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Arthur W. Barnard, Alex Hughes, Aaron L. Sharpe, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), David Goldhaber-Gordon

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[Absorptive pinhole collimators for ballistic Dirac fermions in graphene](https://mdr.nims.go.jp/datasets/ccc00cd1-7448-4c4f-b2f2-26e51ba21fca)

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Absorptive pinhole collimators for ballistic Dirac fermions in grapheneARTICLEReceived 27 Jan 2017 | Accepted 28 Mar 2017 | Published 15 May 2017Absorptive pinhole collimators for ballistic Diracfermions in grapheneArthur W. Barnard1, Alex Hughes1, Aaron L. Sharpe2, Kenji Watanabe3, Takashi Taniguchi3& David Goldhaber-Gordon1Ballistic electrons in solids can have mean free paths far larger than the smallest featurespatterned by lithography. This has allowed development and study of solid-state electron-optical devices such as beam splitters and quantum point contacts, which have informed ourunderstanding of electron flow and interactions. Recently, high-mobility graphene hasemerged as an ideal two-dimensional semimetal that hosts unique chiral electron-opticaleffects due to its honeycomb crystalline lattice. However, this chiral transport prevents thesimple use of electrostatic gates to define electron-optical devices in graphene. Here wepresent a method of creating highly collimated electron beams in graphene based on collinearpairs of slits, with absorptive sidewalls between the slits. By this method, we achieve beamswith angular width 18� or narrower, and transmission matching classical ballistic predictions.DOI: 10.1038/ncomms15418 OPEN1 Department of Physics, Stanford University, Stanford, California 94305, USA. 2 Department of Applied Physics, Stanford University, Stanford, California94305, USA. 3 National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. Correspondence and requests for materials should beaddressed to A.W.B. (email: barnarda@stanford.edu) or to D.G.-G. (email: goldhaber-gordon@stanford.edu).NATURE COMMUNICATIONS | 8:15418 | DOI: 10.1038/ncomms15418 | www.nature.com/naturecommunications 1mailto:barnarda@stanford.edumailto:goldhaber-gordon@stanford.eduhttp://www.nature.com/naturecommunicationsIn the absence of scattering, electrons propagate freely ascoherent waves, analogous to light in free space. Capitalizingon this behaviour, electron-optical elements including beamsplitters1,2, quantum point contacts3,4, lenses5, wave guides6,7 andmirrors8 have been fashioned in solid-state two-dimensionalelectron systems9 (2DESs). The 2DES in graphene hosts chiralelectrons10–14, with unique refractive properties and associatednovel opportunities for electron optics12,13,15,16. Until recently,disorder-induced scattering has limited implementation ofthese ideas. Encapsulation of graphene in hexagonal boronnitride (hBN)17,18 now enables striking manifestations ofrefractive ballistic transport15 including quasiparticle dynamicsin superlattices19, snake states20 and Veselago lenses21.A collimated electron source could be the final piece needed tounlock the potential of electron refraction in graphene, enablingdiverse applications such as ballistic transistors22,23, flyingqubits24 and electron interferometers25. In conventionalsemiconductor 2DESs, electrons can be collimated by quantumpoint contacts3 to form narrow beams. In graphene, however,electrons are not readily confined by gates and alternativeproposals26–28 for collimation in graphene have yet to be realized.Here we demonstrate experimentally and validate computa-tionally an electron collimator based on a collinear pair of pinholeslits in hBN-encapsulated graphene. We show that grounded edgecontacts17—analogous to peripheral surfaces painted black in anoptical system—can efficiently remove stray electron trajectoriesthat do not directly traverse the two pinholes, leaving ageometrically defined collimated beams.ResultsCollimator design and function. An absorptive pinhole colli-mator is constructed from an etched graphene heterostructurewith a two-chamber geometry wherein independent electrodesmake ohmic contact to each chamber (Fig. 1a). The contact to thebottom chamber (red, Fig. 1a) serves as the source for chargecarriers, while the contact to the top chamber (black, Fig. 1a) actsas an absorptive filter. To realize a collimating configuration, thefilter contact (F) is grounded and the source contact (S) is currentbiased; charge carriers are isotropically injected from the source,but only those trajectories that pass through both pinhole aper-tures reach the graphene bulk. Applying a uniform magnetic fieldcan steer the collimated beam. For an uncollimated configuration,the filter and source contacts are electrically shorted.Our device consists of hBN-encapsulated graphene etchedinto a Hall-bar-like geometry with the voltage probes replacedby collimating contacts (Fig. 1b). The hBN layers are bothdBNB80 nm thick and the device is assembled on dox¼ 300 nmSiO2 atop a degenerately doped silicon substrate used as a backgate to tune charge carrier density n. To test the collimationbehaviour of an individual injector in the ballistic regime, weperform a non-local magnetotransport measurement, injectingfrom one collimator and probing trajectories that reach acrossthe width of the device (Wdev¼ 2 mm) in the collimated anduncollimated configurations (green and blue respectively, Fig. 1c).We inject from the lower right collimator (labelled S4,F4)throughout this Article and, in this case, measure the voltage ofthe upper right collimator (labelled S3,F3) relative to a reference(F1). In the presence of a B-field, electron trajectories that passfrom the injector to collector flow from the injector at an angley ¼ sin� 1qBWdev2‘ffiffiffiffinpp , where q is the quasiparticle charge. From this,we find that the angular full width at half maximum (FWHM) is70� when injecting in the uncollimated configuration and 18�when injecting in the collimated configuration.For an uncollimated source3, the angular conductance isexpected to go as G yð Þ ¼ 2e2hffiffinppw0cos yð Þ, where 2e2hffiffinppis the fluxdensity at the Fermi level and w0 cos(y) is the projected width ofthe contact. The collector has an acceptance angle of w0WdevcosðyÞ,leading to an expected cos2(y) distribution (yFWHM¼ 90�).The 70� FWHM for our uncollimated data is in reasonableagreement with this expectation given that the reference contactcollects more electrons at higher B-fields and thus suppresses thesignal at high angles.In our collimators, the flux density at the Fermi level isidentical to that in a single slit, but the projected width isgeometrically defined by the pinhole width w0 and pinholeseparation L0. For small angles |y|otan� 1w0/L0, the projectedwidth w(y)¼ cos(y)[w0� L0|tan(y)|] (left, Fig. 1d). At largerangles, no carriers should transmit, yielding:G yð Þ ¼ 2e2hffiffiffinprcos yð Þ w0� L0 tanðyÞj j½ �; yj jotan� 1 w0L0: ð1ÞConvolving over the acceptance angle of the collector (seeSupplementary Note 1 for details), we calculate the angularconductance distribution (middle, Fig. 1d) for both theuncollimated case (blue) and the collimated case (green) withw0¼ 300 nm and L0¼ 850 nm, consistent with the fabricatedcollimator dimensions. The FWHM of the collimator emission is22� for theory and 18� for experiment (right, Fig. 1d), showingthat our injectors efficiently filter wide-angle trajectories andtransmit narrowly collimated beams.Conductance of collimators. Having established that the angulardistribution of injected charge carriers is well described byclassical ballistic theory, we now measure our collimators’conductance to determine how efficiently electrons traverse thepinholes. For this, we bias the injector in the collimatingconfiguration (F4 grounded) and measure the current reachingall remaining electrodes as a function of gate voltage (Fig. 2a).The conductance of the collimator tunes sublinearly with n:G � ffiffiffiffiffiffiffiffiffiffiffiffiffin� n0p(dotted line, Fig. 2a). This qualitatively agrees withballistic expectations G �ffiffiffinpð Þ: integrating equation (1) over allangles, we expect:G ¼ 4e2hffiffiffiffiffiffiffiffin=pp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiL20þw20q� L0� �: ð2ÞThe small offset n0B1.6� 1011 cm� 2 in our measurementappears to result from diffraction by collimator slits (Fig. 2a, seeSupplementary Notes 3 and 4 for details). Comparingequation (2), with the fit in Fig. 2a assuming ncn0), indicates aconductance that is 35% of expectations. This is a lower boundfor the transmission probability, because the collimating filter(F4) can reabsorb electrons that have diffusely scattered off ofdevice edges.To understand the impact of diffuse scattering and betterestimate the transmission probability, we measure the currentcollected at specific detectors as a function of B-field. Havingsourced Isource ¼ 50 nAo kBTeRsource(see Supplementary Note 6 fordetails), we collect current in detectors collinear with (red andblue, Fig. 2b) and adjacent to (black, Fig. 2b) the injector. Currentcollected at the collinear detector with a wide acceptance angle(red) peaks near B¼ 0, as the collimated beam travels straightacross the device. The apparent background current is B3–5% ofIsource. At BB120 mT, ballistic cyclotron orbits instead reach theadjacent detector, leading to a prominent peak in current detectedat S1 (black) with F1 grounded. Coincident with this peak, thediffuse background of the collinear detector dips, as ballistictrajectories are consumed by the adjacent detector, reducing thenumber of electrons that eventually find their way into thecollinear detector.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms154182 NATURE COMMUNICATIONS | 8:15418 | DOI: 10.1038/ncomms15418 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsIn light of the non-trivial diffuse background, we measurecurrent with a narrow acceptance angle at the collector, rejectingmost scattered electrons and thus better determining thetransmission probability of the collimator. The resulting doublycollimated beam (blue) has a FWHM of 8.5�. Together, all thesecollinear apertures act as a single collimator with L0¼ 3,750 nm(the separation between the farthest-apart apertures). All of theinjected current passes through the first aperture, so the fractional90°60°30°0°−30°−60°−90°W (�)L0W0−100 −50 0 50 100−2002040BMagnetic field (mT)S1S2 S3S4F1F2 F3F4Uncollimated Collimatedcb90°60°30°0°−30°−60°−90°R (Ω)�adFigure 1 | Absorptive pinhole collimators. (a) Double pinhole collimator schematic. Current is sourced from bottom contact (red), passes through thebottom aperture and is either absorbed by the top contact (black) or passes into the device bulk. Only trajectories that pass through both aperturesreach the bulk, producing a collimated beam. The collimated beam is steered by an external B-field. (b) Optical micrograph of device with four collimatorsin a Hall-bar-like geometry. Scale bar, 2 mm. (c) Measuring angular distribution. Non-local resistance at n¼ 1.65� 1012 cm� 2 (Fermi wavelength:lf¼ 27.6 nm) is plotted with VS3F3 measured relative to VF1 when current is sourced from both S4 and F4 (blue), and only from S4, whereas F4 is grounded(green). The narrowness of the central peak for the F4-grounded data results from collimation. (d) Theoretical collimation behaviour versus experiment.Left: diagram of effective collimator width w(y) at a fixed angle for classical ballistic trajectories. Middle: polar plot of theoretical angular dependence for a300 nm-wide point contact (blue) and a w0¼ 300 nm, L0¼850 nm collimator (green). Right: experimental data from c mapped to angle.−0.2 0 0.2 0.4 0.6 0.801234−200 −100 0 100 20000.050.10.15Magnetic field (mT)I/IsourceConductance (e2  h–1)Density (1012 cm−2)a bFigure 2 | Conductance of single and paired collimators. (a) Conductance of collimator measured in a three terminal configuration: S4 is current-biased,F4 is grounded and all remaining terminals are measured with a single current amplifier. The measured conductance (blue) scales asffiffiffiffiffiffiffiffiffiffiffiffiffin� n0p(blackdotted line), qualitatively agreeing with ballistic conduction of bulk graphene. Numerical solutions to the 2D Dirac equation (red dots) account well forlow-density effects associated with diffraction. (b) Conductance measurements through angularly sensitive collectors. Current is collected at F3þ S3 (red),S3 (blue) and S1 (black) with all remaining contacts grounded. F3þ S3 has a broad background due to diffuse edge scattering and imperfect ohmiccontacts. S3 has a FWHM of 8.5� due to double collimation and has minimal diffuse background. The peak height of S3 indicates nearly perfect ballistictransmission.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms15418 ARTICLENATURE COMMUNICATIONS | 8:15418 | DOI: 10.1038/ncomms15418 | www.nature.com/naturecommunications 3http://www.nature.com/naturecommunicationscurrent collected should be G w0¼300 nm; L0¼3;750 nmð ÞGðw0¼300 nm; L0¼0Þ ¼ 0:040. Themaximum of the doubly collimated peak is 0.056 (Fig. 2b).Subtracting a background of 0.005–0.015 (see SupplementaryNote 5 for details) suggests transmission through the full path is1.18±0.12 times the expected value. The 20% beamwidthnarrowing observed above for a single collimator (18� versus22� expected) may indicate modest focusing, which would beconsistent with slightly enhanced transmission through thedouble collimator. The excellent quantitative agreement showsthat charge carriers transmit nearly perfectly from slit to slit. Bydemonstrating not only narrow beams but also high transmissionprobabilities, our measurements show that absorptive pin-holefiltering could produce low-noise, coherent, collimated beams ofelectrons in 2DESs that cannot be depleted by electrostatic gating.Transverse electron focusing. Having experimentally demon-strated that absorptive pinhole collimators can controllably emitelectron beams in hBN-encapsulated graphene heterostructures,we illustrate our technology’s utility by aiming a beam at theedges of our graphene device to learn about the low-energyscattering behaviour of etched edges in these heterostructures. Weperform three simultaneous non-local resistance measurements(Fig. 3a) to probe the specularity of reflections off various edges ofthe device. In Fig. 3b, we map R1 ¼ V1Iinas a function of B-field andelectron density. In both the electron-doped and hole-dopedregimes, a peak near B¼ 0 corresponds to ballistic quasiparticlesbeing collected by the collinear contact in the absence of magneticdeflection. Peaks in R1 also appear at higher fields, primarily inthe hole-doped regime (no0). For reference, we plot contourscorresponding to cyclotron radius r¼W/2. Any features outsidethe parabolas (roW/2) cannot correspond to direct ballisticquasiparticle transport across the width of the device and mustinvolve scattering. These data imply that holes undergo multiplereflections at high B-fields, suggesting that the edges may scattermore specularly when hole-doped than when electron-doped.To directly probe the specularity of reflections in our device,we perform a collimated transverse-electron focusing (TEF)measurement8,29. Probe V3 at the lower left detector is even moresensitive than traditional TEF measurements to scattering thatmodifies ballistic trajectories, as here the injector and detectorhave narrow emission and acceptance angles, respectively.R3 ¼ V3Iinas a function of electron density and B-field has severaldistinct features associated with specific cyclotron radii (Fig. 3c),in particular for hole doping. At r1¼ 1.25 mm, there is a sharppeak with a FWHM of B300 nm in both the hole and electronregimes. Although a conventional TEF peak would occur atr1 ¼ Llat2 , where Llat¼ 2.3 mm is the lateral separation of injectorand detector, our measured peak corresponds to slightly greatercyclotron radius. This is expected for our collimator geometry: weillustrate the expected r1 trajectory in Fig. 3a and plot itscorresponding contour in Fig. 3c, indicating excellent agreementwith our measurement (see also Supplementary Note 2 forcalculation). Trajectories at r1 are insensitive to edge scattering,whereas at smaller r (larger B) additional peaks imply specularreflection. In the electron-doped regime the presence of a−100102030−20020−1 0 1−100102030++V2+V1r = W/2r =2Wr1r1V3−400 −200 0 200 400−2−101201020−200 0 200−2−1012−100102030a bcExperimentSimulationRadius of curvature−1 (μm−1)Magnetic field (mT)R1 (Ω)R2 (Ω)R3 (Ω)R1 (Ω)R3 (Ω)Density (1012 cm−2 )Density (1012 cm−2 )Magnetic field (mT)dFigure 3 | Probing edge scattering. (a) Non-local resistance measurement schematic. (b) Resistance map characterizing angular profile of injectedtrajectories. A central peak near B¼0 corresponds to the beam passing straight across the width of the device (a small angular offset is due to fabricationimperfections). The remainder of the electron-doped regime (n40) is nearly featureless, whereas the hole-doped regime (no0) has several auxiliarypeaks. Dotted lines correspond to cyclotron orbits with radius equal to the half of device width (r¼Wdev/2); features outside the two parabolas cannotcorrespond to direct ballistic trajectories between injector and collector. (c) Collimated transverse electron focusing. A sharp feature at r1¼ 1.25mmcorresponds to trajectories that pass through four pinholes. Features at higher magnetic field must involve specular reflections off of the device edge. Thereis no such feature on the electron side, whereas there is a noticeable band on the hole side. (d) Comparison of experimental data with classical ballisticsimulation. Experimental data (blue) are taken at n¼ 2.7� 1012 cm� 2 and simulation (red) assumes fully diffuse edge scattering and 67% ohmictransmission.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms154184 NATURE COMMUNICATIONS | 8:15418 | DOI: 10.1038/ncomms15418 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsprominent peak at r1 with no appreciable secondary peak suggestscompletely diffuse scattering, whereas in the hole-doped regimethe presence of a significant secondary peak suggests appreciablespecular reflection.To validate this understanding and quantitatively determinethe degree of specularity, we next carry out device-scalesimulations of ballistic trajectories—treating electrons as classicalpoint-like particles is warranted given that the Fermi wavelengthlf is in most cases much smaller than geometric features in ourdevice and given that most trajectories are captured in ohmiccontacts before having a chance to interfere. Modelling thefabricated device geometry including all ohmic contacts, wesimulate electron emission from the injector, allowing forreflection off edges and interaction with floating or groundedohmics. With two free parameters, transmission of ohmics ptransand probability of diffuse edge scattering pdiffuse, we simulatethe measurement configuration shown in Fig. 3a–c (seeSupplementary Note 7 for simulation details). The strikingsimilarities between simulation (ptrans¼ 67% and pscatter¼ 100%)and measurement suggest that edge scattering is diffuse in ourdevice in the electron-doped regime (Fig. 3d, see SupplementaryMovie 1 for visualizing a B-sweep). Similar analysisyields ptrans¼ 10% and pscatter¼ 67% in the hole-doped regime,quantitatively demonstrating significant electron-hole asymmetryin both ohmic contact properties and specularity of edgescattering in our device. This asymmetry may occur due to finiteedge doping that induces smooth electrostatic edge barriers30 inthe p-doped regime.DiscussionThe strong agreement between theory and experiment for bothindividual collimators and our entire collimating device indicatesthat absorptive collimation in high-mobility graphene devices canbe predictably and robustly applied in a variety of geometries,opening the door for scientific and technological use of narrowelectron beams in 2DESs. For example, Klein tunnelling12,13,31and Andreev reflections32 are highly angularly dependentphenomena whose experimental signatures are obscured intypical transport experiments. In such cases, collimation-basedmeasurements will illuminate the physics by quantitatively testingtransmission and reflection at specific angles rather thanintegrated over a range of angles as in past experiments. Inaddition, novel technologies such as ballistic magnetometers maybe built on the sharp magnetotransport features we achieve.Collimated sources are an important addition to the growingtoolbox of electron-optical elements in ballistic graphene devicesthat enable a new class of transport measurements.MethodsSample fabrication. Flakes of graphene (from highly oriented pyrolytic graphite,Momentive Performance Materials ZYA grade) and of hBN (from single crystalsgrown by high-pressure synthesis) were prepared17 by exfoliation (3M Scotch 600Transparent Tape) under ambient conditions (35–60% relative humidity) onn-doped silicon wafers with 90 nm thermal oxide (WRS Materials). Theheterostructure was assembled by a top–down dry pick-up technique19. Thecompleted heterostructure was deposited on a chip of nþþ -doped silicon with300 nm thermal oxide (WRS Materials). Polymer residue from the transfer processwas removed by annealing the sample in a tube furnace for 1 h at 500 �C undercontinuous flow of oxygen (50 s.c.c.m.) and argon (500 s.c.c.m.)33. Device patternswere defined by e-beam lithography and reactive ion etching19. Ohmic contactswere established to the device using electron-beam evaporated Cr/Au electrodes tothe exposed graphene edge17.Measurement. All measurements were performed at 1.6 K in the vapour spaceof a He flow cryostat with a superconducting magnet. Lock-ins (StanfordResearch Systems SR830) at 17.76 Hz were used in all measurements; voltageswere measured with Stanford Research Systems SR 560 voltage preamplifiersand currents were measured with Ithaco 1,211 current preamplifiers. Thecharge density n was calculated from Shubnikov-de-Haas oscillationsnVg¼ 5:51�1010cm�2V�1� �, in good agreement with the expected geometriccapacitance.Data availability. The data sets generated during and/or analysed during thecurrent study are available from the corresponding authors on reasonable request.References1. Oliver, W. D., Kim, J., Liu, R. C. & Yamamoto, Y. Hanbury Brown andTwiss-type experiment with electrons. Science 284, 299–301 (1999).2. Henny, M. et al. The Fermionic Hanbury Brown and Twiss experiment. Science284, 296–298 (1999).3. Molenkamp, L. W. et al. Electron-beam collimation with a quantum pointcontact. Phys. Rev. B 41, 1274–1277 (1990).4. Nakaharai, S., Williams, J. R. & Marcus, C. M. Gate-defined graphene quantumpoint contact in the quantum Hall regime. Phys. Rev. Lett. 107, 036602 (2011).5. Sivan, U., Heiblum, M., Umbach, C. P. & Shtrikman, H. Electrostatic electronlens in the ballistic regime. Phys. Rev. B 41, 7937–7940 (1990).6. Hartmann, R. R., Robinson, N. J. & Portnoi, M. E. Smooth electron waveguidesin graphene. Phys. Rev. B 81, 245431 (2010).7. Williams, J. R., Low, T., Lundstrom, M. S. & Marcus, C. M. 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Nano Lett. 12, 4449–4454 (2012).AcknowledgementsWe thank M. Lee and T. Petach for fruitful discussions. This work was financiallysupported by the Gordon and Betty Moore Foundation through Grant GBMF3429,by a Nano- and Quantum Science and Engineering Postdoctoral Fellowship (A.W.B.),by a Ford Foundation Predoctoral Fellowship (A.L.S.) and a National Science FoundationGraduate Research Fellowship (A.L.S.). K.W. and T.T. acknowledge support from theElemental Strategy Initiative conducted by the MEXT (Japan). T.T. acknowledgessupport from JSPS Grant-in-Aid for Scientific Research under grants 262480621 and25106006. Part of this work was performed at the Stanford Nano Shared Facilities (SNSF)supported by the National Science Foundation under award ECCS-1542152Author contributionsA.W.B., D.G.-G., A.H. and A.L.S. conceived of the measurements. A.L.S. fabricatedthe device. A.W.B., A.H. and A.L.S. performed transport measurements. A.W.B. andA.H. performed numerical simulations. A.W.B. wrote the manuscript with input from allother authors. K.W. and T.T. grew the bulk hBN crystals.Additional 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: Barnard, A. W. et al. Absorptive pinhole collimators for ballisticDirac fermions in graphene. Nat. Commun. 8, 15418 doi: 10.1038/ncomms15418 (2017).Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.This work is licensed under a Creative Commons Attribution 4.0International License. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unless indicated otherwisein the credit line; if the material is not included under the Creative Commons license,users will need to obtain permission from the license holder to reproduce the material.To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/r The Author(s) 2017ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms154186 NATURE COMMUNICATIONS | 8:15418 | DOI: 10.1038/ncomms15418 | www.nature.com/naturecommunicationshttp://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://www.nature.com/naturecommunications title_link Results Collimator design and function Conductance of collimators Figure™1Absorptive pinhole collimators.(a) Double pinhole collimator schematic. Current is sourced from bottom contact (red), passes through the bottom aperture and is either absorbed by the top contact (black) or passes into the device bulk. Only traject Figure™2Conductance of single and paired collimators.(a) Conductance of collimator measured in a three terminal configuration: S4 is current-biased, F4 is grounded and all remaining terminals are measured with a single current amplifier. The measured cond Transverse electron focusing Figure™3Probing edge scattering.(a) Non-local resistance measurement schematic. (b) Resistance map characterizing angular profile of injected trajectories. A central peak near B=0 corresponds to the beam passing straight across the width of the device (a  Discussion Methods Sample fabrication Measurement Data availability OliverW. D.KimJ.LiuR. C.YamamotoY.Hanbury Brown and Twiss-type experiment with electronsScience2842993011999HennyM.The Fermionic Hanbury Brown and Twiss experimentScience2842962981999MolenkampL. W.Electron-beam collimation with a quantum point contactPhys We thank M. Lee and T. Petach for fruitful discussions. This work was financially supported by the Gordon and Betty Moore Foundation through Grant GBMF3429, by™a™Nano- and Quantum Science and Engineering Postdoctoral Fellowship (A.W.B.), by™a™Ford Foundat ACKNOWLEDGEMENTS Author contributions Additional information