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Philipp Schmidt, Katarina Stanojević, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Bernd Beschoten, Vincent Mourik, Christoph Stampfer

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[Anisotropic supercurrent suppression and revivals in a graphene-based Josephson junction under in-plane magnetic fields](https://mdr.nims.go.jp/datasets/ba08848f-03ce-4011-998d-276880c92d86)

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Anisotropic supercurrent suppression and revivals in a graphene-based Josephson junction under in-plane magnetic fieldsPHYSICAL REVIEW B 111, 245301 (2025)Anisotropic supercurrent suppression and revivals in a graphene-basedJosephson junction under in-plane magnetic fieldsPhilipp Schmidt ,1,2,* Katarina Stanojević ,1,* Kenji Watanabe ,3 Takashi Taniguchi ,4 Bernd Beschoten ,1Vincent Mourik ,5 and Christoph Stampfer 1,2,†1JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, 52074 Aachen, Germany2Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany3Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan4International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan5JARA Institute for Quantum Information (PGI-11), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany(Received 1 February 2025; revised 28 April 2025; accepted 16 May 2025; published 6 June 2025)We report on a tunable Josephson junction formed by a bilayer graphene ribbon encapsulated in WSe2 withsuperconducting niobium contacts. We characterize the junction by measurements of the magnetic field–inducedinterference pattern and the AC Josephson effect manifested as Shapiro steps, examining current-dependenthysteresis and junction dynamics. The latter can be tuned by temperature, gate voltage, and magnetic field.Finally, we examine the evolution of the supercurrent when subjected to in-plane magnetic fields. Notably, weobserve strong anisotropy in the supercurrent with respect to the orientation of the in-plane magnetic field. Whenthe field is parallel to the current direction, the supercurrent is suppressed and shows revivals with increasingmagnetic field, whereas it remains almost unaffected when the field is oriented in a perpendicular direction. Wesuggest that this anisotropy is caused by the dependence of supercurrent interference on the junction geometry.DOI: 10.1103/PhysRevB.111.245301I. INTRODUCTIONJosephson junctions exploit the quantum mechanical phe-nomenon where a supercurrent flows between two supercon-ductors separated by a thin insulating or normal conductingweak link [1–5]. The unique properties of graphene providea tunable weak link with highly transparent interfaces dueto absence of Schottky barriers [6,7], while the high car-rier mobility of graphene, enabling ballistic transport [8,9],together with its ability to host proximity-induced supercon-ductivity, make it an attractive candidate for next-generationJosephson junctions [10,11]. Graphene Josephson junctionsoffer several advantages over conventional junctions. Theirtunability via electrostatic gating allows for dynamic con-trol of junction properties, potentially leading to tailored andreconfigurable quantum devices [12–15]. Additionally, theimplementation of a high spin-orbit material such as WSe2,that gets proximity-coupled to a bilayer graphene, allows usto implement Josephson junctions that potentially host topo-logically protected states [16], which are of importance for theongoing search for non-Abelian phases of matter [17–20].*These authors contributed equally to this work.†Contact author: stampfer@physik.rwth-aachen.dePublished by the American Physical Society under the terms of theCreative Commons Attribution 4.0 International license. Furtherdistribution of this work must maintain attribution to the author(s)and the published article’s title, journal citation, and DOI.In recent years, graphene-based Josephson junctions havebeen intensively investigated [7,21–43]. So far, the influenceof a magnetic field applied in the plane of the Josephsonjunction has not been systematically and angle-resolved in-vestigated. However, tuning the Zeeman energy in theseJosephson junctions by an in-plane magnetic field is crucialfor the formation of topologically protected states [16,44–46].In this paper, we report on a study of a tunable graphene-based Josephson junction formed by a bilayer graphene ribbonencapsulated in WSe2 with superconducting niobium (Nb)contacts. We present a detailed characterization of the junc-tion, which includes magnetic interference as well as Shapirostep measurements where we examine the difference betweenthe switching currents and the damping behavior. Further-more, we investigate the evolution of the supercurrent whenthe junction is subject to in-plane magnetic fields. A stronganisotropy of the supercurrent is observed with respect to theorientation of the in-plane magnetic field, and we suggest thatin-plane geometric interference effects may be its origin.II. SAMPLE LAYOUT AND BASIC TRANSPORTCHARACTERISTICSA schematic and an atomic force micrograph of our deviceare shown in Figs. 1(a) and 1(b), respectively. The device con-sists of a bilayer graphene flake symmetrically encapsulated insingle layers of WSe2 and thicker flakes of hexagonal boronnitride (hBN) using automated flake search [47] and dry trans-fer stacking [8]. The stack is etched into a w = 2.1 µm-wideribbon by SF6/O2 reactive ion etching (RIE) through a poly-methyl methacrylate resist mask, which has been patterned2469-9950/2025/111(24)/245301(8) 245301-1 Published by the American Physical Societyhttps://orcid.org/0000-0002-1278-1727https://orcid.org/0009-0001-9903-0116https://orcid.org/0000-0003-3701-8119https://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0003-2359-2718https://orcid.org/0000-0003-1522-7403https://orcid.org/0000-0002-4958-7362https://ror.org/04xfq0f34https://ror.org/02nv7yv05https://ror.org/026v1ze26https://ror.org/026v1ze26https://ror.org/02nv7yv05https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevB.111.245301&domain=pdf&date_stamp=2025-06-06https://doi.org/10.1103/PhysRevB.111.245301https://creativecommons.org/licenses/by/4.0/PHILIPP SCHMIDT et al. PHYSICAL REVIEW B 111, 245301 (2025)NbwlNb1 µm400−40-2 0I (μA)2V (μV)dV/dI (Ω)3002001000I20 6500-2-20 0 20I (μA)dV/dI (Ω)1.20.80.40.0(c)6004000I(μA)−20 0 201.20.80.40.00 1 4 5I (μA)2001-120−20-1 1V = 30VBGrV (V)BGs R (Ω)IsIrV (V)BG(d)(e) (f)NbNbhBNshBN BLG2 3  SiOWSe 2WSe 22T (K)-30Sixyφ10-10V = 30VBG++(a)(b)0300 nmIsFIG. 1. (a) Schematic of the Josephson junction. Side and top views of the device with a length of 250 nm and a width of 2.1 µm is shown.The bilayer graphene (BLG) is located between two flakes of WSe2, encapsulated in hBN and contacted by superconducting niobium (Nb)contacts. The van der Waals heterostructure is placed onto a Si++/SiO2 back gate. (b) Scanning force microscope image of the examineddevice showing the etched ribbon and the two niobium contacts. (c) DC voltage and differential resistance dV/dI as a function of bias currentat VBG = 30 V. The bias current was swept from negative to positive values. (d) Differential resistance as a function of applied back gate voltageand bias current. (e) Extracted switching current Is and resistance Rs as function of back gate voltage. (f) Temperature-dependent switchingcurrent Is and retrapping current Ir at VBG = 30 V.by standard electron beam lithography. The bilayer grapheneis electrically contacted to 25-nm-thick superconducting Nbelectrodes, fabricated by RIE and consecutive sputter deposi-tion through the same resist mask without any cleaning stepsin between. This defines the junction length of l = 0.25 µm.The device is placed on a highly doped silicon substrateserving as a back gate, with a 285-nm-thick separating SiO2gate dielectric. This allows us to adjust the charge carrierdensity of the bilayer graphene to n = α(VBG − V 0BG), whereαBG represents the gate lever arm, which is proportional tothe capacitive coupling between the back gate and the bilayergraphene. For more details on the fabrication procedure anda characterization of the Nb film, see Secs. S1 and S2 in theSupplemental Material [48].All measurements were conducted in a He3/He4 dilutionrefrigerator at a base temperature of 30 mK, using a four-terminal low-frequency lock-in technique with an appliedcurrent bias, see Sec. S3 in the Supplemental Material [48].In Fig. 1(c), we show a representative V-I curve as well asthe differential resistance of the Josephson junction at a backgate voltage of VBG = 30 V. Here, the bias current is sweptfrom negative to positive values. The switching current Is canbe identified as the switching from the superconducting tothe resistive state at positive bias current, while the switchingfrom the resistive to the superconducting state at negativebias currents defines the retrapping current Ir. In Fig. 1(d),the differential resistance dV/dI of the device is shown asa function of the bias current I and back gate voltage VBG.The superconducting regime (visible as the dark blue region)appears around I = 0 for both electron doping (VBG > −8 V)and hole doping (VBG < −8 V), clearly distinct from theresistive regime at higher bias current values. The extractedgate voltage–dependent switching current Is and switchingresistance Rs are shown in Fig. 1(e). The IsRs product of thejunction ranges from 40 to 180 µV, see Sec. S6 in the Supple-mental Material [48]. Furthermore, we show the temperaturedependence of Is and Ir at VBG = 30 V, see Fig. 1(f). Thetemperature-dependent difference between Is and Ir, whichemerges <2 K, can be understood by evaluating the qualityfactor of the junction Q = √2eIsR2sC/h̄ in the frameworkof the resistively and capacitively shunted junction (RCSJ)model that describes the dynamics of a Josephson junction byconsidering it as a parallel combination of a resistor, capacitor,and an ideal Josephson element [49,50]. Here, the junctioncapacitance, estimated by fitting the RCSJ model to a mea-sured V-I curve (see Sec. S5 in the Supplemental Material [48]for details), is C = 0.1 pF, and by measuring Is, the qualityfactor is determined, which changes from Q > 1 to Q < 1at a temperature of 2.5 K. Therefore, the junction dynamicschanges from the underdamped to the overdamped regimewhere Is and Ir become equal. Further details on the dampingand quality factor are presented in Sec. S7 in the SupplementalMaterial [48].III. SHAPIRO STEPSTo study the junction dynamics in more detail, we investi-gate the influence of microwave radiation on the V-I curve ofthe junction. Applying microwave radiation leads to the ACJosephson effect, which is manifested in additional plateausin the DC voltage [51], known as Shapiro steps. These stepsoccur at integer multiples of h f /2e and result from the phase245301-2ANISOTROPIC SUPERCURRENT SUPPRESSION AND … PHYSICAL REVIEW B 111, 245301 (2025)100-10P (dBm)(a)4 GHz(b)counts norm.counts (a.u.)-4 -2 0 2V (hf/(2e))40-400 400V (μV)40050-50dV/dI (Ω)6002000I (nA)-200 2000 -4-2 0 2V (hf/(2e))4-400 400I (nA)-200 2000155-5-4100-10P (dBm)155-50 500dV/dI (Ω)0 1(d)(c)-5 0 5400-400200-2000B  (mT)z200-20-10 0 10I (nA)B  (mT)z0 500dV/dI (Ω)0.01 10.1I  / Is s0V(V)BG(e)(f)I  sI  rFIG. 2. (a) Differential resistance as a function of RF signal power and bias current measured at a drive frequency of 4 GHz and a backgate voltage of VBG = 30 V. A magnetic field of Bz = 1.25 mT was used to decrease the switching current. (b) Normalized histogram of theDC voltages in units of h f /(2e) as a function of RF signal power. More Shapiro steps emerge with increasing power. (c) DC voltage (red)and differential resistance (black) as a function of bias current at an RF power of 13.8 dBm. (d) The sum of the histogram with pronouncedpeaks at integer values of Vdc in units of h f /(2e). (e) Differential resistance as a function of perpendicular magnetic field Bz and bias currentfor VBG = 0 V. (f) Extracted normalized switching current as a function of Bz and back gate voltage VBG.locking across the junction to the external frequency. Here, his the Planck constant, f the frequency of the radio frequency(RF) signal source, and e the elementary charge. The forma-tion of Shapiro plateaus with increasing microwave poweris visible in Fig. 2(a), where the measurement was takenat VBG = 30V and f = 4 GHz. Here, the differential resis-tance is shown as a function of applied bias current I andthe applied signal power. The pattern qualitatively resemblesthe expectation for weakly damped Josephson junctions wherethe extension of the steps surpass Is and superconductingpockets develop in the normal conducting region. We alsoobserve broad regions of microwave power where the resis-tive transition is an extended line instead of single pointsexpected for the Bessel function behavior of overdampedJosephson junctions [52]. This behavior has also been ob-served in other graphene Josephson junctions [53–55] andmay be explained by the junction being underdamped andhaving a high plasma frequency. The first Shapiro plateaustarts to develop at −7 dBm, whereas at higher powers, manydifferent plateaus emerge separated by sharp peaks in thedV/dI curve, as depicted in Fig. 2(c). Moreover, the quan-tization of these steps can be seen in the power-dependenthistogram of the DC voltages in Fig. 2(b), where the stepsemerge at integer multiples of h f /2e. This is also reflectedin sharp peaks of the sum histogram, see Fig. 2(d). All in-teger Shapiro steps are present without any subinteger stepsappearing, unlike what is observed in other two-dimensionalJosephson junctions [56,57], suggesting that the current phaserelationship is not strongly skewed. Additional Shapiro stepmeasurements are shown in Sec. S8 in the Supplemental Ma-terial [48].IV. SUPERCURRENT INTERFERENCENext, we examine the magnetic field dependence of theswitching current for both out-of-plane and in-plane direc-tions. We start with out-of-plane magnetic fields and measurethe differential resistance vs both the current I and the out-of-plane magnetic field Bz. The phase difference between thetwo superconductors induced by the magnetic field leads toa modulation of the switching current Is [58], as illustratedin Fig. 2(e). Analyzing the periodicity of the modulationpattern leads to an effective junction length of 603 nm anda magnetic penetration depth of λ ≈ 175 nm, with the areaof the weak link determined from atomic force microscopymeasurements, see Sec. S4 in the Supplemental Material [48]for details. The resulting penetration depth is in reasonableagreement with λNb = 150 nm reported for niobium [59]. Wenote that the oscillation period of the supercurrent modulationpattern remains unchanged irrespective of the applied gatevoltage, see Fig. 2(f). This is in contrast with previous workon BLG/WSe2, where a 2�0 signature has been observed inthe interference pattern at charge neutrality [43].In Fig. 2(e), a pronounced difference between the switch-ing current and the retrapping current can be seen aroundthe central lobe. This behavior can again be explained by atunable quality factor Q as the magnetic field–induced mod-ulation of the switching current leads to a transition of thequality factor from Q ≈ 3 at the central lobe to Q ≈ 1 athigher lobes, accompanied by a transition from the under-damped to the hysteresis-free junction dynamics.We now analyze the behavior of the junction for an in-planemagnetic field (B||) varying the angle (ϕ), which is defined in245301-3PHILIPP SCHMIDT et al. PHYSICAL REVIEW B 111, 245301 (2025)0-2 0 4I (μA)(a)1.5-1.5-4 20°45°90°135°180°225°270°315°20 mT50 mT75 mT100 mT150 mT200 mT0200 400300 mTI (μA)(c) (e)2-2 0°0 600(b) (d) (f)90030000 120 240φ (deg)1.51.00.501-10 200 400 6000200 400I (μA)2-2 90°0 6001-160 180 300120060036015000 200dV/dI (Ω) 0 200dV/dI (Ω)B  ||B  (mT)z B  (mT)|| B  (mT)||B  (mT)||0 200dV/dI (Ω)B  ||1B  (mT)||10°240°270°01.5-1.501.5-1.5sI  (μA)240° 90°180°270° 0°FIG. 3. (a) Differential resistance as function of current and out-of-plane magnetic field for B|| = 150 mT at in-plane angles ϕ = 0◦, 240◦,and 270◦. (b) Polar representation of the maximum of Is, extracted from the interference measurements, as a function of ϕ for varying B||.(c) and (d) Differential resistance as function of current and B|| applied in the direction of the current (ϕ = 0◦) and perpendicular ϕ = 90◦.(e) Extracted switching current as a function of B|| for various in-plane angles ϕ. The gray bar indicates the region of nondetectable switchingcurrent. (f) In-plane magnetic field of the first supercurrent minimum B1|| for different angles ϕ. Solid gray line represents a fit to the geometricalmodel described in the text. An outlying point at 90◦ at ∼3 T is not included. See Sec. S10 in the Supplemental Material [48] for the extraction(for minima up to 300 mT) or extrapolation procedure (for minima beyond 300 mT).Fig. 1(a). First, the Bz-induced interference pattern is shownin Fig. 3(a) at B|| = 150 mT applied at different angles. Whenthe in-plane magnetic field is oriented parallel to the directionof the current (ϕ = 0◦ and 180◦), the supercurrent is moststrongly suppressed [see upper panel in Fig. 3(a)]. However,it reappears at skewed angles, such as 240◦, and reachesa maximum when the field is perpendicular to the current(ϕ = 270◦). This behavior is summarized in a polar plot ofthe maximum switching current plotted as a function of thein-plane angles and the amplitude of B|| in Fig. 3(b). Withincreasing amplitude of B||, the supercurrent shows increasedanisotropy. While Is is largely unaffected when B|| is orientedperpendicular to the current direction at ϕ = 90◦ and 270◦,it is suppressed when the field is parallel to it. It becomeszero near B|| = 150 mT and even reappears at larger fieldamplitudes. Additional data on the evolution of the interfer-ence pattern subject to in-plane magnetic fields are presentedin Sec. S9 in the Supplemental Material [48].Sweeping B|| for different in-plane angles, as shown inFig. 3(c), reveals not only significant anisotropy in the switch-ing current but also supercurrent revival effects dependingon the orientation of the magnetic field. This is in starkcontrast with the configuration where the magnetic field is ori-ented perpendicular to the current direction for ϕ = 270◦ [seeFig. 3(d)], where the supercurrent only decreases by ∼200 nAover the entire range of the magnetic field. This anisotropyis further illustrated in Fig. 3(e) by showing the extractedmaximum supercurrent for various angles. For angles per-pendicular to the supercurrent flow direction, a monotonousdecrease of ≈15% throughout the investigated field range isobserved, while tilting the in-plane magnetic field toward thesupercurrent flow direction leads to a progressively strongersuppression of the supercurrent, with the field of the firstminimum eventually reaching the smallest value of 150 mT.To further analyze this anisotropy, we extract the in-plane magnetic field value B1||, corresponding to the firstminimum of Is (see Sec. S10 in the Supplemental Mate-rial [48] for a discussion and details) and plot it as a functionof ϕ, see Fig. 3(f). Assuming a finite effective thicknessof the junction deff , the in-plane magnetic field induces amagnetic flux �|| = B||deff [|w cos (ϕ)| + |l sin (ϕ)|]. In casesupercurrent suppression and its anisotropy are caused byinterference effects, the first supercurrent minimum ap-pears at magnetic fields of order B1|| = �0/{deff [|w cos (ϕ)| +|l sin (ϕ)|]}. A fit of this model to the extracted data results inan effective thickness of deff = 6.3 nm.Supercurrent interference under in-plane magnetic fieldscan be understood in a qualitative microscopic picture. In aperfectly homogeneous two-dimensional Josephson junction,supercurrent is carried by identical Andreev bound states(ABSs) in many identical parallel transport channels. Here,magnetic flux is threaded through the out-of-plane orbitalcomponent of the ABS wave function for any in-plane an-gle ϕ (in principle allowing for interference for any valueof ϕ), but due to the identical orbital wave functions, nointerference occurs. However, such an idealized picture is not245301-4ANISOTROPIC SUPERCURRENT SUPPRESSION AND … PHYSICAL REVIEW B 111, 245301 (2025)realistic, as it ignores microscopic disorder that will cause themany ABSs present to have, at best, similar but not identi-cal orbital wave functions. This will lead to the buildup ofphase differences between the individual ABSs under in-planemagnetic field, and the total supercurrent integrated over theentire junction will display an averaged orbital interferenceeffect.Possible disorder mechanisms in our devices are residualgeometric disorder after encapsulating bilayer graphene be-tween WSe2 and hBN and electrostatic disorder, for example,due to defects and contaminants at the various interfaces inthe layer stack [60,61]. Additionally, a narrow section of thejunction in the contact area may be more strongly disordered,which may enhance supercurrent interference effects.Beyond disorder-enabling supercurrent interference ef-fects, the assumption of a homogeneous in-plane magneticfield is not realistic. Flux focusing effects caused by thepresence of superconducting contacts may allow for smallout-of-plane components of the magnetic field, which areexpected to be highly dependent on the exact device geometry.In an earlier work [62], the anisotropy of in-plane supercur-rent interference was fully attributed to flux focusing. Furthertexture may be added to the magnetic field by irregularitiesin the shape of the superconducting contacts and the possibil-ity of vortices also entering the niobium film under in-planemagnetic fields.Our experiment cannot discriminate between the possiblecauses of supercurrent interference. Assuming such effectsare significant, we expect supercurrent interference for anyvalue of ϕ and a geometric dependence on ϕ, rationalizingour phenomenological fitting procedure. We conjecture thatdeff introduced above is a phenomenological parameter thatabsorbs microscopic disorder effects, flux focusing, and othermagnetic field inhomogeneities into a single fitting parameter.Its value of 6.3 nm is about an order of magnitude larger thanthe thickness of the bilayer graphene, which means that theeffective transverse area of the junction through which fluxcan be threaded is enlarged by the various possible causes ofsupercurrent interference.Relating deff to a microscopic model and assessing itsvalue, while disentangling the effect of flux focusing, requiresmodeling efforts beyond the scope of this paper. Such model-ing could rely on introducing a randomization of the junctiongeometry in an otherwise standard classical approach fol-lowing [52]. Alternatively, a quantum mechanical electronictransport approach could be followed, extending such mod-eling carried out for quasi-one-dimensional nanowire-basedJosephson junctions [63] to two-dimensional Josephson junc-tions. Any such modeling should be approached with cautiondue to risks of overfitting the data by introducing additionalmodeling parameters when attempting to create more realisticmodels.Alternative mechanisms predicting decay and revival of su-percurrent under in-plane magnetic fields rely on spin physicsstemming from the semiconducting band structure incorpo-rated into the effective Hamiltonian of the Josephson junction.Such proposed effects include 0π transitions of the groundstate of the junction due to the Zeeman effect [64,65], similartransitions but to arbitrary phase differences φ0 (so-called φ0junctions) [66,67] due to additional spin-orbit interaction, ormore exotic physics such as topological phase transitions.However, for significant spin splitting to occur, which is aprerequisite for such effects, much larger magnetic fieldsof the order of several Teslas are anticipated in bilayergraphene. We observe supercurrent minima already at valuesas low as 150 mT, rendering spin-physics-related explanationsimplausible.V. CONCLUSIONIn summary, we have presented a tunable lateral Josephsonjunction consisting of bilayer graphene encapsulated in WSe2.We have been able to tune the junction quality factor andthus its damping regime by external parameters, such as backgate voltage, magnetic field, and temperature. This is evidentfrom the magnetic field–induced modulation of the switchingcurrent and the retrapping current. Furthermore, we see well-defined Shapiro steps under RF driving of the junction. Weobserve a highly anisotropic suppression and revival of the su-percurrent when the Josephson junction is subject to in-planemagnetic fields. We suspect that this anisotropic behavior iscaused by orbital interference of the supercurrent. Furtherresearch on quasi two-dimensional Josephson junctions atfinite in-plane magnetic fields is required to obtain an in-depthunderstanding in these systems. We caution against narrativesthat fail to consider interference effects when invoking super-current suppression and revival to support claims of observingspin phenomena originating from the semiconducting bandstructure.ACKNOWLEDGMENTSWe thank L. Banszerus, S. Anupam, and S. M. Frolovfor insightful discussions. This project has received fundingfrom the Deutsche Forschungsgemeinschaft under Germany’sExcellence Strategy—Cluster of Excellence Matter and Lightfor Quantum Computing EXC 2004/1—390534769, fromthe European Research Council under the European Union’sHorizon 2020 research and innovation programme (GrantAgreement No. 820254), and the Helmholtz Nano Facil-ity [68]. K.W. and T.T. acknowledge support from theJSPS KAKENHI (Grants No. 21H05233 and No. 23H02052)and World Premier International Research Center Initiative,MEXT, Japan.P.S., V.M., and C.S. conceived this experiment. P.S. andK.S. fabricated the device, performed the measurements, andanalyzed the data. P.S. performed the simulation. K.W. andT.T. synthesized the hBN crystals. B.B., V.M., and C.S. super-vised the project. P.S., K.S., and V.M. wrote the manuscriptwith contributions from all authors. P.S. and K.S. contributedequally.DATA AVAILABILITYThe data that support the findings in this paper are openlyavailable [69].245301-5PHILIPP SCHMIDT et al. PHYSICAL REVIEW B 111, 245301 (2025)[1] B. D. Josephson, Possible new effects in superconductive tun-nelling, Phys. Lett. 1, 251 (1962).[2] P. G. de Gennes, Boundary effects in superconductors, Rev.Mod. Phys. 36, 225 (1964).[3] P. W. Anderson and J. M. Rowell, Probable observation of theJosephson superconducting tunneling effect, Phys. Rev. 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