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Ayelet Zalic, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Snir Gazit, Hadar Steinberg

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[High Magnetic Field Stability in a Planar Graphene-NbSe<sub>2</sub> SQUID](https://mdr.nims.go.jp/datasets/23defeae-b4e1-4409-a124-8b6efd9d9023)

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High Magnetic Field Stability in a Planar Graphene-NbSe2 SQUIDHigh Magnetic Field Stability in a Planar Graphene-NbSe2 SQUIDAyelet Zalic, Takashi Taniguchi, Kenji Watanabe, Snir Gazit, and Hadar Steinberg*Cite This: Nano Lett. 2023, 23, 6102−6108 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Thin NbSe2 retains superconductivity at a high in-plane magnetic field up to 30 T. In this work we construct a novelatomically thin, all van der Waals SQUID, in which current flowsbetween NbSe2 contacts through two parallel graphene weak links.The 2D planar SQUID remains uniquely stable at high in-planefield, which enables tracing critical current interference patterns asa function of the field up to 4.5 T. From these we extract theevolution of the current distribution up to high fields,demonstrating sub-nanometer sensitivity to deviation of currentflow from a perfect atomic plane and observing a field-driventransition in which supercurrent redistributes to a narrow channel.We further suggest a new application of the asymmetric SQUIDgeometry to directly probe the current density in the absence of phase information.KEYWORDS: graphene, NbSe2, Josephson interference, planar SQUID, high magnetic fieldTransition-metal dichalcogenide (TMD) superconductorssuch as NbSe2 can be mechanically exfoliated to yieldthin layers down to the monolayer limit.1,2 Thin NbSe2superconducting electrodes sustain very high in-plane magneticfields (B∥) beyond the Pauli limit, due to suppressed orbitaldepairing and Ising spin−orbit coupling (ISOC), which locksspins in the out-of-plane orientation.1 The superconductinggap persists nearly unchanged up to 10 T3 and remainsobservable up to 25 T in tunneling measurements.4It is useful to incorporate thin TMD superconductors indevices that utilize their unique properties at high B∥. NbSe2has been coupled laterally to graphene to realize NSjunctions.5,6 Devices consisting of NbSe2 flakes coupled onboth sides of a narrow graphene channel (Figure 1a) are well-behaved Josephson junctions (JJs).7,8 Our two-dimensionalplanar Josephson junctions (2DJJs), constructed exclusivelyfrom van der Waals (vdW) materials by transferring a crackedNbSe2 flake on top of graphene, are unique in retaining aJosephson effect at high parallel magnetic fields.In this work, we extend the all-vdW 2DJJ concept to aSQUID geometry, with current flowing between NbSe2contacts through parallel monolayer graphene (MLG) andfew-layer graphene (FLG) weak links (see Figure 1b). In thisstructure, the graphene flakes are supported by a flat, insulatinghexagonal boron nitride (hBN) substrate, and all interfaces areatomically clean (Figure 1c), ensuring a planar geometry. Thestability of the SQUID in magnetic field allows us to trace theevolution of IC(B⊥) interference patterns up to B∥ = 4.5 T. Wereconstruct the distribution of current flow from IC(B⊥),presenting a new method utilizing the asymmetric SQUIDgeometry without the need for phase retrieval. At high B∥, weobserve a qualitatively apparent transition, indicating anarrowing of the current channel in the MLG. Furthermore,we find that our SQUID is highly sensitive to the nanometer-scale height difference between the MLG and FLG currentplanes.For our SQUID we use a single cracked NbSe2 flake, ofapproximately 13 nm thickness, as seen in the cross-sectionalTEM measurement (see the Supporting Information); thelength of both junctions, imposed by the NbSe2 crack, is d =140 nm in the direction of the current flow (see Figure 1d). Itis important to distinguish between different planes ofreference in the sample. The “in-plane” magnetic field B∥ isdefined as oriented parallel to the mean SQUID plane: theplane connecting the centers of the MLG and FLG flakes(Figure 1e). This plane is at a small angle, θ, with respect tothe plane of the MLG flake.We begin by showcasing the basic properties of 2D SQUIDin Figure 2. Current−voltage characteristics of the SQUIDswitch from zero to finite resistance at the critical current IC,which we define according to a voltage threshold (Figure 2a).The transition from superconducting to normal conductance issharpest at B∥ = 0 T. Figure 2b illustrates the modulation of thecritical current by varying the charge carrier density. In ourSQUID the common back-gate tunes both FLG and MLGReceived: April 25, 2023Revised: June 17, 2023Published: June 22, 2023Letterpubs.acs.org/NanoLett© 2023 The Authors. Published byAmerican Chemical Society6102https://doi.org/10.1021/acs.nanolett.3c01552Nano Lett. 2023, 23, 6102−6108Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on July 15, 2023 at 06:01:46 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ayelet+Zalic"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Snir+Gazit"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Hadar+Steinberg"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.nanolett.3c01552&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/nalefd/23/13?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/13?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/13?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/13?ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01552?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org/NanoLett?ref=pdfhttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://acsopenscience.org/open-access/licensing-options/densities simultaneously; therefore, it is not possible topinpoint the MLG Dirac point exactly (it is likely in theregion of minimal IC around 10 V).Upon application of a small (mT scale for our devices)magnetic field perpendicular to the junction (B⊥), thesuperconducting order parameter Δeiφ acquires a position-dependent phase and undergoes interference. This leads to aFourier relation between the critical current IC(B⊥) and themaximal local critical current density J0(x)9=I B J x e x( ) ( ) dikxC 0 (1)where +k d B2 (2 )0, such that a loop connecting any twopoints x1, x2 and extending across the junction length d intothe superconductors up to the London penetration depth λencloses a magnetic flux of k(x2− x1)/2π in units of Φ0 (seeFigure 1d).The interference pattern of IC(B⊥) at zero gate voltage andB∥ = 0 T is shown in Figure 2c. The rapid oscillations of IC,with a magnetic field period ΔB = Φ0ASQ ≈ 380 μT, reflect thearea of the SQUID ASQ = 2δ(2λ + d) = 5.4 μm2. This areaimplies an effective penetration length λ = 930 nm, longer thanλL ≈ 200 nm yet shorter than the Pearl length Λ = 2λL2/t ≈ 6μm. The SQUID oscillations are modulated by an envelopewhich derives from the areas of the MLG and FLG channels, asillustrated by a schematic of two channel interference in Figure1h. Note that the measured B∥ = 0 T pattern is not perfectlysymmetrical with respect to B⊥. This could be a signature ofvarious symmetry-breaking effects15,16 but is most likely due tovortices in the vicinity of the junction or a small trappedparallel flux.The introduction of B∥ dramatically changes this pattern. AtB∥ = 2.8 T (Figure 2d), the SQUID oscillation persists andmaintains its periodicity, whereas the envelope is no longerdiscernible. The data now resemble the two-point interferencepattern in Figure 1g. The contrast between zero- and high-fieldinterference patterns is one of the main results of our work.The transition to a two-point SQUID indicates a change in thesupercurrent distribution, which becomes focused within anarrow channel at higher fields.To gain initial insight into the expected IC(B⊥) in theSQUID, we make two simplifying assumptions: (i) the phasedynamics are local and (ii) the current−phase relation issinusoidal. Both assumptions are typical for graphene-basedJJs. However, ballistic graphene JJs may exhibit measurableskewness in the current−phase relation,12 while in ultrathinsuperconducting contacts, the Pearl length Λ = 2λL2/t replacesλL as the relevant field decay scale and the dynamics becomepotentially nonlocal.13 Our smaller than bulk SQUIDperiodicity ΔB, discussed above, might hint at nonlocaldynamics; however, the typical nonlocal geometric relationΔB = 1.8Φ0/WS2,13 with WS being the width of thesuperconductor, is too large for our measured periodicity.This raises the need for future geometry-controlled experi-ments.Figure 1. (a) Planar NbSe2-graphene-NbSe2 JJ geometry. (b) SEMimage of the device. The conducting NbSe2 appears as a smooth darkgray region with a crack in the middle. An hBN flake used to pick upthe cracked NbSe2 covers the top-left corner, while the hBN substrateis visible inside the crack. Both are insulators and appear white andgrainy in SEM due to charging. Bridging the crack, the MLG flakeappears light gray and the FLG region as dark gray. Pink outlines ofMLG and FLG flakes extending beneath NbSe2 are overlaid from anoptical microscope image prior to stacking. (c) False-color cross-sectional TEM measurement of the FLG region showing atomicallyclean interfaces between NbSe2 and FLG and between FLG and hBN.(d) Schematic showing B⊥ flux through one possible currentcirculation path, with an area (2λ + d)|x2 − x1|. (e) Schematicillustration of FLG and MLG parallel weak links of differentthicknesses. Directions x̂ and ŷ are in the plane of the flakes, and z ̂is perpendicular. The mean SQUID plane is shown in blue, at anangle θ. B∥ is parallel to the SQUID plane, and B⊥ is perpendicular toit. Crack length d is in the direction of current flow (f−h) Illustrationof interference patterns for different junction geometries: (f) singlechannel (Fraunhofer), (g) two point (SQUID), and (h) two channel(Fraunhofer envelope modulates SQUID oscillation).Figure 2. (a) Current−voltage traces at B∥ = 0 T, B∥ = 2.8 T, and zerogate voltage. The voltage threshold for determining critical current isshown in black. (b) Current−voltage traces as a function of gatevoltage at zero field. Gate modulates the critical current, with aminimum at around 10 V (the MLG Dirac point) (c) Interferencepattern at B∥ = 0 T, with a ΔB ≈ 380 μT oscillation corresponding tothe SQUID area and an envelope reflecting the area of the MLG andFLG junctions. A white line marks the threshold detection of IC. (d)Interference pattern at B∥ = 2.8 T. The SQUID oscillation maintainsperiodicity similar to that of (a), but the envelope is no longer visible.Note that the measured B⊥ range at B∥ = 2.8 T is smaller than at 0 Tto avoid entry of vortices.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01552Nano Lett. 2023, 23, 6102−61086103https://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig2&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01552?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asUsing the assumptions described above, we begin byapproximating a spatially uniform current density in eachchannel. Applying eq 1 to this simplified model produces atwo-channel diffraction pattern14 (see Figure 1h), with thefinite FLG/MLG widths (WF, WM) generating Fraunhofer-likeenvelopes (Figure 1f) modulating the SQUID oscillations(Figure 1g). We describe the exact expression and thecalculation leading to it in the Supporting Information.Below, we refer to this as the “Analytical Model”.To investigate the supercurrent distribution systematically,we first turn to study how the B∥ = 0 T interference patternevolves with respect to the applied gate voltage. We measure ICas a function of B⊥ and VG continuously, as shown in the colorplot in Figure 3a. The overall SQUID periodicity remains fairlyconstant, whereas the critical current magnitude and theFigure 3. (a) IC (color scale) vs B⊥ and gate voltage. (b) Normalized current density extracted from (a) using a maximum entropy method (seetext). (c) Normalized autocorrelation function (see text) of the current density (color scale) vs l, the autocorrelation shift in the x coordinate.Compare the sideband bounded in pink dashed lines, which is proportional to the MLG current density convolved with the narrow FLG currentchannel, to the MLG current density bounded in pink lines in (b). (d) Interference patterns at gate voltages of −30, 0, and 30 V with two-channelanalytical fit. (e−g) Current density profiles corresponding to the analytical fits in (d). (h) Interference patterns at gate voltages of −30, 0, and 30 Vwith maximum entropy fit. (i−k) Current density profiles corresponding to fits in (h).Figure 4. (a) IC (color scale) vs B⊥ and B∥, at zero gate voltage. The white dashed line marks the geometric angle θ ≈ 0.025° between the SQUIDplane and the MLG. (b) Normalized current density extracted using the maximum entropy method from the data in Figure S4. (c) Normalizedautocorrelation function of the current density from (a). Compare the sideband to the MLG current density in (b). (d) Interference patterns at B∥= 0, 2, and 2.5 T with two-channel analytical fit. (e−g) Current density profiles corresponding to the analytical fits in (d) (h) Interference patternsat B∥ = 0, 2, and 2.5 T with maximum entropy fit. (i−k) Current density profiles corresponding to fits in (h).Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01552Nano Lett. 2023, 23, 6102−61086104https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?fig=fig4&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01552?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asenvelope both evolve with the gate voltage�indicating avariation in current distribution. Figure 3d shows selectedinterference patterns from Figure 3a at VG = −30, 0, 30 V.We fit these curves using the analytical model describedabove, where the free parameters are the MLG and FLGwidths WM, WF, the distance between their centers 2δ (seeFigure 1e), and the ratio between their critical current densitiesJM/JF (see the Supporting Information for details). Figure 3e−g shows the current density profile for each VG trace extractedfrom the fit. For 2λ + d = 2 μm, we find that fit parametersWM,WF, δ agree with the dimensions determined from SEMmeasurements shown in Figure 1d (see comparison table inthe Supporting Information). The extracted current densitiesin Figure 3e−g show that the MLG current modulates stronglywith gate, increasing at negative gate voltage.We now turn to a detailed investigation of the field-driventransition shown in Figure 2, tracing the interference patternscontinuously with increasing B∥. In Figure 4a we plotIC(B⊥,B∥), at VG = 0 V. This interference plot is extremelystable, up to B∥ = 4 T, barring minor flux jumps around B∥ =2.8 T, likely due to vortices entering the vicinity of the junction(see the Supporting Information). B∥ is kept strictly aligned tothe SQUID plane by careful compensation of the out-of-planecoil. This precise alignment procedure utilizes the phase of thefast SQUID oscillations and allows us to avoid flux jumps up tohigher fields than in previous works.8,27 B⊥ is defined asgeometrically perpendicular to B∥. Note that we control thefield along the axes of the lab magnets, which are not exactlyaligned with the SQUID plane; we describe the compensationand alignment procedure in detail in the SupportingInformation.The data exhibit a diagonal drift of the MLG envelopetoward negative B⊥, evident in a shift of the maximal IC and ofthe first Fraunhofer nodes. This diagonal is due to deviationfrom a perfect planar geometry: the step height h betweenMLG and FLG planes creates an angle θ between the SQUIDplane and the MLG. With B∥ aligned exactly to the SQUIDplane, it contributes a component B∥(sinθ) of fluxperpendicular to the MLG and FLG flakes. The condition ofzero flux through the MLG, for which the Fraunhofer envelopefunction is maximal, thus drifts toward negative values of B⊥,following the linear relation B⊥(max(IC)) = −B∥(sinθ) tocompensate (see full calculation the Supporting Information).The angle θ ≈ 0.025° extracted from the fit indicates a stepheight of around 1 nm, while the TEM measured FLGthickness is 2.4 nm; this probably indicates a distribution ofcurrent throughout the FLG, with the mean SQUID planebeing determined by the center of the FLG flake. There couldalso be an additional step or curvature in the hBN outside therange of the TEM. The 2DJJ SQUID is thus an extremelysensitive tool for tracking deviations from the atomic planargeometry.The effect of field-driven current redistribution is apparentin the transition to a SQUID-like interference pattern. Figure4d shows a series of interference patterns at B∥ = 0, 2, and 2.5T, together with the best fit of our analytical model. Thecurrent densities corresponding to the fit appear in Figure 4e−g, showing a narrower current profile in the MLG as B∥increases.The analytical curves fit the data reasonably well for thecentral lobes of the interference patterns (see Figures 3d and4d), but the higher order lobes are far more pronounced in thedata compared with the fit, hinting that the current densitydistribution has finer spatial detail beyond the two uniformconduction channels. We thus turn to extract the currentdistribution in greater detail. Since the interference patternreflects the absolute value of the Fourier transform of thecurrent density, phase information is lost and it is impossible todirectly apply an inverse Fourier transform. The oft-citedDynes−Fulton approach to phase retrieval assumes a nearlysymmetric current distribution, and so is not applicable in ourcase.17We use an approach that we term “the maximum entropymethod” suitable for reproducing current distributions with nosymmetry requirements. The method postulates a currentdensity profile sampled at N discrete spatial points and subjectto known physical constraints to calculate the critical currentvia a forward Fourier transform. The current density profile isthen adjusted to obtain the best fit of the calculatedinterference pattern to the data, as in ref 18, with an additionalmaximum entropy constraint in order to avoid spurious sharpchanges in current density.19 See the Supporting Informationfor the full details of our fitting algorithm, including ourapproach toward calibrating parameters and avoiding over-fitting (based on the L curve20).To demonstrate the maximum entropy method, we return tothe interference patterns measured at B∥ = 0 T and differentgate voltages (Figure 3), and extract the current densities at VG= −30, 0 and 30 V, shown (normalized by the maximal J0 foreach gate) in Figure 3i−k. To confirm self-consistency, weapply eq 1 to reproduce the interference pattern correspondingto the extracted current density. We compare these to themeasured patterns in Figure 3h; the obtained fit is indeed farbetter than the analytical fit in Figure 3d, especially in thehigher order lobes. In Figure 3i−k, we observe that theextracted current within the MLG is distributed with twopeaks; this could be related to some device-specific feature, orperhaps these are the familiar graphene edge channels firstobserved in refs 10 and 11. The color plot in Figure 3b showsthe full evolution of the extracted current density with the gatevoltage.The fit obtained by the maximum entropy method isremarkably successful. Nevertheless, it is a complex methodwith many algorithmic as well as physical parameters. Since weare interested in circumventing the phase-retrieval problemaltogether, we introduce a new method that harnesses ourasymmetric SQUID geometry. We employ the narrower FLGjunction as a direct probe of the current density in the widerMLG junction. This method leans on the Wiener−Khinchintheorem, which states that the energy spectral density of afunction and its autocorrelation C(l) are Fourier transformpairs. In our case, |IC(B⊥)|2 is the energy spectral density ofJ0(x) and thus| | = = * +F I B C l J x J x l x( ( ) ) ( ) ( ) ( ) dC20 0 (2)Note that here, to calculate the autocorrelation, we performa forward Fourier transform of the energy spectral density,which does not require any knowledge of the phase. Thiscalculation is always possible; however, only for a specificasymmetric SQUID geometry, the autocorrelation of J0(x) alsoprovides direct information about J0(x) itself. Consider anideal two-channel device, where the current density in the onechannel is extremely narrow, approximated by the Dirac deltafunction, whereas the current in the other channel is widelydistributed. The separation between the centers of the twoNano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01552Nano Lett. 2023, 23, 6102−61086105https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01552?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aschannels is larger than their combined widths. Theautocorrelation in this case contains a term equal to thecurrent density in the wider channel (see calculations in theSupporting Information).In our device, the FLG is a few times narrower than theMLG and carries a similar total current. In this instance, theautocorrelation convolves the FLG and MLG densities,resulting in a feature which qualitatively resembles the MLGcurrent density “smeared” at the scale of the FLG width andcentered at l = −2δ equal to the distance between the centersof the two channels. Figure 3c shows the autocorrelation as afunction of gate; the resulting “sideband” centered at l = − 2.7μm is qualitatively similar in its form to the extracted currentdensity in Figure 3b. There is a clear qualitative agreementbetween the MLG current distributions extracted by maximumentropy and autocorrelation, shown between the pink lines inFigure 3b,c. This confirms the validity of these two verydifferent methods.We now apply these methods to extract a visual picture ofthe evolution of the current density with a parallel magneticfield. Figure 4b shows the current density extracted using themaximum entropy fit of an IC(B⊥,B∥) data set (see theSupporting Information). This map allows us to visualize howthe current density in the MLG redirects into a narrowchannel. The interference patterns produced by the maximumentropy procedure fit most of the measured patterns closely, asshown for selected values of B∥ = 0, 2, and 2.5 T in Figure 4h.The extracted current densities at this succession of fields aredepicted in Figure 4i−k, illustrating again the narrowing of thecurrent-carrying channel in the MLG as B∥ increases.This phenomenology is apparent also in the current densityextracted by autocorrelation. The sideband marked by pinklines in Figure 4c, centered around an autocorrelation shift l =2.7 μm (equal to the distance between MLG and FLGchannels), is qualitatively similar to the maximum entropyMLG current density shown in Figure 4b and also exhibits anarrowing of the current channel in the MLG commencing atB∥ = 2 T.The transition toward narrow supercurrent channels hasalready been hinted at in our previous work�indeed, multiplediffusive MLG−NbSe2 junctions also undergo a transition toSQUID-like interference patterns where all lobes are of similarheight at high B∥.8 In that work, the patterns were toodisordered to fit to eq 1, and we could not rule out the role ofripples due to the SiO2 substrate.8 In the present work, thedevice is flat due to the use of an hBN substrate. In addition,the signal is sufficiently stable to allow a quantitative fitting. Allmodels, assuming an experimental geometry corroborated bySEM and TEM, yield a clear transition between a distributedcurrent density in the MLG at low fields, to a narrowsupercurrent channel at high B∥.We note that a similar effect of SQUID-like interferencepatterns at high B∥, seen by Suominen et al., was attributed tosuppression of supercurrent in the bulk of the JJ due to amagnetic dipole formed by tilted flux lines.21 In our geometry,however, SQUID-like interference indicates one channel in theMLG, not necessarily on the edge. The flux focusing effect isalso weaker in thin NbSe2 electrodes, where the tilt of the fieldlines is minimal due to a long London penetration length.Thus in our devices, the origin of field-induced currentredistribution is an open question. It suggests the existence ofat least one conductance channel with resilience to high B∥.The suppression of a 2DJJ supercurrent vs B∥ is determined bythe interplay of the Thouless and Zeeman energy scales,8,22 theThouless energy being a transport energy scale determined bythe inverse of the traversal time of the junction.23 Hence, thesuperior resilience of a single channel could be theconsequence of a higher Thouless energy if a particularchannel allows faster traversal of the junction. This could be,for example, a guided edge mode or a shorter channel in anonuniform junction geometry. However, the presence of asimilar effect in a number of devices in ref 8 suggests that it isnot related to a particular geometry. Favored channels couldalso be the ones that experience minimal scattering in adisordered potential landscape. Alternatively, graphene couldinherit Ising spin−orbit coupling by proximity to the NbSe2within the extended contact region between the twomaterials.24 Such an interaction would enhance the stabilityof the carriers to the in-plane field, and spatial variation of theinduced coupling could lead to preferred channels. All in all,we find that the in-plane magnetic field appears to createnarrow superconducting channels in graphene-NbSe2 2DJJs, anintriguing effect which has yet to be understood.There has been a recent surge of interest in planar JJs withspin−orbit coupling,25−28 driven by predictions for topologicaleffects tuned by parallel magnetic field.29−32 Looking to thefuture, further exploration of 2DJJs at high parallel field canshed light on the role of spin−orbit effects in the hybridgraphene-TMD structure.24,33,34Methods. We exfoliated hbN on markered SiO2 andlocated substrate flakes of thicknesses around 20−40 nm. Weexfoliated graphene to SiO2 directly and NbSe2 first to PDMSand then stamped the PDMS on SiO2 to transfer the flakes.This method supplied large, thin flakes of NbSe2 that were notobtained by exfoliating directly from the blue tape to SiO2. Weused an optical microscope to search for two long, narrowgraphene flakes which are within a few μm distance of eachother for the channels of the SQUID, as well as NbSe2 flakesthat are a few layers thick and have an observable crack, lessthan 500 nm wide. We then employed a successivepolycarbonate (PC) pickup technique35 to pick up first theNbSe2 and then the graphene strips oriented perpendicular tothe crack and finally deposited the stack on the hBN substrate.We applied standard e-beam lithography and e-beamevaporation to create Ti/Au contacts to the NbSe2, removingsurface oxide using in situ argon ion milling prior toevaporation. Four-probe measurements were conducted in aBluFors dilution cryostat with a 3 T/9 T vector magnet and abase temperature of 20 mK.■ ASSOCIATED CONTENT*sı Supporting InformationThis work contains a Supporting Information document withthe following chapters: The Supporting Information isavailable free of charge at https://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552.Parallel field alignment procedure, vortex penetrationand device stability to out-of-plane flux, analyticalcalculation of two-channel interference pattern, max-imum entropy reconstruction of the current profile viaMarkov Chain Monte Carlo simulated annealing, andcurrent density extraction using the Wiener−Khinchintheorem (PDF)Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01552Nano Lett. 2023, 23, 6102−61086106https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?goto=supporting-infohttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01552?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01552/suppl_file/nl3c01552_si_001.pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01552?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as■ AUTHOR INFORMATIONCorresponding AuthorHadar Steinberg − The Racah Institute of Physics, TheHebrew University of Jerusalem, Jerusalem 91904, Israel; TheCenter for Nanoscience and Nanotechnology, HebrewUniversity of Jerusalem, Jerusalem 91904, Israel;orcid.org/0000-0002-7409-5087; Email: hadar@phys.huji.ac.ilAuthorsAyelet Zalic − The Racah Institute of Physics, The HebrewUniversity of Jerusalem, Jerusalem 91904, Israel; The Centerfor Nanoscience and Nanotechnology, Hebrew University ofJerusalem, Jerusalem 91904, IsraelTakashi Taniguchi − International Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Kenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119Snir Gazit − The Racah Institute of Physics and The FritzHaber Research Center for Molecular Dynamics, The HebrewUniversity of Jerusalem, Jerusalem 91904, IsraelComplete contact information is available at:https://pubs.acs.org/10.1021/acs.nanolett.3c01552Author ContributionsA.Z. fabricated the devices and performed the measurements,data analysis, analytical and numerical simulations. All authorscontributed to the writing of the manuscript.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThe authors wish to thank Y. Anahory, M. Aprili, E.Grynszpan, N. Katz, A. Keselman, C. H. L. Quay, and P.Ramachandran for insightful discussions. This work wasfunded by Israel Science Foundation Quantum Initiativegrant 994/19, Israeli Science Foundation grant 861/19, andBSF grant 2016320. S.G. acknowledges support from the IsraelScience Foundation, Grant No. 586/22. A.Z. is grateful to theAzrieli Foundation for Azrieli Fellowships. K.W. and T.T.acknowledge support from JSPS KAKENHI (Grant Numbers19H05790, 20H00354, and 21H05233).■ REFERENCES(1) Xi, X.; Wang, Z.; Zhao, W.; Park, J.-H.; Law, K. T.; Berger, H.;Forro, L.; Shan, J.; Mak, K. F. Ising pairing in superconducting NbSe2atomic layers. Nature Physics 2016, 12 (2), 139−143.(2) Tsen, A. W.; Hunt, B.; Kim, Y. D.; Yuan, Z. J.; Jia, S.; Cava, R. J.;Hone, J.; Kim, P.; Dean, C. R.; Pasupathy, A. N. 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