Multiterminal Quantized Conductance in InSb Nanocrosses
Sabbir A. Khan, Lukas Stampfer, Timo Mutas, Jung-Hyun Kang, Peter Krogstrup, Thomas S. Jespersen
MMultiterminal Quantized Conductance in InSb Nanocrosses
Sabbir A. Khan*,
1, 2
Lukas Stampfer*, Timo Mutas, Jung-HyunKang,
1, 2
Peter Krogstrup,
1, 2 and Thomas S. Jespersen ∗ Microsoft Quantum Materials Lab Copenhagen, 2800 Lyngby, Denmark Center for Quantum Devices, Niels Bohr Institute,University of Copenhagen, 2100 Copenhagen, Denmark (Dated: January 8, 2021)By studying the time-dependent axial and radial growth of InSb nanowires, we map the conditionsfor the synthesis of single-crystalline InSb nanocrosses by molecular beam epitaxy. Low-temperatureelectrical measurements of InSb nanocross devices with local gate control on individual terminalsexhibit quantized conductance and are used to probe the spatial distribution of the conductingchannels. Tuning to a situation where the nanocross junction is connected by few-channel quantumpoint contacts in the connecting nanowire terminals, we show that transport through the junctionis ballistic except close to pinch-off. Combined with a new concept for shadow-epitaxy of patternedsuperconductors on nanocrosses, the structures reported here show promise for the realization ofnon-trivial topological states in multi-terminal Josephson Junctions.
Combining intrinsic confinement and high crystal qual-ity, III-V semiconductor nanowires (NWs) have consti-tuted an important experimental platform for mesoscopicphysics and quantum devices for the past two decades[1–4]. Renewed interest was triggered by proposals forengineering exotic topological phases in strong spin-orbitinteraction (SOI) one-dimensional (1D) NWs with prox-imity induced superconductivity [5, 6]. This led to signifi-cant theoretical works and experimental efforts in deviceengineering and material developments of hybrid semi-conductor/superconductor structures [7, 8]. In addition,proposals for realizing quantum operations by braidingthe world lines of non-abelian Majorana quasi-particlesin networks of 1D hybrid nanowires [9] create a needto extend the conventional linear NW platform towardsbranched hybrid structures. Different schemes are be-ing developed towards planar NW networks [10–14] andvapor-liquid-solid NW growth has been extended to sim-pler branched structures either by changing the growthdirections during growth [15–19] or by merging non-parallel NWs grown from tilted substrate facets [20, 21].The high mobility and strong SOI make indium anti-mony (InSb) the optimal candidate for transport mea-surements, however, branched InSb NW structures andnanocrosses have not so far been reported using molecu-lar beam epitaxy (MBE) – traditionally leading to crys-tals with the lowest impurity concentration.Here, we demonstrate controlled synthesis of InSbnanocrosses (NCs) using MBE, where the challenge of ini-tiating InSb growth is overcome using a two-step proce-dure, beginning with a short segment of InAs supportingthe subsequent InSb NW. A NC geometry is enabled bygrowing NWs from facing, non-parallel (cid:104) (cid:105) facets. Wemap the conditions for NC formation in terms of relativecatalyst position, axial growth rates, and radial growthof InSb NW. Structural characterization using transmis-sion electron microscopy (TEM) confirms a single-crystalZinc-Blende (ZB) phase across the InSb NC. Further, we study the low-temperature electron transport of theInSb NCs with local gate-control of each individual ter-minal. Each terminal exhibits quantized conductance,and from analysis of the combined transport through twoquantized constrictions we infer ballistic transport alsoover the NC junction, except for global gate potentialsclose to pinch-off. Finally, we demonstrate a new conceptfor merging the NC geometry with pre-defined substratestructures to enable in situ patterning of epitaxial su-perconductors, which have been shown to substantiallyenhance the performance of hybrid devices [22–24].
RESULTS AND DISCUSSION
Growth of InSb Nanocrosses.
The growth of InSbNCs was enabled using InAs (100) substrates contain-ing (111)B faceted trenches, which were fabricated bychemical etching following along the lines of Ref. [22].Au catalyst particles with relative lateral distances ∆ x ,∆ y were defined on opposing facets using electron beamlithography. See Fig. 1 a for a definition of the coordinatesystem and a scanning electron microscope (SEM) micro-graph of a typical substrate before growth. The result ofthe final NW structure depends critically on the rela-tion between ∆y, the diameter d Au of the supersaturatedAu catalyst that defines the initial diameter d ( t ) of theInSb NW during axial growth, and the amount of radialgrowth when the NW reach to it’s final diameter d ( t f ).For ∆y < d Au the NWs meet “head-to-head” and theaxial growth is interrupted preventing the formation offour-terminal crosses [25, 26]. This situation is discussedin the Supporting Information (S1-S6). For ∆y exceed-ing the final NW diameter d ( t f ), the two NWs remainseparated, while for a finite off-set d Au < ∆y < d ( t f ) theresulting structure and the possibility of forming con-nected four-terminal crosses depends on the relation be-tween ∆ y , d Au , d ( t MP ), and d ( t ). Here, t MP refers to the a r X i v : . [ c ond - m a t . m e s - h a ll ] J a n FIG. 1.
Substrate design and InSb nanocross forma-tion. a , Tilted scanning electron micrograph (SEM) of InAs(111)B trenches with deposited Au catalyst particles. Theschematics illustrate the notation used for describing the lay-out. b , Schematics of the evolution of nanowires to mergeand create nanocrosses. In the time scale, growth starts att , nanowires pass each other at t MP and t f is the final growthtime. When L < λ (step (i) and (ii)), the radial growth is lim-ited and nanowires pass each other without merging. WhenL ∼ λ (step (iii) and (iv)), the radial growth overcomes ∆yspacing and nanowires merge from the side-facets. Hence,radial growth from t MP to t f determines the nanocross for-mation. c , Schematic of the final nanocross structure. d ,Growth demonstration of InSb nanocrosses from the identicalsubstrate design shown in panel ( a ). Scale bars in ( a ) and( d ) are is 1 µ m. time when the two catalyst particles pass each other atthe closest point. The sequence is illustrated in Fig. 1 b .Ideally, the growth front (the size of which is given by d Au = d ( t = 0)) of the two NWs pass each-other withminimal separation thus, continuing axial growth whilethe simultaneous radial overgrowth eventually merges thetwo NWs epitaxially at the meeting-point. The finalstructure is schematically shown in Fig. 1 c and a typ-ical example of MBE grown NCs is presented in Fig. 1 d .To find the optimal parameters for NC formation fivegrowths of different growth-times between 41 and 75 min-utes were performed, and Fig. 2 a shows the measured av-erage InSb lengths and final diameters from NWs grownin trenches (with ∆x = 4 . µ m and pitch size of 970 nmbetween Au catalysts). Both length and diameter in-crease with time but while the diameter more than dou-bles in this time interval, the length only increases by afactor of 1.5. This trend is also evident from the decayingaspect ratio extracted in Fig. 2 b . The InSb NW growthis initiated by axial growth via the liquid-solid transition,with an initial diameter d , which is determined by thevolume and contact angle of the Au particle at the pointof supersaturation with In and Sb. After some time, theNW length becomes comparable to the incorporation lim-ited diffusion length λ and adatoms cannot reach to theAu particle, initiating radial growth on the side facets. Ingeneral, radial growth can be divided into three stages:no radial growth (L << λ ), transition stage (L ≈ λ ), andconstant radial growth (L >> λ ). The extracted radialgrowth rate is presented in Fig. 2 c from which is can beseen that the main part of the InSb growth resides in thetransition stage for the studied growth times from 43 to70 minutes (see Fig. 2 c ). Note that, the growth param-eters were chosen to promote radial growth, rather thanlong NW with high aspect ratio, as this is required forthe formation of high quality NCs.Extrapolating the diameter in Fig. 2 a to t = 0, we es-timate a diameter of the growth front of ∼
100 nm andchoosing ∆y ≈
185 nm, the growth fronts is expected topass uninterrupted at t MP . The length of the combinedInAs/InSb NW at the meeting point L MP = ∆ x/ θ with θ = 35 ◦ being the inclination angle of the (111)Bfacet, is determined by the position of the Au catalystparticles and was 2 . µ m for our substrates. The InAsstem was grown to a length of ∼ . µ m leaving 1 . µ mfor the InSb to reach the meeting point (MP). As seenin Fig. 2 a , the NWs reach this point after a growthtime shorter than t MP (cid:46)
30 min having then a diame-ter d ( t MP ) ∼
100 nm, and therefore, the NWs pass eachother at the MP as separate structures. Figure 2 d showsan example of a growth performed for 75 min leading tohigh throughput NCs formation. Here, the final length ofthe InSb NWs were ∼ µ m with diameter of ∼ ± FIG. 2.
Growth dynamics and structural analysis of InSb nanocrosses. a , Length and diameter of InSb nanowires atdifferent growth times. Here, the time for growing the InAs stem is excluded. b , Aspect ratio as a function of InSb growthtime. c , Radial growth rate data extracted from panel (a). d , Tilted SEM image of the high yield InSb nanocrosses, whereNWs are merged with the radial growth. e , Representative TEM of a nanocross. Zinc Blende crystal structure is maintainedbefore and after merging. Arrows indicate growth direction. f-g , High resolution TEM images of regions highlighted in panel(e). In the acute corner (g), few stacking faults are observed (indicated by arrow) in the merged section. h , TEM image of thepure wurtzite InAs stem. Scale bars in panels (d-h) are, (d): 1 µ m, (e): 100 nm, (f-g): 2 nm, (h): 5 nm. e-h ) and further details are provided in SupportingInformation S1. Figure 2 e shows the overall structureof a NC (grown along the direction of the arrows) andconfirms that all the four arms along with the mergedregion maintain the same crystal structure throughout.The high contrast structure in the middle region is aconsequence of the difference in thickness of the struc-ture. No stacking-faults or crystal defects were observedin the NC arms. Figure 2 f shows a high-resolution imageof the obtuse corner between the NWs. The ZB crystalphase is maintained also in the structure closest to thesurface, which is grown radially from the side facets andresponsible for the merging of the crystals. A twin-planeis observed at the point of merging, which we attributeto misalignment or different stacking order of the twophases. Correspondingly, Fig. 2 g shows a high resolutionimage of the acute corner where multiple stacking faultsare observed in the surface layers growh radially (arrows)presumably also caused by misalignment of the twocrystals. These, however, only appear in the radiallygrown part of the crystal and do not propagate into thecore of the wires. Figure 2 h shows the high resolution(HR)-TEM image of wurtzite (WZ) InAs stem withoutany disorders. InAs stems get thinner with longer InSbgrowth time due to the As decomposition. Low Temperature Transport Characterization.
We now consider the low-temperature electrical proper-ties of the MBE-grown InSb NCs. Previous studies ofInAs [27–30] and InSb NCs [17, 21, 31] have confirmedtransport both along and between the two merged NWs,where both ballistic transport at high fields [31] andphase-coherence [21] have been demonstrated. A mainreason for using branched nanostructures is the poten-tial to individually gate control nanowire branches, thusenabling e.g. measurements of the local density of states[32], a control of the effective size of the scattering matrixin coherent multi-terminal junctions [33], or eventuallybraiding Majorana zero modes in topological junctions[9]. So far, however, only global electrostatic gating hasbeen demonstrated.For device fabrication, NCs were located on the growthsubstrate using SEM and subsequently transferred us-ing a manual micro-manipulator to highly doped Si sub-strates capped with 500 nm of SiO . Ohmic contacts toeach terminal (denoted T , T , T , T
4) were defined by e-beam lithography and deposition of Ti/Al metals. Subse-quently, 10 nm of HfO x was deposited using atomic layerdeposition and four individual Ti/Au top gates (poten-tials V G1 , V G2 , V G3 , V G4 ) were defined on the NC termi-nals. The gates overlap the electrodes and ∼
100 nm ofthe exposed InSb, and their separation is 300 − a shows an SEM micrograph of the device. The FIG. 3.
Individual gate control of a multi-terminal nanocross device a , Scanning electron micrograph of a InSbnanocross device with four contacted terminals (T1-T4) and four individual top gates partly overlapping both contact metalsand the InSb. The gates are biased at V G1 , ..., V G4 and the measurement circuit used to simultaneously measure the conductances G , G , and G are shown. The two ac biases V B1 and V B2 are applied with the two incommensurable frequencies f and f and lock-in detection of the currents I , I and voltages V , V are carried out at frequency f , while the rest is measuredat f , as indicated by the colors. b , Two-terminal conductance vs. back gate potential of all possible connections through thecross. Top gates were grounded except for the green and purple traces where T4 was in pinch off ( V G = − c , Responseof the three conductances G , G , G to tuning each pair of top gates for V bg = 10 V and V G = − back-gate ( V bg ), acts globally and in particular at thecenter of the cross. Terminals T3 and T4 were connectedon the chip and most measurements had V G = − T a allowing si-multaneous measurements of all relevant combinations G = dI /dV , G = dI /dV , and G = dI /dV (See Methods). Measurements were performed in a di-lution refrigerator at an electron temperature ∼
20 mK.We note that Al is a superconductor at the measurementtemperatures, however, no signatures of superconductiv-ity were detected, presumably due to a disordered inter-face between InSb and the Ti/Al electrodes as furtherdiscussed below.Figure 3 b shows the back gate dependence of the con-ductance of individual connections T1 - T3/T4 (red), T2- T3/T4 (orange), and T1 - T2 (blue) measured withthe remaining terminals floating and top-gates grounded. For the purple and green traces the connections (T1-T3)and (T2-T3) were measured with V G4 = − V bg , as expected for a n -type semiconductor andthe conductance values for V bg = 15 V is relatively highfor such devices indicating low resistance Ohmic contact.The G ( V bg ) traces exhibit pronounced reproducible oscil-lations, which are attributed to conductance fluctuationsdue to phase coherence as commonly observed in NWdevices at low temperatures [2].The threshold for T1-T3/T4 is V th ∼ V bg acts non-uniformly on the terminals activating T2 at higher V bg .Also, closing T4 ( V G4 = − V th to6V suggesting that for V bg (cid:46) dG/dV bg ∼ µ S / V, and estimating the back-gate ca-pacitance by a simplified model of a NW above a planarback gate [34], we find a field effect mobility µ of ∼ FIG. 4.
Ballistic transport through InSb nanocross. a , G vs. V G1 and B for V bg = 10 V. Corresponding line-cuts areshown in b , showing the development of quantized steps at e /h . c , As a , but measured vs. V bg for B = 6 T. The positions ofthe line traces in d are shown with the corresponding colors with a offset of 0.5V. e , G vs. V G1 and V G2 characterizing theserial connection through the two constrictions at B = 6 T and V bg = 10 V. Line traces in f are indicated by colors, and arrowsin e and f indicate corresponding positions along the line cuts. For clarity, red/green traces in f are horizontally off set withrespect to blue/orange. cm / (Vs). This rough estimation disregards field focus-ing by the cross geometry and screening from electrodesand top-gates, but the value is comparable to the valuesreported for individual InSb NWs [35].Turning now to the gate control and capacitive cross-coupling of individual arms of the NC, we fix V bg = 10 V,and Fig. 3 c shows the three simultaneously measuredconductances G , G , G (columns) vs. different pairsof top gates. The non-swept gates were kept at 2V, thuskeeping the corresponding terminal open; the configura-tion for each panel is indicated by the icons. All top gatesshow a consistent threshold at ∼ V G (vertical axis) mod-ulate the connection between T2 and T3 (panel I) andbetween T1-T2 (panel III), while G is unaffected (panelII). Also, for panels I, V, IX on the diagonal, which show G nm as a function of V Gn and V Gm , finite conductance is only obtained when both gates are at positive poten-tial. Cross-coupling due to the geometric proximity dis-torts conductance features from horizontal/vertical andthe largest effect is observed between V G1 and V G2 inpanel IX exhibiting a ∼
12% cross-coupling. The mainresult of Fig. 3 is thus to establish the possibility for in-dividually controlling the legs of the NC.Although the gates act locally on the terminals of thecross and transport is coherent at low temperature, themeasurements in Fig. 3 c do not show clear quantized con-ductance presumably due to quantum interference andscattering dominating the transport. Previous studies ofsingle nanowires [36] and globally gated NCs [31] havefound that a magnetic field can suppress scattering andenhance the signatures of ballistic transport. Figures4 a,b show G vs. perpendicular magnetic field B and V G2 with V G1 = V G3 = 2 V (T1 and T3 fully open). V G2 thus control the main barrier for transport and for B (cid:38) G ( V G2 ) increases in discrete steps of e /h , the FIG. 5.
In situ shadow epitaxy for hybrid semiconductor/superconductor nanocrosses a , Schematic cross sectionof the trench substrate with a suspended bridge before growth. The growth direction of the two nanowires are indicated bydashed arrows. b , Tilted scanning electron micrograph of the substrate before growth. The SiO x section is colored blue and Aucatalyst particles beneath the bridge are seen as white dots. c , SEM image of the nanocross growth below the shadow bridge.Substantial overgrowth is observed both on the SiO x mask and in the trench. During In situ hybridization, Al deposition isaligned in a way that the bridge shadows the middle of the nanocross. Scale bars in ( b ) and ( c ) are 1 µ m. conductance of single, spin-split one-dimensional chan-nels below the gate. This is further emphasized by theline-traces in Fig. 4 b .To study further the properties of the local barrier onthe NC, Fig. 4 c shows G vs. V G2 and V bg for B = 6T.See Supporting Information S7( d,e ) for the remaininggate combinations. In all cases, regions of quantizedconductance are clearly observed confirming the ballistic1D nature of the gate-defined constrictions of the NCterminals. Two distinct transitions are distinguishable;one nearly independent of V bg (arrow in panel (c)), andothers which are modulated by both V bg and V G . Weattribute these to spatially separated transport pathsboth acting as quantum point contacts; one locatedclose to the top gate and thus unaffected by V bg and theother closer to the bottom of the semiconductor terminaland thus affected by both gates. Figure 4 d showsextracted traces at the positions in Fig. 4 c indicated byarrows, highlighting the flatness of the plateaus and theeffective doubling of the step height when simultaneouslycrossing transitions from both families (blue curve).Understanding of such complexity in the effectivedevice geometry, observed even when back-scatteringis suppressed by the magnetic field is important forinterpreting and utilizing nanowire networks for complexquantum devices. Further insight of individual pathscould potentially be gained through detailed analysis ofthe properties at finite bias or utilizing additional localgates, however, these are beyond the scope of this study.The observation of quantized conductance shows thattransport is ballistic at a length scale of the effective constriction induced by the top gates. Compared toprevious studies, the possibility of introducing ballisticpoint contacts at the individual terminals allows furtherinsight into the transport specifically through thecrossing region. For two ballistic constrictions in series(QPC1 and QPC2), a fully diffusive transport in theintermediate NC will result in an ohmic addition to thetotal conductance G t = G QPC1 G QPC2 / ( G QPC1 + G QPC2 )while, in the case of a fully ballistic intermediate trans-port, G t = min( G QPC1 , G
QPC2 ). To this end Fig. 4 e shows a measurement at B = 6 T and V bg = 10 V of G vs. V G1 and V G2 while keeping T3 and T4 in pinch-off( V G3 = V G4 = − f , extracted at V G2 ∼ .
75. In this case,T2 is fully open, and the total conductance increasesstep wise upon gradually opening T1. The green traceshows a similar situation except T2 is now maintainedat the first plateau. Interestingly, upon opening up T1,the conductance first shows a plateau at ∼ / × e / V G1 ,the conductance increases to e / f ). Thus, transportbetween the two constrictions, i.e. through the mergedNWs, appears ballistic except close to pinch off. Thecorresponding results from the other combinations ofterminals are presented in Supporting Information S8consistent with this scenario. A plausible scenario isthat the first modes are located closer to the surface andthus subject to stronger scattering than at higher den-sities, where transport occur through the bulk of the NC. In situ
Shadow Patterning of Nanocrosses . Thescattering in the junction, the need for high magneticfields to observe quantized conductance of the constric-tions, and the absence of proximity induced superconduc-tivity from the evaporated Al leads, may be traced backto disorder related to the device processing. Replacingevaporation and post processing with growth of epitaxialsuperconductors is a well established method for avoid-ing disorder-related degradation of device performance[8]. However the fragility of InSb is a challenge for de-vices based on InSb/Al epitaxial hybrids as all knownetchings of Al also severely damages the InSb semicon-ductor and degrade device performance. Recently, in situ “shadow” approaches [18, 21–24] have been developedallowing patterning of epitaxial superconductor growth,yielding reproducible transport characteristics and ob-servations of ballistic transport at B = 0 T for singlenanowires. These in situ shadow concepts, developedfor single NWs, are however, incompatible with the NCgeometry, where controlled shadows of the central junc-tion region is required for most applications. Figure 5demonstrates a new adaptation of the approach in Ref.[23] to accommodate the NC geometry. The substrateswere prepared with SiO x shadow structures suspendedover the trenches. The design features four 1 µ m widestrips bridging each trench. These support a 150 nmwide cross-bar suspended along the middle of the trench.The cross-bar act as a shadow-structure for the junctionof NC grown to have their merging point below the sub-strate surface plane. Figure 5 a shows a schematic sideview of the substrate and panel b shows a SEM micro-graph of the substrate before the growth (see Methodsfor details). Figure 5 c shows an example of a InSb NCgrown below the cross-bar. Substantial overgrowth onthe SiO x mask is also observed in this case, effectivelywidening the shadow bridge, and further optimization ofgrowth parameters and/or bridge design is needed. Theresults, however, demonstrate the feasibility of this ap-proach, and we expect that the electrical performance ofthe shadow crosses will increase similarly to the resultsreported for conventional nanowire devices fabricated by in situ shadow techniques [22, 23]. CONCLUSION
In conclusion, we have presented a detailed study ofMBE grown InSb NCs. From the time-dependence ofaxial and radial growth of InSb NWs, we determined thecombination of geometric and growth parameters optimal for NC growth featuring a coherent crystal structures.InSb NC devices were fabricated with individual electro-static control of all terminals, each showing clear quan-tized conductance at low temperature and high magneticfields. Analyzing the combined action of two point con-tacts connected in series through the cross, showed thatinter-wire transport in the NC is quasi-ballistic exceptclose to pinch-off, where signatures of diffusive trans-port occurs. Finally, we developed and demonstrateda shadow-technique allowing epitaxial growth of hybridsemiconductor/superconductor NCs with in situ shadowjunctions aligned to the NC intersection point. The ap-proach can be applied for any choice semiconductor andsuperconductor, but is demonstrated here for InSb/Alhybrid crosses. The technique is expected to dramat-ically reduce disorder-related scattering and thus be animportant step towards clean quantum transport in com-plex multi-terminal nanowire devices.
METHODS
Substrate Fabrication and Nanocross Growth.
InAs (100) 2-inch wafers are used for substrate fabrica-tion. (111)B trenches are created on the substrate usingH SO and H O solution based wet-etching process, asdiscussed in [22]. Later, electron beam lithography isused for defining the position of the Au seed particleson the (111)B trenches with an offset for forming NCs.Post-exposure development is done using standard 1:3MIBK: IPA solution. Electron beam evaporator with arate of 1 ˚A/s is used for depositing Au thin layer. Subse-quently, lift-off is performed using acetone dipping. Next,cleaning is done with 2 min of sonication with acetone,rinsing with IPA and milli-q water. Finally, 2 min oxygenplasma treatment is conducted to avoid resist residues onthe substrate.InSb NCs are grown using Veeco GEN II MBE sys-tem. Initially, substrate is annealed at 590 ◦ C with ar-senic over-pressure. Subsequently, InAs stem is growntypically for 12 min (prior to NC segment), where As/Influx ratio is maintained 9.78, resulting the length of thestems are ∼ µ m. Depending on the substrategeometry the growth time (length) of InAs stem is var-ied. Next, the As flux is terminated and Sb flux is in-troduced in the system maintaining continuous In flux.Consequently, InSb segments are grown on top of thestems using Sb/In flux ratio ∼ ∼ ◦ C (settemperature).For hybridization of the NCs, Al deposition is per-formed in situ in the MBE growth chamber. After theNC growth, the substrate is cooled down to ∼ − ◦ C.Usually, 8-10 hours is the waiting period before the tem-perature is reached and growth chamber is ready for Aldeposition. Low temperature limits the adatom diffusionlength and thermodynamically drives to form continu-ous Al thin film on InSb NW. Upon the temperatureis reached, the deposition angle is adjusted with the Alsource, which confirms the shadow region in the middleof the NC. Before unloading, 15 min of oxidization is per-formed to create AlO x passivation layer and avoid the Aldewetting issue in the elevated temperature. Structural Characterization.
The morphology ofthe NCs are characterized by SEM. Crystal structuresand intersection of the NCs are characterized by TEMand HR-TEM of FEI Tecnai T20 G2 (200 kV of accel-eration voltage, Thermionic LaB6/CeB6 e-beam source,point resolution of 0.24 nm, line resolution of 0.14 nm,and STEM resolution of 1.0 nm).
Electrical Measurements.
The electrical setup isshown in Fig. 3(a). Terminals 1 and 2 are ac voltagebiased with two incommensurable frequencies (indicatedby blue and red colors), and both resulting ac currentsare measured using lock-in detection at terminal 3 yield-ing G = dI /dV and G = dI /dV , where V and V are the local voltage drops measured separatelywith lock-in detection at the respective frequencies. Thebias at T f thus yielding G = dI /dV . Fabrication of Shadow Bridges.
Shadow bridgeswere fabricated along the lines of Ref. [23]: 150 nm ofSiO x were deposited by plasma enhanced chemical va-por deposition (PECVD) on InAs (100) substrates andpatterned by EBL and HF etching into the pattern ofbridges supporting the cross-bar for shadowing. Subse-quently, the InAs trenches were etched using a separateEBL step and the same wet etchant as discussed before.Catalyst particles were defined by EBL on the facets asshown in Fig. 1. Careful alignment is required to ensurea NC junction forming directly below the shadow bar. SUPPORTING INFORMATION
The Supporting Information is available at: https://sid.erda.dk/share_redirect/B9S92R2aTL
AUTHOR CONTRIBUTION
S.A.K, J-H.K. performed the MBE growth, materialanalysis and optimization supervised by P.K.; L.S, T.M.performed electrical measurements, analyzed the results,and developed the shadow concept supervised by T.S.J.;S.A.K, L.S. and T.S.J. wrote the manuscript with inputfrom all authors.
ACKNOWLEDGEMENT
S.A.K, J-H.K. and P.K. was funded by EuropeanUnion Horizon 2020 research and innovation programunder the Marie Sk(cid:32)lodowska-Curie Grant No. 722176(INDEED), Microsoft Quantum and the European Re-search Council (ERC) under Grant No. 716655 (HEMs-DAM). T.S.J was supported by research grants from Vil-lum Fonden (00013157), The Danish Council for Inde-pendent Research (7014-00132), and European ResearchCouncil (866158). Authors thank to C. B. Sørensen forthe maintenance of the MBE system. ∗ [email protected][1] C. Thelander, P. Agarwal, S. Brongersma, J. Eymery,L. F. Feiner, A. Forchel, M. Scheffler, W. Riess, B. J.Ohlsson, U. Goesele, and L. Samuelson, Mater. Today , 28 (2006).[2] Y. Doh, J. van Dam, A. Roest, E. Bakkers, L. Kouwen-hoven, and S. De Franceschi, Science , 272 (2005).[3] S. Nadj-Perge, S. M. Frolov, E. P. A. M. Bakkers, andL. P. Kouwenhoven, Nature , 1084 (2010).[4] L. Hofstetter, S. Csonka, J. Nygard, and C. Schoenen-berger, Nature , 960 (2009).[5] Y. Oreg, G. 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