibits gate-drivenFabry–Pérot oscillations, which manifest both in thenormal resistance RN and in the critical current IC.The device is robust to magnetic field directed bothin (B∥) and out (B⊥) of the plane of the junction—sustaining a finite critical current at B⊥ reaching closeto 1 T out of plane, and B∥ = 8 T. In the latter casewe find a suppression of 2 orders of magnitude inthe critical current. To explain the observed IC sup-pression, we develop a tight-binding model whichaccounts for both the Zeeman splitting and the orbitaleffect of the graphene-NbSe2 vdW gap. The interlayerspacing, although only 0.52 nm wide [21], appears tohave a decisive effect on the suppression of supercur-rent at the high B∥ limit.We fabricate the device using a cracked flake ofNbSe2 placed on a graphene ribbon, fully encapsu-lated by hBN from both the top and bottom (seeillustration in figure 1(a) and microscope image ofthe device shown in figure 1(b)). The NbSe2 flakeis contacted on either side of the crack by evapor-ated Ti-Au electrodes in a four-probe geometry. TheNbSe2 crack length in the direction of the currentflow measures approximately L1 ≈ 160 nm, while theunderlying graphene ribbon has a width ofW≈ 1µmand a length of L2 ≈ 9 µm beneath the NbSe2 con-tacts. The NbSe2 in the vicinity of the crack is onlyabout 3–5 layers thick (evaluated by optical contrast).At such thicknesses, the superconducting gap ismeas-urably reduced, down to 0.75–1 meV, in comparisonwith the bulk gap of 1.2 meV. Ising spin–orbit coup-ling has an appreciable effect on the retention of thegap at high in-plane magnetic fields [16, 23]. Thegraphene carrier density is adjusted via a top gate elec-trode that is insulated from the device by the top hBNflake, which is 11 nm thick, as shown in figures 1(a)and (b).We begin our characterization by exploring thecritical current as a function of the gate voltage,shown in figure 1(d). IC and RN exhibit Fabry–Pérot oscillations at electron doping, indicating bal-listic supercurrent transport in a cavity [10–13]. Bothmodulate with gate voltage such that their productmaintains constant, ICRN ≈ 0.5∆/e away from theDirac point. This is smaller than the theoreticallyexpected proportionality constant of 2.44∆/e forshort ballistic graphene JJ [24]. However, exper-imental observations show values near 2∆/e in22D Mater. 12 (2025) 041004Al-contact junctions [25], and in ballistic graphenejunctions this constant has been found to be evensmaller [26].The F-P oscillations are most pronounced onthe electron side, VG > 0, and are a consequence ofthe formation of PN junctions between the n-dopedgraphene between the NbSe2 leads, and the stronglyp-doped graphene underneath them. From the peri-odicity of the FP oscillations, 2kFLFP, we extract thelength of the P-N-P cavity LFP ≈ 150 nm.The resulting NbSe2-graphene contacts have atransparency of ≈0.82 for VG =−0.5 V (hole dop-ing), and≈0.6 for VG = 0.5 V (electron doping), cal-culated following [11] (see supplementary section 1for details). Transparency is lower on the electron sidedue to the formation of P-N junctions. On the holeside, transparency might be limited by the p-p’ junc-tions formed as a result of higher hole doping withinthe contact region.The highly transparent contact yields a large crit-ical current density of ≈4000 nAµm−1 at VG =−1V, comparable to state-of-the-art Nb edge contacts[22] (see figure 1(e)). This device is nominally inthe ballistic short junction regime, with the Thoulessenergy ETh = h̄vF/L1 ≈ 4meV [11], a few times largerthan the superconducting gap (∆= 1.2 mV for bulkNbSe2 and smaller for thin NbSe2). In figure 1(f) weshow the normalized temperature dependence of theICRN product.The junction remains superconducting up to5.5 K, not far below the TC of 3–4 layer NbSe2. TheJosephson effect in our junction is retained in both in-plane and out-of-plane magnetic fields. To show this,we first turn to transport measurements with mag-netic fields applied perpendicular to the plane of thejunction. In figure 2(a), we explore the junction dif-ferential resistance at zero bias as a function ofVG andmagnetic field, up to B⊥ = 2.7 T. The device exhibitstwomain features: At high fields, transport is normal,with a Landau fan typical of the quantumHall regimemeasured in a 2-terminal geometry. At lower fields,superconductivity is observed below the white curvesmarked in the figure. These curves indicate the limitof the semiclassical regime given by rC = L, where rCis the cyclotron radius. There are even hints of super-conductivity well into the quantum Hall regime (seesupplementary section 2).At the mT limit the junction is unstable. Unlikethe Fraunhofer interference pattern usually observedin JJs, including NbSe2-graphene JJs we reportedin earlier studies [19, 20], here we observe a peri-odic saw-tooth pattern consisting of four lobes of≈400 µT, shown in figure 2(b). This measurementwas taken at VG =−0.25 V. We believe that thesejumps are associated with vortices which enter theNbSe2 flakes far from the junction. Individual vor-tices are expected to have an outsized effect at theFigure 2. Perpendicular magnetic field. (a) Landau Fanmeasurement of the differential resistance at zero biasvoltage, as a function of B⊥ and VG. The device exhibitsquantum Hall conductance above 1.5 T. Superconductivitysurvives in most of the semi-classical regime L< rC(boundary shown in white). (b) IC(B⊥) at low fieldsexhibits discrete jumps in IC at flux in multiples of≈ 400 µT, likely associated with remote vortices. Thisdataset was taken at VG =−0.25 V.ultra-thin limit, where the vortex-induced current-redistribution is governed by the Pearl length scale.The Pearl length isΛ = 2λ2L/d, where λ is the Londonpenetration length, and d is the flake thickness. At thepresent case, the currentmaps extends over the size ofthe entire flake.We now turn to the measurements in parallelmagnetic field B∥, which constitute the main resultsof this work. Figure 3(a) shows maps of junctionvoltage vs. applied current andVG. The measurementis repeated at several values of B∥. At each value of B||,we compensate B⊥ to reach a maximal critical cur-rent [19, 20]. We note that this can be done even con-sidering the vortex instability described above. Theleftmost scan, corresponding to B∥ = 0 extends thedata shown in figure 1(d). At B∥ = 0 T hole carriershad a larger critical current, as explained by the highertransparency of the channel in the absence of a P-N-Pjunction. Remarkably, as we increase B∥ we continueto observe FP oscillations at all fields in the rangeaccessible to ourmagnet, up to 8T.However, themag-nitude of IC decays from the µA scale at zero field,to the order of 10nA at B∥ = 8T. This result confirmsthe retention of superconducting ballistic transport atthese high fields. The periodicity of the oscillationsremains consistent and their visibility even increases.In figure 3(b) we plot IC(B∥), measured at VG =−0.4 Vwhile tracking IC decay. The exact mechanismleading to this decay is not obvious, and is the focus ofthe remaining part of this work. In what follows, wediscuss three possible mechanisms for critical currentsuppression: (i) Suppression of the NbSe2 supercon-ducting gap ∆; (ii) The effect of Zeeman splitting ofthe Andreev bound states (ABS) and (iii) Threadingmagnetic flux through the vdW gap between theNbSe2 and graphene.Considering the first mechanism, involving theeffect of ∆, it is well known that in thin NbSe2 thegap remains stable well above 10 T [15]. We can rule32D Mater. 12 (2025) 041004Figure 3. (a) Junction voltage as a function of current and VG at different values of in-plane magnetic field. The boundarybetween 0 and finite voltage regions indicates the critical current. The data exhibits Fabry Pérot oscillations of both IC and RN,shown here at selected values of B∥ = 0 T, 5 T, 6 T, and 8 T (from left to right). (b) Critical current decay vs. B∥. Data in orange.Blue and green solid lines are tight-binding calculations, assuming induced gap of∆∗ = 0.6 meV, with and without the effect offlux threading respectively (further details on the tight-binding model are given in the supplementary material section S2.2). (c)Differential resistance vs. bias voltage and B∥. Andreev reflection peaks hardly change their voltage as a function of B∥,confirming that the field has only a small effect on the superconducting gap.out the role of ∆ in suppressing IC in our deviceby measuring the differential resistance as a functionof bias voltage, shown in figure 3(c) (data taken atlarge hole doping VG = −1.5 V). The data exhibitsa conductance enhancement at low bias and resist-ance peaks at ±2∆, as expected for Andreev reflec-tion. Multiple Andreev reflection features at sub-gapenergies 2∆/n are not detected. The main resistancepeak 2.1 meV likely represents 2∆ for the large NbSe2gap. It is notable that the peak maintains near con-stant bias voltage as a function of magnetic field, con-firming that∆ is hardly affected by the field as expec-ted for thin NbSe2. The origin of the lower energyspectral feature is not clear, and could be relatedto the induced gap in graphene. The smaller NbSe2gap, studied in [16] should not be visible at the thinNbSe2 limit.A second mechanism which would lead to crit-ical current suppression is related to the spin-splittingof the ABS within the junction. However this sup-pression is only expected when the Zeeman splitting2EZ = gµBB is of order of the Thouless energy ETh.As mentioned above ETh ≈ 4 meV in our device andhence a significant suppression of the current wouldbe expected only at fields of order 35 T. In figure 3(b)we plot the predicted critical current in presence ofZeeman splitting, as obtained using a tight-bindingmodel. As can be clearly seen this effect alone cannotaccount for the decay of the critical current observedexperimentally at fields of order 8 T.Given that neither ∆ nor the Zeeman effect areexpected to suppress the critical current, we seek foran alternative mechanism based on the parallel accu-mulation of flux within the junction, as depicted infigure 4(a) [27]. We know that NbSe2 couples tothe graphene channel over an extended overlap area.Assuming the vdW gap is d= 0.6 nm wide, and theoverlap region is about 1 µm long, the resulting areaaccumulates a single flux quantum for an in-planefield component Bx ≈ 3.5 T.This, in turn, suggests that we cannot disreg-ard the contribution of this flux when calculatingthe properties of the junction. We therefore developa theoretical model which accounts for the orbitaleffect of the in-plane magnetic field on the proximityinduced gap (figure 4(a)). The model is based on aneffective hexagonal lattice representing the proxim-itized graphene, with a position-dependent inducedgap ∆∗. We use the model to calculate the phase-dependent Andreev spectra. The ground state energyof the junction, EGS, is then obtained by summingover the populated states. To extract the critical cur-rent we assume T= 0 and use Ic =max∣∣∣2e dEGSdφ∣∣∣. Adetailed description of the model appears in supple-mentary section 3.In the presence of an in-plane field, an electrontunneling from the NbSe2 to the graphene beneathit acquires a position dependent phase ϕ(x,y) =Az(x,y)d, where Az is the perpendicular componentof the vector potential. Hereafter, we use a gauge inwhich the vector potential is given by A⃗= (0,0,yBx −xBy). This in turn leads to a variation of 2ϕ(x,y) in thephase of the superconducting order parameter. In theshort junction limit we can neglect the effect of thephase modulation along x (the direction perpendicu-lar to the current). Thus to capture the orbital effectof the field in the numerical simulation, we introducea position dependent phase for the superconductingorder parameter ∆∗(y) = ∆∗eiqy, where q= 2eh̄ Bxd.We use this model to calculate IC for realistic sys-tem parameters. The results are plotted in figure 3(b).To reach these results, we first extract the ABS spec-tra, which are shown in figure S2. To clarify the rolesof the Zeeman and orbital terms, we show simpli-fied spectra obtained for a short, transparent junctionin figures 4(b)–(d). For comparison, panel (b) shows42D Mater. 12 (2025) 041004Figure 4. (a) Schematic setup of the junction used in thetheoretical modeling. (b)–(d) Simplified energy spectra inthe limit of a short perfectly transparent junction obtainedusing the tight-binding model (see supplementarymaterials section S4.2) for (b) B= 0, (c) B= 1T neglectingthe orbital effect, i.e. for d= 0, here Zeeman splitting of theABS is clearly seen , and (d) B= 1T including both theZeeman contribution and the orbital effect of the magneticfield as discussed in the text. Note the suppression of thegap and the shift in the crossing of Andreev bound statesaway from φ = π.the well-known ABS spectrum for B= 0. In panel (c),only the Zeeman coupling is included giving rise toZeeman split spin-polarized spectra. Importantly, asdiscussed above and illustrated in figure 3(b), theseonly give rise to a minimal suppression in IC, and donot reproduce the current suppression we observe.To fully reproduce the observed suppression wehave to account for both Zeeman and orbital effects.This calculation, shown in figure 4(d), indeed resultsin a suppressed induced gap, while the ABS crossingshifts away from φ = π. From these spectra we pro-ceed to calculate IC(B∥), noting that Bx = B∥ cos(θ),where θ = 45◦ (see figure 1(c)). To quantitativelycompare the data to the model, we fit for the inducedgap ∆∗. In figure S4 we plot the result of the cal-culation for value of ∆∗ = 0.4,0.6,0.8 meV for boththe temperature dependence and the magnetic fielddependent data. As seen in the figures, the fit suc-cessfully reproduces both data-sets at∆∗ = 0.6 meV.IC(B∥) calculated using the full model, with the abovevalue of ∆∗ is shown in figure 3(b), and appears toagree very well with the data.The 2DJJ reported thus exhibits remarkable sta-bility vs. both in-plane and out-of-plane magneticfield. Specifically, we have shown that the responseto in-plane field relies strongly on the nature ofthe extended contact region between NbSe2 andgraphene, and in particular the flux threaded withinthe atomically thin vdWgap. The role of threaded fluxhas already been acknowledged in studies involvingtwo dimensional electron systems [27]. Naturally, thisproblem should not be as severe for the angstrom-scale vdW gaps. However, one should note that recentwork on NbSe2 at high parallel fields [28] suggeststhat the role of the inter-layer flux is highly importantin inducing exotic superconducting phases. Finally,our results imply that in order to achieve Josephsondevices that do not decay at all with B∥, and exhibitpronounced characteristics of 0-π transitions andother spin driven phenomena, it is desirable to limitthe extent of the overlap region. Such tests would beaddressed in future studies. In conclusion our studyreports on an all vdW device with exceptional sta-bility towards applied magnetic fields. Such devicesmay be useful as part of field-stable quantum archi-tectures. The lack of oxide may make them morestable towards two-level system decoherence—a sub-ject which should be addressed in future studies.Data availability statementThe data that support the findings of this study areopenly available at the following URL/DOI: https://zenodo.org/records/15163380.AcknowledgmentsThe authors wish to thank H Dausy, F Pientka, C HQuay andMAprili for their input. This workwas fun-ded by an Israeli Science Foundation Grant 164/23.A Z is grateful to the Azrieli Foundation for AzrieliFellowships. KW and T T acknowledge support fromthe Elemental Strategy Initiative conducted by theMEXT, Japan, Grant Number JPMXP0112101001,JSPS KAKENHI Grant Number JP20H00354 and theCREST(JPMJCR15F3), JST. A K acknowledges fund-ing by the Israel Science Foundation (Grant No.2443/22). Fabrication for this project was carried outat the Harvey Kruger Center for Nano Science andNano Technology at the Hebrew University.ORCID iDsEinav Grynszpan 0000-0002-9420-0315Kenji Watanabe 0000-0003-3701-8119Anna Keselman 0000-0002-5226-8522Hadar Steinberg 0000-0002-7409-5087References[1] Buzdin A I 2005 Proximity effects in superconductor-ferromagnet heterostructures Rev. Mod. Phys. 77 935[2] Pientka F, Keselman A, Berg E, Yacoby A, Stern A andHalperin B I 2017 Topological superconductivity in a planarJosephson junction Phys. Rev. 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