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Amis Sharma, Chun-Chia Chen, Jordan McCourt, Mingi Kim, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Leonid Rokhinson, Gleb Finkelstein, Ivan Borzenets

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[Fermi Velocity Dependent Critical Current in Ballistic Bilayer Graphene Josephson Junctions](https://mdr.nims.go.jp/datasets/d5aee837-6962-4840-ab72-0699eeee4e80)

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Fermi Velocity Dependent Critical Current in Ballistic Bilayer Graphene Josephson JunctionsFermi Velocity Dependent Critical Current in Ballistic BilayerGraphene Josephson JunctionsAmis Sharma, Chun-Chia Chen, Jordan McCourt, Mingi Kim, Kenji Watanabe, Takashi Taniguchi,Leonid Rokhinson, Gleb Finkelstein, and Ivan Borzenets*Cite This: ACS Nanosci. Au 2025, 5, 65−69 Read OnlineACCESS Metrics & More Article RecommendationsABSTRACT: We perform transport measurements on proximi-tized, ballistic, bilayer graphene Josephson junctions (BGJJs) in theintermediate-to-long junction regime (L > ξ). We measure thedevice’s differential resistance as a function of bias current and gatevoltage for a range of different temperatures. The extracted criticalcurrent IC follows an exponential trend with temperature:exp(−kBT/δE). Here δE = ℏνF/2πL: an expected trend forintermediate-to-long junctions. From δE, we determine the Fermivelocity of the bilayer graphene, which is found to increase withgate voltage. Simultaneously, we show the carrier densitydependence of δE, which is attributed to the quadratic dispersionof bilayer graphene. This is in contrast to single layer grapheneJosephson junctions, where δE and the Fermi velocity are independent of the carrier density. The carrier density dependence inBGJJs allows for additional tuning parameters in graphene-based Josephson junction devices.KEYWORDS: Graphene, Bilayer Graphene, Josephson Junctions, Fermi Velocity, Andreev LevelsBallistic graphene Josephson junctions (GJJs) have beenwidely utilized as a platform to study novel quantumphysics phenomena1,2 and devices,3 including: entangled pairgeneration,4,5 topological states arising from the mixing ofsuperconductivity and quantum Hall states,6 as well as photonsensing via bolometry/calorimetry.7 Superconductor−normalmetal−superconductor Josephson junction (SNSJJ) hostsAndreev bound states (ABS), which carry supercurrents acrossthe normal region of the JJ; in order to enter the ballisticregime, a disorder-free weak link and high transparency at theSN interface are necessary. Hexagonal Boron-Nitride (hBN)encapsulated graphene as a weak link enables highly trans-parent contacts at the interface while keeping graphene cleanthroughout the fabrication process.8 Here, we studyproximitized, ballistic, bilayer graphene Josephson junctions(BGJJs). Bilayer graphene devices (in contrast to monolayer)allow extra potential tunability via a nonlinear dispersionrelation, applied displacement field, or lattice rotation.1The critical current (IC) of SNSJJ in the intermediate-to-long regime, where the junction length (L) ≥ superconductingcoherence length (ξ0), scales with temperature (T) as IC =exp(−kBT/δE). Here, δE = ℏνF/2πL, an energy scale related tothe ABS level spacing.2,9−13 Note that in the intermediateregime (L ≈ ξ0) δE is found to be suppressed.5 A previousstudy of GJJs found that in this regime the relation was heldmore precisely when ξ was taken into account along with L,that is, δE = ℏνF/2π(L + ξ).2,13 Monolayer graphene displays alinear dispersion relation, which results in a constant Fermivelocity (νF0). Thus, in ballistic GJJs, δE remains independentof the carrier density. In comparison, bilayer graphene displaysa quadratic dispersion relation at low energies. In BGJJs westudied, a back-gate voltage (VG) controls the carrier density,and δE dependence on VG is observed. Using δE, we extractthe Fermi velocity in bilayer graphene: It is seen that νFincreases with VG and saturates to the constant value, νF0, ofthe monolayer graphene.Our device consists of a series of four terminal Josephsonjunctions (on SiO2/Si substrate) made with hBN encapsulatedbilayer graphene contacted by Molybdenum−Rhenium(MoRe) electrodes. Bilayer graphene is obtained via thestandard exfoliation method. It is then encapsulated inhexagonal boron-nitride using the dry transfer method.14MoRe of 80 nm thickness is deposited via DC magnetronsputtering. The resulting device has four junctions of lengths400, 500, 600, and 700 nm. The width of the junctions is 4 μm.Received: December 31, 2024Revised: March 14, 2025Accepted: March 17, 2025Published: March 19, 2025Letterpubs.acs.org/nanoau© 2025 The Authors. Published byAmerican Chemical Society65https://doi.org/10.1021/acsnanoscienceau.4c00080ACS Nanosci. Au 2025, 5, 65−69This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on April 30, 2025 at 10:47:19 (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="Amis+Sharma"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Chun-Chia+Chen"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jordan+McCourt"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Mingi+Kim"&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="Leonid+Rokhinson"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Leonid+Rokhinson"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Gleb+Finkelstein"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ivan+Borzenets"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acsnanoscienceau.4c00080&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/anaccx/5/2?ref=pdfhttps://pubs.acs.org/toc/anaccx/5/2?ref=pdfhttps://pubs.acs.org/toc/anaccx/5/2?ref=pdfhttps://pubs.acs.org/toc/anaccx/5/2?ref=pdfpubs.acs.org/nanoau?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acsnanoscienceau.4c00080?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/nanoau?ref=pdfhttps://pubs.acs.org/nanoau?ref=pdfhttps://acsopenscience.org/researchers/open-access/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/The device is cooled in a Leiden cryogenics dilutionrefrigerator operated at temperatures above 1 K, andmeasurements were performed using the standard four-probelock-in method. A gate voltage VG is applied to the Si substratewith the oxide layer acting as a dielectric, which allowsmodulation of the carrier density.2,5,6,15−17 Figure 1(a) displaysthe differential resistance (dV/dI) map of the 400 nm junctionat T = 1.37 K; we see zero resistance (black region) across allapplied VG indicating the presence of supercurrent. As the biascurrent Ibias is swept from negative to positive values, thejunction first reaches its superconducting state at a value |Ibias |= IR, known as the retrapping current. Then, as |Ibias| isincreased to higher positive values, the junction transitions tothe normal state at |Ibias| = IS, known as the switching current.Figure 1(a) shows that the junction can sustain a larger regionof critical current as we modulate the carrier density to highervalues via VG. Figure 1(b) displays line traces extracted fromthe dV/dI map which shows hysteresis in IR and IS. This is acommonly observed phenomenon in underdamped junc-tions15,18 or can also be attributed to self-heating.16,17,19 Themeasured switching current IS is slightly suppressed comparedto the junction’s “true” critical current IC. However, previousmeasurements on the statistical distribution of IS in similargraphene devices found that IS is suppressed from IC by nomore than 10% for critical currents up to a few μA.2,20−22Extracting the critical current IC from the differential mapsfor different temperatures, we can see that IC falls exponentiallywith inverse T (Figure 2c) We also extract the conductance ofthe junction in the normal regime (IBias ≫ IC). Figure 2(b)shows this conductance (G) for the 400 nm junction device.Due to the significant contact resistance (RC) of the device, themeasured conductance G is uniformly suppressed compared tothe ballistic limit expectation. However, when accounting forRC within the fit, we find that the conductance G scales as theFigure 1. (a) Differential resistance (dV/dI) versus gate voltage (VG) and bias current Ibias taken at T = 1.37 K. The black region around zero biascorresponds to the superconducting state. Ibias is swept up (from negative to positive). Thus, the transition at negative bias corresponds to theretrapping current IR, while the transition at positive bias is the switching current IC. (b) Vertical line cut of the resistance map taken at VG = 15 V,T = 1.37 K, showing the device’s dV/dI versus bias current. Blue line corresponds to Ibias swept up, with red line swept down (positive to negative).Figure 2. (a) Device picture. Image shows a series of junctions with different lengths: 400 nm, 500 nm, 600 and 700 nm. (b) The ballisticconductance vs gate voltage for L = 400 nm junction. The blue curve corresponds to the fit for ballistic devices, with an addition of a contactresistance. The inset shows junction resistance minus the parasitic contact resistance plotted against gate voltage from the Dirac point for all ourdevices. (c) Critical currents IC of L = 400 nm junction plotted against temperature T, for various gate voltages, on a semilog scale. The plots showVG dependence of IC: the gray lines show that the slope of the curve for the lowest plotted gate VG = 8 V is smaller than the slope of the highestplotted gate VG = 21 V.ACS Nanoscience Au pubs.acs.org/nanoau Letterhttps://doi.org/10.1021/acsnanoscienceau.4c00080ACS Nanosci. Au 2025, 5, 65−6966https://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig2&ref=pdfpubs.acs.org/nanoau?ref=pdfhttps://doi.org/10.1021/acsnanoscienceau.4c00080?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-assquare-root (as opposed to linearly) of VG (blue curve ofFigure 2(b)). This is consistent with ballistic transport.2,23 Tofurther demonstrate the ballistic nature of the device, wepresent normal resistances (RN) of junctions of length 500,600, and 700 nm with the fitted, constant contact resistance RCsubtracted (Figure 2(b) inset). The inset plot shows that thevalues of RN − RC are independent of the junction length,demonstrating the ballistic nature of the devices.To extract δE of the junction, we go to the discussion of ICvs the temperature trends in Figure 2(c). Here, the y-axis isplotted in logarithmic scale. From the slope of the curveslog(IC) = −(kB/δE)T for each gate, one can extract δE versusVG (plotted in Figure 3a). Unlike for the case of monolayergraphene, a clear dependence on VG is seen (The observedtrend further supports the view that our devices operate in thelong ballistic regime. Diffusive Josephson junctions areg o v e r n e d b y t h e T h o u l e s s e n e r g yE R R V V1/ ( )N C G DTh [ ]22,24 which does not matchthe trend with respect to VG seen in Figure 3(a)). The energyδE scales linearly with the Fermi velocity vF (Figure 3(b)).Note that calculating vF from δE for junctions in theintermediate regime requires knowledge of the superconduct-ing coherence length ξ. In the fit discussed below, we use ξ’sdependence in vF.We now compare the experimentally obtained δE (and vF)to the theoretical expectation. With the dispersion relation forbilayer graphene written as k m( 1 2 / 1)12 12 212= + * ,we get the express ion for the Fermi veloci ty:vF m2 ( )(2 )F FF1 112= ++ * .25−27 Here, γ1 = 0.39 eV a parameterdescribing the interlayer coupling,25 k is the momentumwavevector, and m* is the effective mass of electrons.Moreover, the Fermi energy F for bilayer graphene scalesas Fnm22= | |* . The carrier concentration n, controlled by theapplied gate voltage VG, is given by n CV Ve TotalG D= with VD asthe gate voltage at the Dirac point. The total capacitance CTotalis a combination of quantum capacitance Cq and gate oxidecapacitance Cox: CTotal C C1 11ox qÄÇÅÅÅÅÅÅÅÅÉÖÑÑÑÑÑÑÑÑ= + . The quantum capaci-tance Cq for bilayer graphene is determined by Cqe m2 22= *,where e is the electron charge. The gate oxide capacitance perunit area is Cox dr0= , where ϵ0 is the vacuum permittivity, ϵr isthe relative permittivity of the oxide, and d is the thickness ofthe oxide layer. For a silicon oxide gate with d = 300 nm we getCox ≈ 115 μF/m2. Thus, the full expression for the Fermivelocity vF isve V V de m e V Vm de m e V V2 ( )(2 ( ( ) ))(2 (2 ( ) ))Fr G D r G Dr G D0 121 02121 0212=* + +* + + *(1)Note that the effective mass m* typically ranges from 0.024 meto 0.058 me for 1 × 1012 ∼ 4 × 1012 carriers/cm2,28 where me isthe electron rest mass. Experimental data provides us with thefollowing: E V v( )G L F2 ( )= + . We also note that ξ has adependence on vF and the superconducting gap Δ: ξ = ℏvF/2Δ.13 To fit δE, the model is set as E V m V d( ) ( , , , )G D= *where m*, Δ, VD, and d are the fitting parameters and VG is theindependent variable. (We use the as-designed length of thedevice L and take ϵr = 3.9 for SiO2.)The resulting fits of the data from the 400 nm junction forδE and vF are plotted as solid lines in Figure 3(a) and Figure3(b) respectively. Moreover, taking the fitted parameters fromTable 1, we calculate the Fermi velocity vF for the availabledata points of all other junctions on the same substrate. Asseen from Figure 3(b), the calculated vF of all devices is ingood agreement with the fit obtained from the 400 nmjunction (this is as expected for devices on the same substrateas long as they have consistent parasitic doping and asuperconductor−graphene contact interface). The fittedparameters are summarized in Table 1. All fall within therange of expected values, with Δ being consistent withpreviously measured values for graphene/MoRe junctions.2Furthermore, using the values obtained from the model, wefind that vF saturates to the value of 1.1 × 106 m/s as VG tendsto infinity.In conclusion, we study the evolution of the critical currentwith respect to the gate in bilayer graphene JosephsonJunctions (BGJJs). Using the critical current-temperatureFigure 3. (a) Energy δE extracted from the slope of log(IC) vs Tplotted against the gate voltage VG from the Dirac point of thejunction with L = 400 nm. We see δE dependence on the carrierdensity modulated via the gate voltage for the junction. (b) Fermivelocity (vF) calculated from δE using the device dimensions andparameters obtained from the fit to theory. The solid line representsthe theoretical trend as fitted to the data for the L = 400 nm junction.In addition, panel (b) shows calculated vF for the other junctionsusing parameters obtained from the L = 400 nm fit.ACS Nanoscience Au pubs.acs.org/nanoau Letterhttps://doi.org/10.1021/acsnanoscienceau.4c00080ACS Nanosci. Au 2025, 5, 65−6967https://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acsnanoscienceau.4c00080?fig=fig3&ref=pdfpubs.acs.org/nanoau?ref=pdfhttps://doi.org/10.1021/acsnanoscienceau.4c00080?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asrelation expected for intermediate-to-long junctions, we extractthe relevant energy scale δE and find that it has a clear gatedependence. As δE is proportional to the Fermi velocity vF inbilayer graphene, we are able to match the observed gatedependence to the theoretical expectation. Our observation iscontrasted with monolayer graphene JJs, which do not have agate-dependent δE. This result showcases the greater tunabilityof BGJJs, and offers additional avenues for device character-ization. Although not observed here, it should be possible toengineer Josephson junctions that transition from the short tothe intermediate/long ballistic regimes in situ via gate voltage.The ability to tune ABS level spacing could have applicationsin self-calibrating sensors, or for matching resonanceconditions in multiterminal superconducting devices.■ AUTHOR INFORMATIONCorresponding AuthorIvan Borzenets − Department of Physics and Astronomy,Texas A&M University, College Station, Texas 77843,United States; orcid.org/0000-0002-1577-8312;Email: borzenets@tamu.eduAuthorsAmis Sharma − Department of Physics and Astronomy, TexasA&M University, College Station, Texas 77843, UnitedStates; orcid.org/0000-0002-7728-3753Chun-Chia Chen − Department of Physics, Duke University,Durham, North Carolina 27701, United StatesJordan McCourt − Department of Physics, Duke University,Durham, North Carolina 27701, United StatesMingi Kim − Department of Physics and Astronomy, PurdueUniversity, West Lafayette, Indiana 47907, United StatesKenji Watanabe − Advanced Materials Laboratory, NIMS,Tsukuba 305-0044, Japan; orcid.org/0000-0003-3701-8119Takashi Taniguchi − Advanced Materials Laboratory, NIMS,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Leonid Rokhinson − Department of Physics and Astronomy,Purdue University, West Lafayette, Indiana 47907, UnitedStatesGleb Finkelstein − Department of Physics, Duke University,Durham, North Carolina 27701, United StatesComplete contact information is available at:https://pubs.acs.org/10.1021/acsnanoscienceau.4c00080Author ContributionsCRediT: Amis Sharma formal analysis, investigation, software,visualization, writing - original draft, writing - review & editing;Chun-Chia Chen data curation, formal analysis, investigation,methodology; Jordan McCourt data curation, formal analysis,investigation, methodology, writing - review & editing; MingiKim investigation; Kenji Watanabe resources; TakashiTaniguchi resources; Leonid P. Rokhinson investigation;Gleb Finkelstein conceptualization, formal analysis, inves-tigation, methodology, project administration, resources,supervision, validation, visualization; Ivan Valerievich Borze-nets conceptualization, formal analysis, investigation, method-ology, project administration, resources, software, supervision,validation, visualization, writing - original draft, writing - review& editing.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSL.R. acknowledges support from NSF (DMR-2005092 award)for contact depositon. G.F. acknowledges support from DukeUniversity. I.V.B. and A.S. acknowledge the support fromTexas A&M University.■ REFERENCES(1) Park, G. H.; Lee, W.; Park, S.; Watanabe, K.; Taniguchi, T.; Cho,G. Y.; Lee, G. H. Controllable Andreev Bound States in BilayerGraphene Josephson Junctions from Short to Long Junction Limits.Phys. Rev. Lett. 2024, DOI: 10.1103/PhysRevLett.132.226301.(2) Borzenets, I. V.; Amet, F.; Ke, C. T.; Draelos, A. W.; Wei, M. T.;Seredinski, A.; Watanabe, K.; Taniguchi, T.; Bomze, Y.; Yamamoto,M.; Tarucha, S.; Finkelstein, G. Ballistic Graphene JosephsonJunctions from the Short to the Long Junction Regimes. Phys. Rev.Lett. 2016, 117, No. 237002.(3) Kroll, J. G.; Uilhoorn, W.; van der Enden, K. L.; de Jong, D.;Watanabe, K.; Taniguchi, T.; Goswami, S.; Cassidy, M. C.;Kouwenhoven, L. P. Magnetic field compatible circuit quantumelectrodynamics with graphene Josephson junctions. Nat. Commun.2018.(4) Chen, W.; Shi, D. N.; Xing, D. Y. Long-range Cooper pairsplitter with high entanglement production rate. Sci. Rep. 2015.(5) Borzenets, I. V.; Shimazaki, Y.; Jones, G. F.; Craciun, M. F.;Russo, S.; Yamamoto, M.; Tarucha, S. High Efficiency CVDGraphene-lead (Pb) Cooper Pair Splitter. Sci. Rep. 2016.(6) Amet, F.; Ke, C. T.; Borzenets, I. V.; Wang, J.; Watanabe, K.;Taniguchi, T.; Deacon, R. S.; Yamamoto, M.; Bomze, Y.; Tarucha, S.;Finkelstein, G. Supercurrent in the quantum Hall regime. Science2016, 352, 966−969.(7) Lee, G.-H.; Efetov, D. K.; Jung, W.; Ranzani, L.; Walsh, E. D.;Ohki, T. A.; Taniguchi, T.; Watanabe, K.; Kim, P.; Englund, D.; Fong,K. C. Graphene-based Josephson junction microwave bolometer.Nature 2020, 586, 42−46.(8) Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.;Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim, P.; Shepard, K. L.;Hone, J. Boron nitride substrates for high-quality grapheneelectronics. Nat. Nanotechnol. 2010, 5, 722−726.(9) Kulik, I. O. Macroscopic Quantization and the Proximity Effectin S-N-S Junctions. Soviet Physics JETP 1970, 30, 944.(10) Bardeen, J.; Johnson, J. L. Josephson Current Flow in PureSuperconducting-Normal-Superconducting Junctions. Phys. Rev. B1972, 5, 72−78.(11) Svidzinsky, A. V.; Antsygina, T. N.; Bratus, E. N. Super-conducting current in wide sns junctions. Soviet Physics JETP 1972,34, 860.Table 1. Fitting Parameters Used to Match the MeasuredδE, and Consequently the Fermi Velocity vF, versus Gate tothe Theoretical Expectation Described in Equation 1aParameter Fitted Value Expected ValueΔ 0.99 meV 0.8 ∼ 1.2 meVd 323 nm 280 ∼ 330 nmm* 0.028 me 0.02 ∼ 0.06 meVD 2.04 V ≈+2 VaWe see that resulting fitted values match closely to what is expected.The expected gate dielectric thickness d is estimated from thesubstrate specifications plus the bottom hBN thickness. The expectedDirac point voltage VD is obtained from the resistance map. Theexpectations for superconducting gap Δ and the effective mass mi areobtained from previous works.5,28ACS Nanoscience Au pubs.acs.org/nanoau Letterhttps://doi.org/10.1021/acsnanoscienceau.4c00080ACS Nanosci. 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