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Hao Zhang, Önder Gül, Sonia Conesa-Boj, Michał P. Nowak, Michael Wimmer, Kun Zuo, Vincent Mourik, Folkert K. de Vries, Jasper van Veen, Michiel W. A. de Moor, Jouri D. S. Bommer, David J. van Woerkom, Diana Car, Sébastien R Plissard, Erik P.A.M. Bakkers, Marina Quintero-Pérez, Maja C. Cassidy, Sebastian Koelling, Srijit Goswami, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Leo P. Kouwenhoven

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[Ballistic superconductivity in semiconductor nanowires](https://mdr.nims.go.jp/datasets/c65ddf33-7f20-4c77-9835-6f2b64da1534)

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Ballistic superconductivity in semiconductor nanowiresARTICLEReceived 1 Mar 2017 | Accepted 18 May 2017 | Published 6 Jul 2017Ballistic superconductivity in semiconductornanowiresHao Zhang1,2,*, Önder Gül1,2,*, Sonia Conesa-Boj1,2,3, Michał P. Nowak1,2,4, Michael Wimmer1,2, Kun Zuo1,2,Vincent Mourik1,2, Folkert K. de Vries1,2, Jasper van Veen1,2, Michiel W.A. de Moor1,2, Jouri D.S. Bommer1,2,David J. van Woerkom1,2, Diana Car3, Sébastien R. Plissard2,3, Erik P.A.M. Bakkers1,2,3, Marina Quintero-Pérez1,5,Maja C. Cassidy1,2, Sebastian Koelling3, Srijit Goswami1,2, Kenji Watanabe6, Takashi Taniguchi6& Leo P. Kouwenhoven1,2,7Semiconductor nanowires have opened new research avenues in quantum transport owing totheir confined geometry and electrostatic tunability. They have offered an exceptional testbedfor superconductivity, leading to the realization of hybrid systems combining the macroscopicquantum properties of superconductors with the possibility to control charges down to asingle electron. These advances brought semiconductor nanowires to the forefront of effortsto realize topological superconductivity and Majorana modes. A prime challenge to benefitfrom the topological properties of Majoranas is to reduce the disorder in hybrid nanowiredevices. Here we show ballistic superconductivity in InSb semiconductor nanowires.Our structural and chemical analyses demonstrate a high-quality interface between thenanowire and a NbTiN superconductor that enables ballistic transport. This is manifested bya quantized conductance for normal carriers, a strongly enhanced conductance for Andreev-reflecting carriers, and an induced hard gap with a significantly reduced density of states.These results pave the way for disorder-free Majorana devices.DOI: 10.1038/ncomms16025 OPEN1 QuTech, Delft University of Technology, 2600 GA Delft, The Netherlands. 2 Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft,The Netherlands. 3 Department of Applied Physics, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands. 4 Faculty of Physics andApplied Computer Science, AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Kraków, Poland. 5 Netherlands Organisation forApplied Scientific Research (TNO), 2600 AD Delft, The Netherlands. 6 Advanced Materials Laboratory, National Institute for Materials Science, 1-1 Namiki,Tsukuba 305-0044, Japan. 7 Microsoft Station Q Delft, 2600 GA Delft, The Netherlands. * These authors contributed equally to this work. Correspondenceand requests for materials should be addressed to H.Z. (email: H.Zhang-3@tudelft.nl) or to Ö.G. (email: Gul.Onder@gmail.com) or to L.P.K.(email: L.P.Kouwenhoven@tudelft.nl).NATURE COMMUNICATIONS | 8:16025 | DOI: 10.1038/ncomms16025 | www.nature.com/naturecommunications 1mailto:H.Zhang-3@tudelft.nlmailto:Gul.Onder@gmail.commailto:L.P.Kouwenhoven@tudelft.nlhttp://www.nature.com/naturecommunicationsMajorana modes are zero-energy quasiparticles emergingat the boundary of a topological superconductor1–3.Following proposals for their detection in asemiconductor nanowire coupled to a superconductor4,5, severalelectron transport experiments reported characteristic Majoranasignatures6–14. The prime challenge to strengthen these signaturesand unravel the predicted topological properties of Majoranas isto reduce the remaining disorder in this hybrid system. Disordercan mimic zero-energy signatures of Majoranas15–19, and resultsin states within the induced superconducting energy gap20, theso-called soft gap, which renders the topological propertiesexperimentally inaccessible21,22. The soft gap problem isattributed to the inhomogeneity of the hybrid interface20,23–25and has been overcome by a recent demonstration of epitaxialgrowth of Al superconductor on InAs nanowires23, yielding ahard gap—a strongly reduced density of states within the inducedsuperconducting gap. However, the Al-InAs nanowire systemstill contains residual disorder showing up in transport asunintentional quantum dots13,23, a common observation inmany previous instances of hybrid nanowire devices9,18,19. Asan alternative material system, we have further developed thecombination of InSb nanowires with NbTiN as our preferredchoice of superconductor6. InSb is in general cleaner (that is,higher electron mobility26–29) than InAs. Moreover, InSb has aB5 times larger g-factor, bringing down the required externalmagnetic field needed to induce the topological phase transition.Our preference for NbTiN relies on its high critical magnetic fieldexceeding 10 T.Here we show ballistic superconductivity in InSb semiconduc-tor nanowires. Our structural and chemical analyses demonstratea high-quality interface between the InSb nanowire and a NbTiNsuperconductor. The high-quality interface enables ballistictransport manifested by a quantized conductance for normalcarriers, and a strongly enhanced conductance for Andreev-reflecting carriers at energies below the superconducting gap. Ournumerical analysis indicates a mean free path of severalmicrometres, implying ballistic transport of Andreev pairs inthe proximitized nanowire. Finally, tunnelling conductancereveals an induced hard gap with a significantly reduced densityof states. These results constitute a substantial improvementin induced superconductivity in semiconductor nanowires, andpave the way for disorder-free Majorana devices.ResultsHybrid nanowire devices and their structural analysis. Wereport on five devices with different geometries all showingconsistent results. An overview of all the devices is given inSupplementary Fig. 1. Figure 1a,b shows a nanowire deviceconsisting of a normal contact (Au), a nanowire (InSb) and asuperconducting contact (NbTiN). This device was first measuredat low temperature showing high-quality electron transport (datadiscussed below). After, the device was sliced open (using focusedion beam) and inspected sideways in a transmission electronmicroscope (TEM). The hexagonal facet structure of the nano-wire is clearly visible (Fig. 1c and Supplementary Fig. 2). Exceptfor the bottom facet that rests on the substrate, the polycrystallinesuperconductor covers the nanowire all around without anyvisible voids.The precise procedure for contact realization is extremelyimportant (see ref. 25). First, the native oxide at the InSb surfaceis wet-etched using a sulfur-based solution followed by an argonNbInSbTiNNbSbTiNS (×5)O ArAVVgateInSbNbTiNat. %NbTiNInSbNbTiNAuInSbSiO28060402000 30252015105InNbTiISi++Distance (nm)a c de fbFigure 1 | TEM analysis of a typical device. (a) Top-view, false-colour electron micrograph of device A. Scale bar, 1 mm. Normal metal contact is Cr/Au(10 nm/125 nm) and superconducting contact is NbTi/NbTiN (5 nm/85 nm). Contact spacing is B100 nm. (b) Device schematic and measurement setup.(c) Low-magnification high-resolution TEM (HRTEM) cross-sectional image from the device (see Methods). Scale bar, 50 nm. The cut was performedperpendicular to the nanowire axis, indicated by the dark bar in a. InSb nanowire exhibits a hexagonal cross-section surrounded by {220} planes. TheNbTiN on the pre-layer NbTi crystallizes as cone-like elongated grains, indicated by the thin black lines. Corresponding fast Fourier transform confirms thepolycrystalline character of the NbTiN region (Supplementary Fig. 2b). (d) HRTEM image near the interface (red square in c) shows that our cleaningprocedure only minimally etches the wire and the InSb crystalline properties are preserved after the deposition. Scale bar, 5 nm. (e) Energy-dispersive X-ray(EDX) compositional map of the device cross-section. Scale bar, 50 nm. (f) EDX line scan taken across the interface as indicated by the red arrow in e.The sulfur content is multiplied by 5 for clarity. The system is oxygen and argon free (contact deposition is performed in an Ar plasma environment).ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms160252 NATURE COMMUNICATIONS | 8:16025 | DOI: 10.1038/ncomms16025 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsetch of sufficiently low power to avoid damaging the InSb surface(see Methods). The inclusion of sulfur at the interface results inband bending with electron accumulation near the surface ofInSb30 (Supplementary Fig. 3). Superconducting film depositionstarts with NbTi, a reactive metal whose inclusion as a wettinglayer is crucial to create a good electrical contact. Figure 1d showsthat our cleaning procedure only minimally etches the wire andthe InSb crystalline properties are preserved after the deposition(details in Supplementary Fig. 2). We detect a thin segregationlayer (B2 nm) between the polycrystalline NbTi and single-crystalline InSb. The chemical analysis (Fig. 1e,f) shows amaterial composition in agreement with our depositionprocedure. More importantly, the inclusion of sulfur is clearlyvisible at the interface whereas the original native oxide iscompletely absent.Ballistic transport. The high-quality structural properties inFig. 1 result in largely improved electronic properties overthe previous instances of hybrid nanowire devices. Figure 2ashows the differential conductance dI/dV while varying the biasvoltage V between the normal and superconducting contacts, andstepping the gate voltage Vgate applied to the global back gate(Fig. 1b). We first of all note that throughout the entire gatevoltage range in Fig. 2 we do not observe signs of the formation ofunintentional quantum dots or any other localization effectsresulting from potential fluctuations. Instead, we observeconductance plateaus at 2e2/h for all devices, typical for ballistictransport and a clear signature of disorder-free devices. For asufficiently negative gate voltage the non-covered nanowire sec-tion between normal and superconducting contacts is depletedand serves as a tunnel barrier. A vertical line cut from this regimeis plotted in Fig. 2b, showing a trace typical for an inducedsuperconducting gap with a strong conductance suppression forsmall V. The extracted gap value is D*¼ 0.8 meV. Increasing Vgatefirst lowers and then removes the tunnel barrier completely.A vertical line cut from this open regime is plotted in Fig. 2c.In this case, the conductance for small V is enhanced compared tothe value above B1 mV. Note that the range in V showingan enhanced conductance in Fig. 2c corresponds to the samerange showing the induced gap in Fig. 2b. The enhancementresults from Andreev processes where an incoming electronreflects as a hole at the normal conductor-superconductorinterface generating a Cooper pair23,24,31,32. This Andreev processeffectively doubles the charge being transported from e to 2eenhancing the subgap conductance. In Fig. 2c, the observedenhancement is by a factor B1.5.The Andreev enhancement is also visible in horizontal line cutsas shown in Fig. 2d. The above-gap conductance (black trace)taken for |V|¼ 2 mV represents the conductance for normalcarriers, Gn. The subgap conductance, Gs, near V¼ 0 (Fig. 2d, redtrace) shows an Andreev enhancement in the plateau region.Figure 2e shows a similar trace from another device where theenhancement in Gs reaches 1.9� 2e2/h, very close to thetheoretical limit: an enhancement factor of 2 in the case of aperfect interface. Finally, we note the dip in subgap conductanceGs following the Andreev enhancement, observed both in Fig. 2dand Fig. 2e. The combined enhancement and dip structureprovides a handle for estimating the remaining disorder by acomparison to theory, as discussed below.Theoretical simulation. We construct a tight binding model ofour devices (Fig. 3a) and numerically calculate the conductanceusing the Kwant package33 (see Methods for details). In Fig. 3b,we plot the conductance traces obtained from the simulation fordifferent disorder strength corresponding to varying mean freepaths le. The calculated subgap conductance reproduces the dipstructure observed in the experiment. We find that the dip iscaused by mixing between the first and the second subband dueto residual disorder (Supplementary Fig. 4). Even for weakdisorder, subband mixing is strongly enhanced near the openingof the next channel, due to the van Hove singularity at thesubband bottom. Hence, the Andreev conductance willgenerically exhibit a dip close to the next conductance step,instead of a perfect doubling. Figure 3c shows the measuredsubgap conductance Gs and above-gap conductance Gn for adevice with a particularly flat plateau. Comparing Fig. 3b andFig. 3c, we find good agreement for a mean free path of severalmicrometres. This implies ballistic transport of Andreev pairs inthe proximitized wire section underneath the superconductor,whose length far exceeds the length of the non-covered wirebetween the contacts (see also Supplementary Fig. 5). Andreevenhancement allows for extracting mean free paths greatlyexceeding the non-covered wire section since the subgapconductance is sensitive to even minute disorder in theproximitized wire section—a new finding of our study. Thissensitivity is due to the quadratic dependence of the subgap210210–3–8–3–8–13GnGsGnGsV (mV)V (mV)120 2–200.10 2–202–2Vgate (V)Vgate (V)Vgate (V)–3–8–13cdbea 0 1 2V (mV)dI/dV (2e2/h)dI/dV (2e2 /h)dI/dV (2e2 /h)dI/dV (2e2 /h)dI/dV (2e2 /h)Figure 2 | Ballistic transport at zero magnetic field. (a) Differentialconductance, dI/dV, as a function of bias voltage, V, and gate voltage, Vgatefor device B. (b) Vertical line cut from a in tunnelling regime (green trace,gate voltage¼ � 12 V). (c) Vertical line cut from a on the conductanceplateau (blue trace, gate voltage¼ � 5.9 V). (d) Horizontal line cuts from ashowing above-gap (Gn, black, |V|¼ 2 mV) and subgap (Gs, red, V¼0 mV)conductance. (e) Above-gap (black) and subgap (red) conductance fordevice C, where Gs enhancement reaches 1.9� 2e2/h.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms16025 ARTICLENATURE COMMUNICATIONS | 8:16025 | DOI: 10.1038/ncomms16025 | www.nature.com/naturecommunications 3http://www.nature.com/naturecommunicationsconductance on the transmission probability (introduced below).In Fig. 3d,e, we compare a conductance measurement similar tothe one in Fig. 2a with the simulation of a ballistic device. Theoverall agreement indicates a very low disorder strength for ourdevices.Hard superconducting gap. The theory for electronic transportfrom a normal conductor via a quantum point contact to asuperconductor was developed by Beenakker31. The subgapconductance is described by Andreev reflections32, and for asingle subband given by Gs ¼ 4e2=h�T2=ð2�TÞ2. The gatevoltage-dependent transmission probability T can be extractedfrom the measured above-gap conductance, given byGn ¼ 2e2=h�T . Figure 4a shows excellent agreement betweenthe calculated and measured subgap conductance up to the pointwhere the measured Andreev enhancement is reduced due tosubband mixing. The highest transmission probability obtainedfrom Andreev enhancement sets a lower bound on the interfacetransparency. Our typical enhancement factor of 1.5 (Figs 2d and3c) implies an interface transparency B0.93 and our recordvalue of 1.9 (Fig. 2e) gives a transparency larger than 0.98(see Measurement setup and data analysis in Methods).The comparison between Gs versus Gn can be continued intothe regime of an increasing tunnel barrier. Figure 4b,c show tracesof dI/dV for successively lower conductances. The subgapconductance suppression reaches Gs=Gn � 1=50, a valuecomparable to the results obtained with epitaxial Al23.A comparison between the measured subgap conductance andBeenakker’s theory (without any fit parameters) is shown inFig. 4d. The excellent agreement over three orders of magnitudein conductance implies that the subgap conductance is very welldescribed by Andreev processes and no other transportmechanisms are involved23,24. The lowest conductance(� 5�10� 4�2e2=h) reaches our measurement limit, causingthe deviation from theory. The inset to Fig. 4b shows how thesubgap conductance increases when applying a magnetic field.Finally, in Supplementary Fig. 6 we show the magnetic fielddependence of the induced gap and Andreev enhancement for amagnetic field along the nanowire axis. We again find a subgapconductance increasing with magnetic field, and an Andreevenhancement vanishing at a magnetic field (o1 T) smaller thanthe critical field of our NbTiN film. We speculate that theincreasing subgap conductance and the decreasing Andreevenhancement are due to vortex formation in our NbTiN film, atype-II superconductor. Future studies should be directed–22–110V (mV)0 1 32–10–20 –15–25–30–2–4–82Simulation–1–210V (mV)–6Vgate (V)0 1 32ExperimentSimulationSimulationRSLN Y QPCLNLWRyzxNNW *SExperiment210–5–15–25Gs, 1 µmGs, 20 µm Gs, 1.5 µmGs, 2.5 µmGs, 5 µmGn, 10 µm2100–2GsGnMean free pathdI/dV (2e2/h)dI/dV (2e2/h)VQPC (mV)dI/dV (2e2 /h)dI/dV (2e2 /h)VQPC (mV) Vgate (V)Experimenta db ceFigure 3 | Theoretical simulation. (a) Theoretical model (top): a cylindrical nanowire (black, grey, white) with length LNþ L (100 nmþ800 nm), wherethe latter part is partially coated by a superconductor leaving the bottom surface uncovered. (Scheme shows L¼ 100 nm for clarity.) The wire radius R is40 nm and the superconducting film has a thickness Rs¼ 10 nm. (Our wire radius varies from device to device between 30 and 50 nm, and we haveconfirmed that our simulations give similar results within this range.) The wire is terminated from both sides with infinite leads (pink). Front lead is normal,back lead is normal/superconductor. Each little circle represents a three-dimensional mesh site with a size of 7 nm. White circles depict a potential barrierwith a width W¼ 60 nm in the uncovered wire section forming a quantum point contact (QPC). Grey circles represent the smoothness of the barrier whichis set to 5 nm. Experimental geometry (bottom): cross-sectional schematic shows the nanowire (NW), the normal contact (N) and the superconductingcontact (S). Superconductivity is induced in the nanowire section underneath the superconducting contact. Transport is ballistic through a proximitized wiresection, whose length far exceeds LN, the length of the non-covered wire between the contacts. (b) Numerical simulation for devices with different meanfree paths (see Supplementary Fig. 5). Black trace is for Gn corresponding to a mean free path 10mm, the rest are for Gs corresponding to a mean free pathranging from 1mm (pink) to 20mm (blue). (c) Above-gap (black) and subgap (red) conductance for device D. (d,e) Comparison between the measurement(device C) and the simulation of a ballistic device with le¼ 10 mm. The induced superconducting gap edges for higher subbands, visible in the simulation asfour symmetric peaks outside the gap around V B±1 mV, are not observed in the experiment (see Methods for details).ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms160254 NATURE COMMUNICATIONS | 8:16025 | DOI: 10.1038/ncomms16025 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationstowards developing a quantitative description of such magneticfield-induced deviation from Andreev transport, whoseunderstanding plays a crucial role in realizing a topologicalquantum bit based on semiconductor nanowires.MethodsNanowire growth and device fabrication. InSb nanowires have been grown byAu-catalysed vapour–liquid–solid mechanism in a metal organic vapour phaseepitaxy reactor. The InSb nanowire crystal direction is [111] zinc blende, free ofstacking faults and dislocations34. Nanowires are deposited one-by-one using amicro-manipulator35 on a substrate covered with 285 nm thick SiO2 serving as agate dielectric for back-gated devices. For local-gated device D, extra set of bottomgates are patterned on the substrate followed by transfer of h-BN (B30 nm thick)onto which nanowires are deposited. The contact deposition process starts withresist development followed by oxygen plasma cleaning. Then, the chip isimmersed in a sulfur-rich ammonium sulfide solution diluted by water (with a ratioof 1:200) at 60 �C for half an hour36. At all stages care is taken to expose thesolution to air as little as possible. For normal metal contacts27, the chip is placedinto an evaporator. A 30 s Helium ion milling is performed in situ beforeevaporation of Cr/Au (10 nm/125 nm) at a base pressure o10� 7 mbar. Forsuperconducting contacts25, the chip is mounted in a sputtering system. After 5 s ofin situ Ar plasma etching at a power of 25 W and an Ar pressure of 10 mTorr, 5 nmNbTi is sputtered followed by 85 nm NbTiN.Measurement setup and data analysis. All the data in this article is measured ina dilution refrigerator with a base temperature of around 50 mK using severalstages of filtering. The determination of the Andreev enhancement factor dependssensitively on the contact resistance subtracted from the measured data. In all ouranalysis, we only subtract a fixed-value series resistance of 0.5 kO solely to accountfor the contact resistance of the normal metal lead. This value is smaller than thelowest contact resistance we have ever obtained for InSb nanowire devices27, whichmakes the values for the interface transparency a lower bound.Structure characterization. The cross-section and lamella for TEM investigationswere prepared by focused ion beam (FIB). FIB milling was carried out with a FEINova Nanolab 600i Dualbeam with a Ga ion beam following the standardprocedure37. We used electron induced Co and Pt deposition for protecting theregion of interest and a final milling step at 5 kV to limit damage to the lamella.High-resolution TEM (HRTEM) and scanning TEM analyses were conductedusing a JEM ARM200F aberration-corrected TEM operated at 200 kV. For thechemical analysis, energy-dispersive X-ray measurements were carried out usingthe same microscope equipped with a 100 mm2 energy-dispersive X-ray silicondrift detector (SSD).Characterization of NbTiN. Our NbTiN films are deposited using an ultrahighvacuum AJA International ATC 1800 sputtering system (base pressure B10� 9Torr). We used a Nb0.7Ti0.3 wt.% target with a diameter of 3 inches. Reactivesputtering resulting in nitridized NbTiN films was performed in an Ar/N2 processgas with 8.3 at.% N2 content at a pressure of 2.5 mTorr using a DC magnetronsputter source at a power of 250 W. An independent characterization of the NbTiNfilms gave a critical temperature of 13.3 K for 90 nm thick films with a resistivity of126 mO � cm and a compressive stress on Si substrate.Details of the theoretical simulation. The system is described by thespin-diagonal Bogoliubov–de Gennes HamiltonianH ¼ ‘ 2k22m��mþVðx; y; zÞ� �tz þDðx; y; zÞtx ; ð1ÞExperimentTheory11110–110–110–210–210–310–2 10–110–310–4Gn, experimentGs, theoryGs, experiment000000.030.070.150.30.50122–2 02–2 0Vgate (V)0–4a dbc10–210–30 T0.75 T0.25 T0.5 T10–1dI/dV (2e2 /h)dI/dV (2e2 /h)dI/dV (2e2 /h)10–1V (mV)V (mV)Gs (2e2 /h)Gn (2e2/h)TheoryGs (2e2 /h)Gn (2e2/h)Figure 4 | Hard gap and Andreev transport. (a) Above-gap (black) and subgap (blue) conductance for device E. Red curve is a theory prediction based onsingle channel Andreev reflection, agreeing perfectly with experimental data without any fitting parameter up to the dip on the right side of the plateauwhere the second channel starts conducting. (b,c) Five typical gap traces corresponding to the five colour bars indicated in d plotted on a linear andlogarithmic scale. The subgap conductance is suppressed by a factor up to 50 for the lowest conductance (red trace). (d) Subgap conductance Gs as afunction of above-gap conductance Gn for device A. Red curve is the theory prediction assuming only Andreev processes. Inset shows Gs versus Gn taken atdifferent magnetic fields.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms16025 ARTICLENATURE COMMUNICATIONS | 8:16025 | DOI: 10.1038/ncomms16025 | www.nature.com/naturecommunications 5http://www.nature.com/naturecommunicationsacting on the spinor C ¼ ðceþ ;ce� ;ch� ; �chþ ÞT . The Pauli matrices act onthe electron-hole degree of freedom. Potential in the nanowire is described byVðx; y; zÞ ¼ ~VqpcðyÞþVDðx; y; zÞ, where ~VqpcðyÞ describes a quantum pointcontact given by~VqpcðyÞ ¼ � eVQPC2 tanh y�YQPC þW=2lh� tanh y�YQPC �W=2li:Here YQPC is the centre position of the barrier (Fig. 3a). Barrier width isW¼ 60 nm, and the barrier height is controlled by VQPC. The softness of thebarrier is given by l which we take 5 nm. VD(x, y, z) accounts for disorder, which ismodelled as a spatially varying potential with random values from a uniformdistribution within a range [�U0, U0] where amplitude U0 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3p=lem�2a3pisset by mean free path le.We approximate the superconductor covering the wire by a layer of non-zeroD for ðx2 þ z2Þ4R and y4LN and z4�R. The huge wave vector difference in thesuperconductor and semiconductor cannot be captured in a numerical simulationof a three-dimensional device. Hence, to capture the short coherence length in thesuperconductor, we take a superconducting shell of thickness RS¼ 10 nm andD¼ 200 meV. We then tune the induced gap to be close to the experimental value(B0.5 meV) by reducing the hopping between the semiconductor and thesuperconductor by a factor of 0.8.The transport properties of the system are calculated using Kwantpackage33 with the Hamiltonian in equation (1) discretized on a three-dimensionalmesh with spacing a¼ 7 nm and infinite input (normal) and output (normal/superconducting) leads. For a given VOPC and excitation energy e we obtain thescattering matrix of the system from which we subsequently extract electron re(e)and hole rh(e) reflection submatrices. Finally, we calculate thermally averagedconductance for injection energy E¼ � eV according toGðEÞ ¼ZdeGðeÞ � @f ðE; eÞ@e� �;where the Fermi functionf ðE; eÞ ¼ 1eðe�EÞ=kb T þ 1;and GðeÞ ¼ N � jj reðeÞ jj 2 þ jj rhðeÞ jj 2. We assume chemical potential to bem¼ 30 meV, which gives N¼ 3 spin-degenerate modes in the leads. The presentedresults are obtained for T¼ 70 mK and InSb effective mass m*¼ 0.014me.Data availability. All data are available at http://doi.org/10.4121/uuid:fdeb81ab-1478-4682-9f48-dec1c83242bd (ref. 38). The code used for the simulations isavailable upon request.References1. Read, N. & Green, D. Paired states of fermions in two dimensions withbreaking of parity and time-reversal symmetries and the fractional quantumHall effect. Phys. Rev. B 61, 10267 (2000).2. Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys. Usp. 44,131–136 (2001).3. Fu, L. & Kane, C. L. Superconducting proximity effect and Majoranafermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407(2008).4. Lutchyn, R. M., Sau, J. D. & Das Sarma, S. Majorana fermions and a topologicalphase transition in semiconductor-superconductor heterostructures. Phys. Rev.Lett. 105, 077001 (2010).5. Oreg, Y., Refael, G. & von Oppen, F. Helical liquids and Majorana bound statesin quantum wires. Phys. 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S.K. prepared the lamellae for the TEM analysis. K.W. and T.T. synthesizedthe h-BN crystals. L.P.K. supervised the project. All authors contributed to the writing ofthe manuscript.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms160256 NATURE COMMUNICATIONS | 8:16025 | DOI: 10.1038/ncomms16025 | www.nature.com/naturecommunicationshttp://arxiv.org/abs/1610.04555http://doi.org/10.4121/uuid:fdeb81ab-1478-4682-9f48-dec1c83242bdhttp://doi.org/10.4121/uuid:fdeb81ab-1478-4682-9f48-dec1c83242bdhttp://www.nature.com/naturecommunicationsAdditional informationSupplementary Information accompanies this paper at http://www.nature.com/naturecommunicationsCompeting interests: The authors declare no competing financial interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/How to cite this article: Zhang, H. et al. Ballistic superconductivity insemiconductor nanowires. Nat. Commun. 8, 16025 doi: 10.1038/ncomms16025(2017).Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, as long as you giveappropriate credit to the original author(s) and the source, provide a link to the CreativeCommons license, and indicate if changes were made. The images or other third partymaterial in this article are included in the article’s Creative Commons license, unlessindicated otherwise in a credit line to the material. If material is not included in thearticle’s Creative Commons license and your intended use is not permitted by statutoryregulation or exceeds the permitted use, you will need to obtain permission directly fromthe copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/r The Author(s) 2017NATURE COMMUNICATIONS | DOI: 10.1038/ncomms16025 ARTICLENATURE COMMUNICATIONS | 8:16025 | DOI: 10.1038/ncomms16025 | www.nature.com/naturecommunications 7http://www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationshttp://npg.nature.com/reprintsandpermissions/http://npg.nature.com/reprintsandpermissions/http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/http://www.nature.com/naturecommunications title_link Results Hybrid nanowire devices and their structural analysis Figure™1TEM analysis of a typical device.(a) Top-view, false-colour electron micrograph of device A. Scale bar, 1thinspmgrm. Normal metal contact is CrsolAu (10thinspnmsol125thinspnm) and superconducting contact is NbTisolNbTiN (5thinspnmsol85thinspnm). C Ballistic transport Theoretical simulation Figure™2Ballistic transport at zero magnetic field.(a) Differential conductance, dIsoldV, as a function of bias voltage, V, and gate voltage, Vgate for device B. (b) Vertical line cut from a in tunnelling regime (green trace, gate voltage=-12thinspV). (c) Hard superconducting gap Figure™3Theoretical simulation.(a) Theoretical model (top): a cylindrical nanowire (black, grey, white) with length LN+L (100thinspnm+800thinspnm), where the latter part is partially coated by a superconductor leaving the bottom surface uncovered. (Scheme Methods Nanowire growth and device fabrication Measurement setup and data analysis Structure characterization Characterization of NbTiN Details of the theoretical simulation Figure™4Hard gap and Andreev transport.(a) Above-gap (black) and subgap (blue) conductance for device E. Red curve is a theory prediction based on single channel Andreev reflection, agreeing perfectly with experimental data without any fitting parameter u Data availability ReadN.GreenD.Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effectPhys. Rev. B61102672000KitaevA. Y.Unpaired Majorana fermions in quantum wiresPhys. Usp.441311362001FuL.Kane We thank A.R. Akhmerov, O.W.B. Benningshof, A. Geresdi, J. Kammhuber and A.J.™Storm for discussions and assistance. This work has been supported by the Netherlands™Organisation for Scientific Research (NWO), Foundation for Fundamental Research on Matter ( ACKNOWLEDGEMENTS Author contributions Additional information