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Martin Endres, Artem Kononov, Hasitha Suriya Arachchige, Jiaqiang Yan, David Mandrus, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Christian Schönenberger

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[Current–Phase Relation of a WTe<sub>2</sub> Josephson Junction](https://mdr.nims.go.jp/datasets/d35a5826-f0cf-4913-b3e1-b41b6a659982)

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Current–Phase Relation of a WTe2 Josephson JunctionCurrent−Phase Relation of a WTe2 Josephson JunctionMartin Endres,* Artem Kononov, Hasitha Suriya Arachchige, Jiaqiang Yan, David Mandrus,Kenji Watanabe, Takashi Taniguchi, and Christian SchönenbergerCite This: Nano Lett. 2023, 23, 4654−4659 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: When a topological insulator is incorporated into aJosephson junction, the system is predicted to reveal the fractionalJosephson effect with a 4π-periodic current−phase relation. Here,we report the measurement of a 4π-periodic switching currentthrough an asymmetric SQUID, formed by the higher-ordertopological insulator WTe2. Contrary to the established opinion, weshow that a high asymmetry in critical current and negligible loopinductance are not sufficient by themselves to reliably measure thecurrent−phase relation. Instead, we find that our measurement isheavily influenced by additional inductances originating from theself-formed PdTex inside the junction. We therefore develop amethod to numerically recover the current−phase relation of thesystem and find the 1.5 μm long junction to be best described inthe short ballistic limit. Our results highlight the complexity of subtle inductance effects that can give rise to misleading topologicalsignatures in transport measurements.KEYWORDS: WTe2, topological superconductivity, higher-order topological insulators, edge states, current−phase relation,asymmetric SQUIDTopological insulators (TIs) belong to a unique class ofmaterials that are insulating in their bulk while hostinggapless boundary states that are protected by time-reversalsymmetry.1 The class of three-dimensional TIs has recentlybeen extended,2,3 realizing that a d-dimensional TI of order ncan develop (d − n)-dimensional hinge or corner states. Apromising candidate of this novel material class that ispredicted to host topological hinge states is the semimetallictransition-metal dichalcogenide WTe2.4−7 While bulk statesdominate transport in the normal state, hinge states becomethe governing transport channel over long distances in thesuperconducting state, as they can carry a higher criticalcurrent due to their reduced dimensionality.8,9 Therefore,Josephson junctions (JJs) formed by a TI as the weak linkbetween two superconducting electrodes provide an idealplatform to probe the topological nature in a transportexperiment. Topological hybrid systems are of great interest, asthey are predicted to host unconventional superconductivity,10the fundamental building block of a potential topologicallyprotected quantum bit.11 The fingerprint of a JJ is the current−phase relation (CPR), the dependence of the supercurrent onthe phase difference φ between the superconducting electro-des. The measurement of the CPR directly reflects theunderlying transport mechanism with which the Cooper pairsare shuttled across the weak link. For a topological weak link,perfect Andreev reflection is expected,12 since spin-momentumlocking in the hinge states prohibits normal electron reflectionat the interface to the superconductor. In the long junctionlimit, the supercurrent is carried by 4π-periodic Andreevbound states of opposite parity, σ+ and σ−, that give rise to acharacteristic sawtooth-shaped Ic. Parity conservation prohibitsthe recombination to the lower energy branch and results in amultivalued Ic with a distinct diamond shape, as plotted inFigure 1a.13 For comparison, the expected CPR of a trivialballistic JJ in the long junction limit is plotted as a black dashedline in the same figure. Accordingly, the literature often infersballistic topological states from the observation of a sawtooth-shaped flux dependence of the critical current.9,14−16Recently, high-quality JJs formed in WTe2 on palladium(Pd) bottom contacts have been reported17,18 and providedevidence of a nonsinusoidal CPR.7,19 Here, we combine suchJJs based on Pd-induced superconductivity in WTe2 withexternal superconducting leads, as illustrated in Figure 1b. Asuperconducting quantum interference device (SQUID)formed out of two such JJs is expected to reflect the CPR,provided that the critical current amplitudes of the two JJs areReceived: April 14, 2023Revised: May 2, 2023Published: May 8, 2023Letterpubs.acs.org/NanoLett© 2023 The Authors. Published byAmerican Chemical Society4654https://doi.org/10.1021/acs.nanolett.3c01416Nano Lett. 2023, 23, 4654−4659Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on May 27, 2023 at 02:19:37 (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="Martin+Endres"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Artem+Kononov"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Hasitha+Suriya+Arachchige"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jiaqiang+Yan"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="David+Mandrus"&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="Kenji+Watanabe"&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="Christian+Scho%CC%88nenberger"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.nanolett.3c01416&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/nalefd/23/10?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/10?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/10?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/10?ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01416?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/highly different and the loop inductance is negligible.20,21Based on this method, we observe a switching currentdistribution with 4π-periodicity that resembles a topologicalJJ.13 Contrary to the topological interpretation, we provide analternative explanation based on inductance effects,22 whichcould be relevant for a number of previous experiments.9,14−16Importantly, the inductance contribution originates from theJJs themselves and exceeds the loop inductance. We furtherdeveloped a numerical model based on the maximization of thesupercurrent in the SQUID loop that allows us to excludescreening effects from the additional inductances and recoverthe real CPR. The calculations suggest that the critical currentof our 1.5 μm long junction is best reproduced in the shortballistic limit, despite its long physical length.We begin with the fabrication of an asymmetric SQUID outof WTe2. In our experiment, both JJs are formed in the sameneedle-shaped WTe2 flake of width w = 1.5 μm. Theasymmetry in critical current Ic of the two involved JJs isachieved by a different spacing between the Pd bottomcontacts lw = 1.5 μm and lr = 0.5 μm for the weak and referencejunction, respectively, as sketched in Figure 2a. The super-conducting loop is formed by etching through the top hBNinto WTe2 and sputtering niobium (Nb) on top. The Nb leadsare between 2.2 and 3 μm wide and 100 nm thick. A detaileddescription of the fabrication process can be found in theSupporting Information. Figure 2a displays an optical image ofthe finished devices. In the following we will focus on the lowerSQUID, enclosed by the dashed line.The critical current of the SQUID is given by the sumof the individual currents Iwand Ir through the two branches of the loop, defined by thecritical current Ici and the normalized CPR f i of the ithJosephson junction. The total flux Φtot threading the loopconnects the phase differences across the two JJs φw − φr =2πΦtot/Φ0 = ϕtot, with ϕtot denoting the external phase. In theabsence of inductances in the loop, ϕtot is simply defined bythe external phase ϕx. The asymmetry Icr ≫ Icw pins φr = φrmax ata fixed phase, for which Icr is maximized.20,21,23 The normalizedCPR of the weak junction fw can then be deduced from themeasurement of(1)In the experiment, Φx = BAo is controlled by an appliedperpendicular magnetic field B threading the effective loop areaAo = 186 μm2. The Meissner screening of the enclosingsuperconducting loop was taken into account by including halfof its width into the loop area. The final device is probed in aquasi four-terminal configuration by sourcing an ac current andmonitoring the voltage drop over the SQUID. We use thecounter technique, as described in the Supporting Information,to measure the switching statistics of the device.Figure 2b presents the measured switching statistics of theSQUID in an extended magnetic field range at basetemperature T = 30 mK of the cryostat. Visible is a multivaluedFigure 1. CPR of a topological JJ. (a) Normalized CPR of atopological JJ in the long junction limit as a function of the junctionphase φ. The 4π-periodic supercurrent through the SQUID is carriedby Andreev bound states of opposite parity, σ+ and σ−, resulting in amultivalued switching current that resembles a diamond-like pattern.A 2π-periodic CPR of a topologically trivial junction is shown as adashed line for comparison. (b) llustration of a JJ fabricated from anelongated WTe2 crystal on top of Pd bottom contacts. Super-conducting Nb contacts were deposited from above after etchingthrough the top hBN (not displayed). The diffusion of Pd into theWTe2 crystal leads to the formation of superconducting PdTex insidethe weak link, through which the topological hinge states can becoupled.Figure 2. Switching statistics of the weak junction in an asymmetricSQUID. (a) Optical image of a SQUID device on the left, with themeasured SQUID highlighted by the dashed box. An illustration ofthe device parameters is provided to the right. (b) High-resolutionmeasurement of the SQUID switching current as a function of appliedmagnetic field through the loop. Oscillation periods of the paritystates σ+ and σ−, respectively, are highlighted in red and light blue,respectively. The period δB = 23.2 μT of a single parity branchdisplays a 4π-periodicity with respect to the designed loop area δB =11.1 μT. (c) Schematic of the SQUID, specifying the deviceparameters, including the additional series inductances Lw and Lr inseries to the weak and reference JJ, respectively.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01416Nano Lett. 2023, 23, 4654−46594655https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01416/suppl_file/nl3c01416_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01416/suppl_file/nl3c01416_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig2&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01416?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asIc that oscillates periodically around the offset current Icr = 160μA of the reference junction. Given the great difference incritical current amplitudes Icr/Icw ≈ 40, we expect the SQUID tobe highly asymmetric and the measured signal to reflect theCPR of the weak JJ. A second set of oscillations appears forfield values from B = −100 μT upward and is explained in theSupporting Information by the behavior of the referencejunction. The extracted oscillation period of a fixed paritybranch, as defined in Figure 1a, is equal to δB = 23.2 μT andtherefore twice the value δB = Φ0/Ao = 11.1 μT expected forthe enclosed loop area Ao. The data represent strikingresemblance to the two parity states of a topological JJ inthe long junction limit with a 4π-periodicity in flux. However,the amplitude of the signal deems this explanation unlikely. Asingle channel in the topological ballistic long junction cancarry a current Ic,4π = EThe/ℏ = vFe/l,13 with ETh being theThouless energy, vF the Fermi velocity, and l the length of theweak link. Ic in our junction would therefore have to be carriedby at least 116 perfectly ballistic channels inparallel, assuming vF = 3.09 × 105 m s−1.24 WTe2 is expected tohost a pair of hinge states on opposite edges of the crystal.19Conducting states have been found to reside at step edges inthe crystal where the number of vdW layers changes,7 but wedo not observe such crystal steps in optical microscopy for theused flake. We conclude that it is unlikely for the current to becarried purely by ballistic hinge states.Instead, multivalued CPR measurements have previouslybeen reported in devices containing a superconducting weaklink with large kinetic inductance that is responsible for strongscreening effects.22,25−28 In strong contrast to previousexperiments, however, the device studied here contains anormal conducting weak link18 and has negligible loopinductance, as will be shown later.The schematic in Figure 2c introduces a set of additionalinductances, Lr and Lw, that are placed in series to thereference and weak junction, respectively, while potentialmutual inductances are assumed to be negligible. In general,the total phase(2)can differ strongly from the phase created by the external fluxϕx = 2πΦx/Φ0, due to the contribution induced by thecurrents Ir and Iw passing through the inductances in theSQUID arms, Lr and Lw. We note that while a screeningcurrent can distort the flux dependence of the critical current,it does not change its periodicity.29Deducing the CPR from the inductive SQUID measurementrequires the knowledge of the phase dependences of Ir(ϕtot)and Iw(ϕtot) themselves. In order to bypass this recursiveconstraint, we make an assumption about the CPRs of the JJsthat is based on the experimental data. We are then going touse this information in the next step to calculate , forwhich Ic(ϕtot) is maximized according to eq 1. Last, we aregoing to include screening effects in the model and obtain therelation Ic(ϕx), which is placed in context to the experimentaldata.Figure 3. SQUID oscillations and numerical model of the CPR. (a) Experimental data of the SQUID oscillations as a function of external flux ϕxshown in blue. The red data points are a fit to the data based on maximizing the critical current in the SQUID loop. Phase winding in thesuperconducting loop is responsible for the multivalued supercurrent. (b) Visual method to maximize Ic as a function of total flux ϕtot. The upperpanel plots the currents Ir and Iw for a short ballistic CPR with an amplitude ratio Icr/Icw = 40. The two currents evolve in opposite directions withincreasing ϕtot, due to φr − φw = ϕtot. The resulting maximized Ic is highlighted by a gray background and is composed of the weak junction and thereference junction CPR for the rising and falling sides, respectively. The lower panel shows the corresponding behavior of the junction phases φrand φw, obtained through the numerical maximization model. The phases are mapped to the range of the CPR. The switch between the observedweak and reference junction branch in the top panel is accompanied by a shift from a fixed φr to φw at flux values of multiples of 2π. (c)Numerically calculated ϕtot versus ϕx using the model described in the main text. Inductance effects give rise to the multivalued ϕx(ϕtot),responsible for the intertwined branches visible in (a).Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01416Nano Lett. 2023, 23, 4654−46594656https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01416/suppl_file/nl3c01416_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416?fig=fig3&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01416?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asOur choice of CPR for the weak junction is based on twoexperimental observations. First, the rising slope of Ic(ϕx) isnonlinear, suggesting the same should hold for the CPR.Second, Ic(ϕx) has self-crossings, implying that the phase of thereference junction does not remain fixed, contrary to theestablished expectation for a highly asymmetric SQUID. Thebehavior is possible if the CPR of the weak junction containsabrupt changes, such as is the case in the ballistic limit of theCPR. We illustrate this behavior later in the text and providean additional discussion in the Supporting Information. Iw(φw)is modeled to be in the 2π-periodic, ballistic short junctionlimit30(3)scaled by the amplitude of Icw. The exact CPR of the referencejunction plays little role in the further discussion, yet, since it isformed in the same material but with reduced length, we alsomodel it as a short ballistic junction, scaled by Icr .Independently, we have used length-dependent measurementsin the Supporting Information and the analysis of the PdTexdiffusion profile in ref 18 to verify that both junctions behaveindeed as JJs and are not shorted by PdTex.31Having made this initial assumption, we continue tocalculate the resulting Ic by maximizing the current throughthe SQUID. The top panel in Figure 3b illustrates a visualmethod to maximize the critical current as a function of ϕtot.The individual currents through the SQUID arms Ir and Iwfollow eq 3. The currents evolve in opposite flux direction, dueto the connection φr − φw = ϕtot. We start at the configurationϕr = ϕrmax and ϕw = ϕwmax, when the currents through thereference and weak junctions are at their maximum, Icr and Icw,respectively. Moving from this point in the negative directionof ϕtot, Ic follows Iw, plotted as a red curve. In the oppositedirection toward positive values of ϕtot, Iw faces a sudden drop.Instead of following Iw, a higher Ic is obtained by following Ir,drawn in dark blue, until the point when Ir intersects with Iw.This creates a small flux range δφtot ∝ πIcw/Icr ≪ π, in which Icis maximized by following Ir rather than Iw, resulting in achanging φr, while ϕwmax = π remains fixed. The situation isillustrated in the lower panel of Figure 3b. Once the twocurrent branches cross with evolving flux, φr returns to itsmaximum value ϕrmax = π and Ic(ϕtot) follows the fluxdependence of Iw. The well-known behavior of the asymmetricSQUID is restored. While δϕtot remains small in the abovescenario, it can extend significantly in the experiment, due tothe inductance effects, as described by eq 2.Given that φr does not necessarily remain fixed in anasymmetric SQUID, we introduce next a numerical procedureto transfer the above model from the dependence of total fluxϕtot to the external flux ϕx, the quantity applied in theexperiment. The slope of Ic(ϕx) is directly related to theinductance of the current carrying arm in the SQUID, via, with LJi being the Josephsoninductance and i = r, w, depending on the considered datamapping the CPR of the reference or the weak junction.First, we numerically maximize the expression(4)with respect to φr(ϕtot) for a given ϕtot. Ir and Iw correspond tothe currents through the respective SQUID arms, i.e.and . The two amplitudes Icr= 160 μA and Icw = 3.75 μA are determined from the fixedcurrent background and the oscillation amplitude of theintertwined branches. The lower panel in Figure 3b plots theobtained φr and φw in blue and red, respectively. Based on thechoice of the CPR function in eq 3, φr is mostly fixed at themaximum value ϕrmax = π, while φw evolves linearly in ϕtot,according to ϕw = φtot + ϕrmax. However, a small range δϕtotexists, where φr changes in flux while φw remains fixed, inagreement with the graphical method introduce above in theupper panel of Figure 3b.Using φr(ϕtot), it is now possible to extract the inductanceeffects and recalculate ϕx = ϕtot − 2π(LrIr − LwIw)/Φ0.Depending on the magnitude of the incorporated inductancesand critical currents, self-inductance effects in the loop causethe connection ϕtot(ϕx) to become multivalued, as is visiblefrom Figure 3c.Finally, Ic(ϕx) is plotted in red in Figure 3a. Despite the longphysical length Lw = 1.5 μm of the junction, we find thebending of the gradually rising slope dIc/dϕx to be wellreproduced by fw being in the 2π-periodic, ballistic shortjunction limit. In both cases, the magnetic field dependences ofthe current amplitudes are assumed to be negligible for thegiven field range. Importantly, despite the great difference incritical current amplitudes of the embedded junctions, themodel confirms that φr does not remain fixed in flux. Theexperimental CPR of the SQUID is composed of the weak andthe reference junction CPR. Even though the CPR of the weakjunction is not necessarily uniquely in the short junction limit,it has to have a sharp transition in flux and therefore be close toballistic in order to ease the shift between the fixed φr and φw.Further, we extract the inductances Lr = 60 pH and Lw = 220pH, by matching the rising and falling slopes of the fit to thedata. An important result that distinguishes ours from previousexperiments is that Lr and Lw by themselves exceed the sum ofgeometrical inductance Lgeo ≈ 27.0 pH32 and kineticinductance Lkin ≈ 5.5 pH33 for the Nb SQUID loop. Possibly,additional JJs can form at the interface between the sputteredsuperconducting leads and the self-formed superconductingPdTex,34 yet given that their critical current has to be largerthan Icr, little inductance contribution is to be expected.Instead, we attribute the origin of additional inductance and itsasymmetry between the SQUID arms to the superconductingPdTex that has self-formed at the interface between WTe2 andPd. Further support of this interpretation is provided in theSupporting Information, including the comparison of the datato different initial CPR assumptions.Finally, the multivalued Ic can also be explained in theframework of excited vorticity states in an inductiveSQUID.25−28,35 Using the parameters obtained from our fit,w e c a l c u l a t e t h e ma gn e t i c s c r e e n i n g f a c t o r1,29 reflecting that an additionalflux quantum can be created by the maximum circulatingcurrent through the weak JJ. The result is a multivalued ϕtot asa function of ϕx, as was shown in Figure 3c for the given deviceparameters. The above behavior can differ strongly even on asingle sample chip. While the second SQUID loop formed onthe same WTe2 flake (compare Figure 2a) reveals the samebehavior of the reference junction with multiple branches, wedo not observe higher-vorticity states in the SQUIDoscillations. The absence of the feature is most likelyNano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c01416Nano Lett. 2023, 23, 4654−46594657https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01416/suppl_file/nl3c01416_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01416/suppl_file/nl3c01416_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c01416/suppl_file/nl3c01416_si_001.pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c01416?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asconnected to the overall smaller Icw, despite the shorter junctionlength with lw = 1.2 μm.In conclusion, the established assumption of a fixedreference junction phase in flux does not hold for highlytransparent junctions, even in the case of highly asymmetriccritical current amplitudes. Furthermore, we have shown thecomplexity of subtle inductance effects that reach beyond thestandard consideration of the loop inductance and might createmisleading topological features. It is therefore crucial for acorrect CPR measurement to consider potential inductancecontributions from the interfaces between the embeddedjunctions with the SQUID loop. The origin of such additionalinductances can go beyond the diffusion of PdTex presentedhere and may include defects implanted at the interfacethrough various fabrication steps.33,36 Despite these limitations,the fitting routine presented here allows reproduction of theexperimental data closely. The best result was obtained byplacing the weak junction in the short ballistic limit, aspresented in the Supporting Information. Our results establishWTe2 as a promising platform for further experiments towardtopological superconductivity.■ ASSOCIATED CONTENTData Availability StatementAll data in this publication are available in numerical form inthe Zenodo repository.37*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c01416.Materials and methods, counter measurement technique,inductance effects in single Josephson junctions,verification of the inductance effects, comparison ofthe CPR configurations in the fitting procedure,instability of the reference junction phase φr, andfrequency dependence of the switching statistics(PDF)■ AUTHOR INFORMATIONCorresponding AuthorMartin Endres − Department of Physics, University of Basel,4056 Basel, Switzerland; orcid.org/0000-0001-7749-3585; Email: martin.endres@unibas.chAuthorsArtem Kononov − Department of Physics, University of Basel,4056 Basel, Switzerland; orcid.org/0000-0002-3778-8239Hasitha Suriya Arachchige − Department of Physics andAstronomy, University of Tennessee, Knoxville, Tennessee37996, United StatesJiaqiang Yan − Department of Physics and Astronomy,University of Tennessee, Knoxville, Tennessee 37996, UnitedStates; Material Science and Technology Division, Oak RidgeLaboratory, Oak Ridge, Tennessee 37831, United States;orcid.org/0000-0001-6625-4706David Mandrus − Department of Materials Science andEngineering, University of Tennessee, Knoxville, Tennessee37996, United States; Department of Physics and Astronomy,University of Tennessee, Knoxville, Tennessee 37996, UnitedStates; Material Science and Technology Division, Oak RidgeLaboratory, Oak Ridge, Tennessee 37831, United States;orcid.org/0000-0003-3616-7104Kenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119Takashi Taniguchi − International Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Christian Schönenberger − Department of Physics, Universityof Basel, 4056 Basel, Switzerland; Swiss NanoscienceInstitute, University of Basel, 4056 Basel, Switzerland;orcid.org/0000-0002-5652-460XComplete contact information is available at:https://pubs.acs.org/10.1021/acs.nanolett.3c01416Author ContributionsM.E. and A.K. contributed equally.Author ContributionsM.E. fabricated the devices. M.E. and A.K. measured thedevices. H.S.A., J.Y., and D.M. provided the WTe2 crystals.K.W. and T.T. provided the hBN crystals. M.E., A.K., and C.S.analyzed the data and wrote the manuscript.NotesSimilar experimental results have been obtained recently in ref16; however, the authors provide a different interpretation.The authors declare no competing financial interest.■ ACKNOWLEDGMENTSThis project has received funding from the European ResearchCouncil (ERC) under the European Union’s Horizon 2020research and innovation programme: grant agreement No.787414 TopSupra, by the Swiss National Science Foundationthrough the National Centre of Competence in ResearchQuantum Science and Technology (QSIT), and by the SwissNanoscience Institute (SNI). A.K. was supported by the GeorgH. Endress foundation. D.M. and J.Y. acknowledge supportfrom the U.S. Department of Energy (U.S.-DOE), Office ofScience-Basic Energy Sciences (BES), Materials Sciences andEngineering Division. H.S.A. was supported by the Gordonand Betty Moore Foundation’s EPiQS Initiative through GrantGBMF9069 and the Shull Wollan Center Graduate ResearchFellowship. D.M. acknowledges support from the Gordon andBetty Moore Foundation’s EPiQS Initiative, GrantGBMF9069. K.W. and T.T. acknowledge support from theElemental Strategy Initiative conducted by MEXT, Japan andthe CREST (JPMJCR15F3), JST and from the JSPSKAKENHI (Grant Numbers 19H05790 and 20H00354).■ REFERENCES(1) Fu, L.; Kane, C. L. Topological insulators with inversionsymmetry. Phys. Rev. B 2007, 76, 045302.(2) Schindler, F.; Cook, A. M.; Vergniory, M. G.; Wang, Z.; Parkin,S. S.; Bernevig, B. A.; Neupert, T. Higher-order topological insulators.Science Advances 2018, 4, No. eaat0346.(3) Benalcazar, W. A.; Bernevig, B. A.; Hughes, T. L. Quantizedelectric multipole insulators. Science 2017, 357, 61.(4) Wang, Z.; Wieder, B. J.; Li, J.; Yan, B.; Bernevig, B. A. 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