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Xi Zhang, Wei Ren, Elliot Bell, Ziyan Zhu, Kan-Ting Tsai, Yujie Luo, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Efthimios Kaxiras, Mitchell Luskin, Ke Wang

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[Gate-tunable Veselago interference in a bipolar graphene microcavity](https://mdr.nims.go.jp/datasets/b4b2a6b1-bc81-4803-96df-63bc0f84bfaa)

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Gate-tunable Veselago interference in a bipolar graphene microcavityArticle https://doi.org/10.1038/s41467-022-34347-wGate-tunable Veselago interference in abipolar graphene microcavityXi Zhang 1,10, Wei Ren1,10, Elliot Bell 1, Ziyan Zhu 2,3, Kan-Ting Tsai 1,Yujie Luo 4,5, Kenji Watanabe 6, Takashi Taniguchi 7, Efthimios Kaxiras2,8,Mitchell Luskin 9 & Ke Wang 1The relativistic charge carriers in monolayer graphene can be manipulated inmanners akin to conventional optics. Klein tunneling and Veselago lensinghave been previously demonstrated in ballistic graphene pn-junction devices,but collimation and focusing efficiency remains relatively low, preventingrealization of advanced quantum devices and controlled quantum inter-ference. Here, we present a graphene microcavity defined by carefully-engineered local strain and electrostatic fields. Electrons are manipulated toform an interference path inside the cavity at zero magnetic field via con-secutive Veselago refractions. The observation of unique Veselago inter-ferencepeaks via transportmeasurement and theirmagneticfielddependenceagrees with the theoretical expectation. We further utilize Veselago inter-ference to demonstrate localization of uncollimated electrons and thusimprovement in collimation efficiency. Ourwork sheds new light on relativisticsingle-particle physics and provide a new device concept toward next-generation quantum devices based on manipulation of ballistic electrontrajectory.The linear dispersion relationship of electrons inmonolayer graphene1,2permits themanipulation of ballistic electron trajectories3–6 in amannerakin to classical optics7–14. It has been demonstrated that an electronpassing through a graphene pn-junction15 can be collimated16,17 throughan angle-dependent Klein tunneling process9,18–20 (analogous to a laser)and can also be refracted by a Veselago lensing process21,22 (analogousto an optical lens) depending on the width and height of the pn-junction barrier. However, in state-of-the-art graphene pn-junctions,there still exist important technical challenges to create a full electronicversion of advanced optical circuits. First, due to the relatively smallpseudo-gap that can be created by an electrostatically-defined pn-junction, the Klein tunneling probability across the junction does notdepend sensitively on the incident angle. In addition to electrons withperpendicular momentum to the junction that flow across it effort-lessly, electrons with a finite incident angle θ relative to the perpendi-cular axis have a non-trivial transmission probability, limiting theresulting collimation efficiency. Moreover, the flatness of the chargeneutrality boundary at which the charge carrier type switches in the pn-junction is highly sensitive to charge inhomogeneity (even in thehighest-quality devices), introducing undesirable astigmatism analo-gous to a deformed lens. These limitations present significant chal-lenges in studying more complex electron-optics processes such ascontrolled quantum interference, and in developing future quantumelectronic devices based on more advanced electron-optical circuits.Received: 12 July 2021Accepted: 20 October 2022Check for updates1School of Physics andAstronomy, University of Minnesota, Minneapolis, MN55455, USA. 2Department of Physics, HarvardUniversity, Cambridge,MA02138,USA. 3Stanford Institute forMaterials and Energy Sciences, SLACNational Accelerator Laboratory,Menlo Park, CA 94025, USA. 4Department of Electrical andComputer Engineering, University ofMinnesota,Minneapolis, MN55455, USA. 5Department ofMechanical Engineering, University ofMinnesota,Minneapolis,MN55455,USA. 6ResearchCenter for FunctionalMaterials, National Institute forMaterials Science, Tsukuba, Ibaraki, Japan. 7International Center forMaterialsNanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki, Japan. 8John A. Paulson School of Engineering and Applied Sciences, HarvardUniversity, Cambridge, MA02138, USA. 9School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA. 10These authors contributed equally:Xi Zhang, Wei Ren. e-mail: kewang@umn.eduNature Communications |         (2022) 13:6711 11234567890():,;1234567890():,;http://orcid.org/0000-0002-5791-4829http://orcid.org/0000-0002-5791-4829http://orcid.org/0000-0002-5791-4829http://orcid.org/0000-0002-5791-4829http://orcid.org/0000-0002-5791-4829http://orcid.org/0000-0003-2148-0990http://orcid.org/0000-0003-2148-0990http://orcid.org/0000-0003-2148-0990http://orcid.org/0000-0003-2148-0990http://orcid.org/0000-0003-2148-0990http://orcid.org/0000-0003-4463-5828http://orcid.org/0000-0003-4463-5828http://orcid.org/0000-0003-4463-5828http://orcid.org/0000-0003-4463-5828http://orcid.org/0000-0003-4463-5828http://orcid.org/0000-0002-9270-2960http://orcid.org/0000-0002-9270-2960http://orcid.org/0000-0002-9270-2960http://orcid.org/0000-0002-9270-2960http://orcid.org/0000-0002-9270-2960http://orcid.org/0000-0001-7902-1282http://orcid.org/0000-0001-7902-1282http://orcid.org/0000-0001-7902-1282http://orcid.org/0000-0001-7902-1282http://orcid.org/0000-0001-7902-1282http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0003-3701-8119http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0002-1467-3105http://orcid.org/0000-0003-1981-199Xhttp://orcid.org/0000-0003-1981-199Xhttp://orcid.org/0000-0003-1981-199Xhttp://orcid.org/0000-0003-1981-199Xhttp://orcid.org/0000-0003-1981-199Xhttp://orcid.org/0000-0002-0895-4445http://orcid.org/0000-0002-0895-4445http://orcid.org/0000-0002-0895-4445http://orcid.org/0000-0002-0895-4445http://orcid.org/0000-0002-0895-4445http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-34347-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-34347-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-34347-w&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-34347-w&domain=pdfmailto:kewang@umn.eduIn this work, we present a novel device architecture of a bipolargraphene microcavity that addresses these challenges with precisestrain and electrostatic engineering. In this new device platform, wedemonstrate novel electro-optics phenomena resulting from inter-ference through consecutive Veselago lensing processes23,24, referredto as “Veselago interference.”We study the electrostatic andmagneticfield dependence using low-temperature transportmeasurements anddemonstrate quantitative agreement to relativistic single-particlephysics. Finally, by utilizing the Veselago interference demonstratedhere, we further localize uncollimated electrons to improve collima-tion efficiency, providing proof-of-concept demonstration of a newcollimation scheme aimed toward future electro-optical devices.Results and discussionSample preparationA piece ofmonolayer graphene (MLG) is encapsulated by two layers ofhexagonal boron nitride (hBN) using the standard dry-transfertechnique25–27. The stack is subsequently transferred on top of twopre-patterned local bottom gates with a ~50 nm lateral gap, and anintentional 8 nm vertical height difference (Fig. 1a). Figure 1b shows anoptical microscope image of the complete device. Atomic-force-microscopy data (Fig. 1c) across the 50 nm gapped region reveals thatthe device remains atomically flat on top of both gates as well as in thegap (see Methods), while lattice distortions are apparent at theboundaries of both gates (see Supplementary Note 2 and 17). Weannealed the device at 350 °C for 5min, so the strain is fully relaxed forthe device region (cavity) in between the two barriers. The bandstructure of the graphene in and out of cavity remains pristine withlinear dispersion relationship, expect for the barrier itself. This is anexperimental design so that Klein tunneling and Veselago physicsremain. The strain-induced band gap28,29 effectively defines two tunnelbarriers. A smooth strain over 8 nm is apparent in the AFM topo-graphy, resulting in an effective Klein barrier of net resistance 0.155 kΩ(see Supplementary Note 14), similar to that of previously-reportedelectrostatically-defined Klein barriers9. While the Klein-tunnelingangle dependence allows rough collimation of injected current, elec-trons with finite-incident angle can tunnel through the strain-definedbarrier with low injection rate, making the regions in between twobarriers an electronic analogy of an optical cavity.Observation of Veselago interferenceFor large (zero) incident angles, each strain-induced barrier providesnear-perfect reflection (transmission) as expected from Klein tunnel-ing angle dependence. For carriers with small but finite incident angleθ, these two tunnel barriers effectively define amicrocavity inbetween,where the injection rate to and loss rate from the cavity are equally low.The confinement of carriers with small incident angles is a meticulousexperimental design to isolate, study, andmanipulate those carriers ofinterest, allowing an interference loop to form via two consecutiveVeselago refractions inside the cavity. In terms of application, thesecarriers are primarily responsible for the relatively low collimationefficiency previously reported. Further suppression of their contribu-tion to electrical transport could be the key to improve collimationefficiency for future electron-optics devices.The two local bottom gates, when biased at opposite voltages (ofequal magnitude), electrostatically define a pn-junction symmetricagainst the charge neutrality boundary in the center of the cavity. Theresulting carrier density distribution and the ballistic trajectory ofcarriers inside the cavity are shown in the color diagram of Fig. 1a, witha lower-bound estimation of electron mobility of ~90,000 cm2 V−1 s−1(see Supplementary Note 3). After being injected into the cavity with asmall incident angle (and probability p << 1), each carrier inside thecavity first undergoes Veselago refraction as the carrier type changesin themiddle of the device, gets reflected from the cavity boundary onthe opposite side (with probability 1 − p ~ 1), then undergoes a secondVeselago refraction that ultimately brings the carrier back to its ori-ginal position. At zero magnetic field, the charge interferes with itself.This results in an increase in measured resistance similar to weaka bd0R (kΩ)3.5n 2(1011 cm-2)10-10-10 0 10n1 (1011 cm-2)height (nm)xy 120(nm)50 nm10-25 25c0length (nm)5 µmFig. 1 | Strain-defined and gate-tunable micro-cavity. a (Bottom) hBN-encapsulated monolayer graphene transferred on top of a pair of atomically flatlocal bottom gates of different heights. (Top) The color plot maps the carrierdensity distribution in the device. Two narrow depletion regions form along theboundaries of the gates, where smooth latticedistortions happen. (Arrows) Ballistictrajectories of Veselago interferenceat |n1| = |n2|.bOptical imageof a typical device.c AFM topography across the cavity. The 8 nm height difference and the smoothbending near the gate boundaries are visible. d The measured resistance as afunction of the electron densities on Gate 1 (n1) and Gate 2 (n2), where resistancepeaks are observed exclusively when n1 and n2 have opposite signs.Article https://doi.org/10.1038/s41467-022-34347-wNature Communications |         (2022) 13:6711 2localization (Fig. 1d), but with twomajor differences. First, the effect isnotweak, as all electrons trapped in the cavity form interference loops,independent of the specific incident angle. Thus, the cavity is alsoefficient in localizing all uncollimated electrons. Second, the effect canbe turned on or off resonance by tuning inference paths with elec-trostatics, without the need for a magnetic field to suppress weaklocalization.Figure 1d shows the measured resistance as a function of thedensities of the two adjacent bottom gate regions, with n1 and n2corresponding to the carrier density in the Gate 1 and Gate 2 regions,respectively. Resistancepeak traces are observedonlywhen the carrierdensities in two regions are of opposite charge (when a pn-junction isformed within the cavity), ruling out the possibility for them to arisefromdisorder. Eachdata point on the interference peak, is contributedby a collection of Veselago interference loops with different individualincident angles and spatial phases, and lack overall coherence (seeSupplementary Note 12). Absence of Fabry-Pérot interference (or lackof oscillatory dependence on carrier density) is expected and experi-mentally cross-checked (see Supplementary Note 13).Figure 2a–c shows the measured 4-probe resistance of three dif-ferent microcavities in the regime as a function of the carrier densityabove Gate 1 and Gate 2. Resistance peaks are visible near |n1| =|n2| (red diamond), |n1| = 4|n2| (green square), 4|n1| = |n2| (blue circle). At|n1/n2| = 1/l2 or l2 for integers l, a charge carrier can undergo twoVeselago refractions and l−1 reflections at the charge neutralityboundary (Fig. 2d–h), forming a closed-loop trajectory back to itsoriginal position (see Supplementary Note 6 and 8) interfering withitself at the first cavity wall where it was originally injected. When thecharge eventually leaves the cavity, the Veselago interference results ina higher chance of the electron escaping via the first cavity wall(reflected back to the source, and does not contribute to the current tothe drain) than the opposite cavity wall (toward the drain, contributingto an uncollimated current to drain). In Fig. 2d, the bold arrow marksthe main inference loop of the first-order interference peak as a con-sequence of two consecutive Veselago refractions. The faded linemarks the trajectory of a smaller portion of carriers that are reflected(instead of refracted) at the pn-junction boundary in the center of thecavity, eventually contributing to the same resistance peak via twoconsecutive Veselago refractions, to the side of the main loop (seeSupplementary Note 10). Similarly, a closed interference loop (bold)can be formed at |n1| = 4 |n2| and 4 |n1| = |n2|, via a sequence of tworefractions (at charge neutrality line close to the cavity boundary withlower doping) and three reflections, leading to the second-orderVeselago interference peaks (see Supplementary Note 6 and 8). TheVeselago interferences are reproduced inmultiple devices (Fig. 2), withslight variations of microscopic details from realistic device specificsand inhomogeneity (see Supplementary Note 4, 7 and 9).Magnetic field, bias and temperature dependenceTo further confirm the nature of Veselago interference, we measurethe 4-probe resistance of the cavity under an out-of-plane externalmagnetic field. The magnetic field dependence shows gradual broad-ening and suppression of observed Vesalago interference peak(Fig. 3b–d), qualitatively agreeing with the expectation and simulatedcarrier trajectory (Fig. 3a and Supplementary Note 15), and are repro-duced in multiple devices (see Supplementary Note 5) with realisticdevice variations in quantitative details. With a small magnetic field,the Lorentz force distorts the shape of interference loop for carriersthat manage to reach the boundary at small incident angle (Fig. 3a).The reflection (refraction) of carriers at the pn-junction boundary isconsequently enhanced (suppressed), reducing the probability offorming a close Veselago interference loop (see SupplementaryNote 15). Figure 3e shows the measured resistance as a function ofmagnetic field and carrier density around the peak position at |n1| =|n2| = 7 × 1011 cm−2, where Δn =0 corresponds to the resonant condi-tion. The width of the interference peak monotonically increases withmagnetic field until it completely disappears. Due to the symmetry ofthe interference loop at |n1| = |n2| , no bias dependence is observed forthe first-order peak (Fig. 3f). No significant temperature dependence isobserved from T = 4K ~ 12 K, as the specifics of the interference loopare expected to be insensitive to thermal excitations (Fig. 3g) (seeSupplementary Note 12).Improving collimation via Veselago interferenceThe angle dependence of the Klein tunneling probability has beenutilized to collimate electron flow in ballistic graphene devices9,18.However, carriers with small-incident angle can still pass through aseries of Klein barriers with a non-negligible probability. This has beena b cDevice 2 ΔR(kΩ)n 2(1011 cm-2)2.50.5n1 (1011 cm-2)2160-15d|n1|= |n2| |n1|= 4|n2| 4|n1|= |n2|e fDevice 3 ΔR(kΩ)0.54n 2(1011 cm-2)n1 (1011 cm-2) 0012-12Device 1n 2(1011 cm-2)ΔR(kΩ)n1 (1011 cm-2)0.52.50-12214Fig. 2 | Veselago interference and localization. a–cMeasured 4-probe resistanceof cavity as a function of n1 and n2 in three devices. Resistance peaks are visible at|n1| = |n2| (red), |n1| = 4|n2| (green), 4|n1| = |n2| (blue) and 9|n1| = |n2| (purple), dWhen|n1| = |n2|, a symmetric pn-junction is defined in the cavity. Carriers injected into thecavity (with a low probability p and a small incident angle) undergo Veselagorefraction, followed by reflection at the oppositive cavity boundary, then a secondVeselago refraction to the original position. At B =0, the process localizes carriersand gives rise to measured resistance peaks. e, f Similarly, a closed interferenceloop (bold) can be formed via a sequenceof two refractions and three reflections at|n1| = 4|n2| and 4|n1| = |n2|, leading to a second-order Veselago interference peak.Article https://doi.org/10.1038/s41467-022-34347-wNature Communications |         (2022) 13:6711 3a major challenge for further improving collimation efficiency foradvanced electron optics. Here, we show that Veselago interferencecan be used to further collimate carriers, particularly those with smallincident angle. Figure 4a shows the device diagram for characterizingthe collimation efficiency of Veselago interference. Source (drain)contacts are intentionally placed at the bottom right (left) corners ofgraphene on top of Gate 2 (1). Two 1µm-wide voltage probes are placedat the top and bottom edges of the graphene on top of Gate 1. Carriersare injected from the source contact and collimated by the cavity wall,allowing only a small portion of carriers with small incident angle toenter the cavity. When |n1 | < |n2|, the uncollimated carriers that escapethe cavity predominantly reach voltage probe B, resulting in a trans-verse voltage proportional to the current density from uncollimatedcharge carriers (Fig. 4b). At 4|n1| = |n2|, Veselago interference furtherlocalizes uncollimated carriers in the cavity (Fig. 4b), resulting in anear-zero measured transverse voltage amongst a high resistancebackground where Veselago interference is off-resonance, demon-strating its efficiency in further collimating small-incident-angle car-riers that would otherwise manage to get across the cavity. The sharpdrop in the transverse voltage at (and only at) the 4|n1| = |n2| (Fig. 4d)demonstrates the added collimation effect from the 2nd order Vese-lago interference, compared to general |n1| < |n2| cases when Veselagointerference and its collimation effect are absent. For the other twointerferencepeaks at |n1| = 4|n2| and |n1| = |n2|, the collimationefficiencyis not characterized by the transverse voltage (Fig. 4c), as the ballisticcarriers (collimated or not) will reach and be diffusively scattered fromthe physical edges of the device before reaching either voltage probe(see Supplementary Note 11).A weak bias dependence (Fig. 4e) is observed for the zerotransverse-resistance dip, as expected from the bias dependence ofsecond-order peaks at |n1| = 4|n2| (see Supplementary Note 9). As aperpendicular magnetic field is applied beyond B =0.3 T, the trans-verse voltage increases both due to the destruction of Veselagointerference as well as the curved trajectory of carriers after passingthrough the cavity (Fig. 4f). No significant temperature dependence isrecorded from T = 4K ~ 12 K (Fig. 4g), also consistent with our previousobservations.In conclusion, we have developed a novel device architecture for amicrocavity in monolayer graphene with strain and electrostatic-fieldengineering. We report a new electro-optics phenomenon: Veselagointerference as a result of electron localization after two consecutiveVeselago refractions in the cavity. The observed low-temperaturemagneto-transport signature agrees quantitatively with Veselago phy-sics and provides further experimental evidence and insights intorelativistic single-particle dynamics. Finally, the electrons that partici-pate in Veselago interference in the cavity are thosewith small-incident-angle momenta, the exact same electrons primarily responsible for therelatively low collimation efficiency in previously studied pn-junctionKlein collimators. By characterizing the collimation efficiency withtransverse voltage probes, we provide proof-of-principle demonstra-tion that Veselago interference helps to further localize these uncolli-mated electrons and thus improves the collimation of current throughthe cavity. Our work provides an important new technical and con-ceptual component toward advanced electron-optic circuits based onthe precise manipulation of ballistic electron trajectories.MethodsGate fabricationTo form a strong strain at the boundary of the pn junction, the gateresponsible for the p- and n-doped regions topographically differs inheight. To achieve this, two main methods are implemented for thedevices studied in this work. The first method (Device 3) employs twoseparate metal gates, each fabricated with a round of electron-beamlithography and evaporation (of different thickness), or alternativelyone electron-beam lithography round while evaporating with a delib-erate tilt of thewafer. In the secondmethod (Devices 1 and 2), one gateis ametal bottomgate and theother is a siliconback gate (shown in Fig.S1). For each method, Cr/Pd-Au alloy (1 nm/varying thickness or 1 nm/7 nm) is deposited. The Pd-Au alloy (40% Pd/60% Au) is chosen toreduce surface roughness compared to conventional Au deposition.After liftoff, the gates are annealed in a high-vacuum environment at350 °C for 5minutes to remove resist residue and ensure atomically-flat topography.Device fabricationWe sequentially pick up hBN, graphene, and hBN flakes using poly-propylene carbonate (PPC) and polydimethylsiloxane (PDMS) stampsvia the standard dry transfer technique. The hBN-encapsulated110n 2(1011cm -2)0-9 n1 (1011 cm -2)R(k)0.52.5B = 0.5 T110n 2(1011cm -2)0-9 n1 (1011 cm -2)B = 0.3 TR(k)0.52.5c da eB(T)n (1011 cm -2)00.5R (k )0.8 1.1-2 20n (1011 cm -2)T (K)R (k )0.8 1.1-2 2g1240fn (1011 cm -2)I DC(nA)R (k )0.8 1.1-500500-2 20110n 2(1011cm -2)0-9 n1 (1011 cm -2)B = 0.1 TR(k)0.52.5b0.1 T0.3 T0.5 TFig. 3 | Dependence onmagneticfield, bias and temperature. a Simulated typicalcarrier trajectories under various small magnetic fields. b, c Veselago interferencepeaks gradually broadens with increasing magnetic field and d is eventually sup-pressedwhenmajority of the carriers fail to form the interference loop. eMeasuredresistance as a function of magnetic field shows the gradual broadening. f No biasdependence is observed for the first-order peak at |n1| = |n2| due to the symmetry ofthe interference loop. g No significant temperature dependence is observed fromT = 4K ~ 12 K.Article https://doi.org/10.1038/s41467-022-34347-wNature Communications |         (2022) 13:6711 4monolayer graphene stack is transferred on top of the prepatternedbottom gates. The sample is rinsed in acetone and IPA and annealedagain in a high-vacuum environment at 350 °C for 5minutes. Thedevice regions on top of both gates as well as in the gap are atomicallyflat and strain-free after annealing, while lattice distortions are onlyintroduced at the boundaries of two bottom gates. Electrical contactsto gates and ohmic contacts to 1D boundaries of the graphene stackare made by electron-beam lithography, dry-etching and subsequentmetal deposition (Cr/Pd/Au, 1 nm/5 nm/140nm). A final round of dry-etching with an electron-beam lithography etch mask defines the lat-eral geometry of the devices.Data availabilityThe data generated in this study have been deposited in the GitHubpublic repository without accession code: X1Zhang123/Source-Data-Gate-tunable-Veselago-Interference-in-a-Bipolar-Graphene-Microcavity-(github.com).Code availabilityRelevant code of carrier trajectory simulations are provided with thispaper and can be found at X1Zhang123/Source-Data-Gate-tunable-Veselago-Interference-in-a-Bipolar-Graphene-Microcavity- (github.-com).All other code are available from the corresponding author uponreasonable request.References1. Geim, A. K. Graphene: status and prospects. Science 324,1530–1534 (2009).2. Crossno, J. et al. Observation of the Dirac fluid and the breakdownof the Wiedemann-Franz law in graphene. Science 351, 1058–1061(2016).3. Zhang, L. M. & Fogler, M. M. Nonlinear screening and ballistictransport in a graphene p−n Junction. Phys. Rev. Lett. 100,116804 (2008).4. Rickhaus, P., Makk, P., Richter, K. & Schönenberger, C. Gate tune-able beamsplitter in ballistic graphene. Appl. Phys. Lett. 107,251901 (2015).5. Liu, M.-H., Gorini, C. & Richter, K. Creating and steering highlydirectional electron beams in graphene. Phys. Rev. Lett. 6,066801 (2017).6. Sivan, U., Heiblum, M., Umbach, C. P. & Shtrikman, H. Electrostaticelectron lens in the ballistic regime. Phys. Rev. B 41,7937–7940 (1990).7. Chen, S. et al. Electron optics with p-n junctions in ballistic gra-phene. Science 353, 1522–1525 (2016).8. Lee,G.-H., Park,G.-H. & Lee,H.-J.Observationof negative refractionof Dirac fermions in graphene. Nat. Phys. 11, 925–929 (2015).9. Wang, K. et al. Graphene transistor based on tunable Dirac fermionoptics. Proc. Natl Acad. Sci. USA 116, 6575–6579 (2019).10. Young, A. F.Quantum interference andKlein tunnelling in grapheneheterojunctions. Nat. Phys. 5, 5 (2009).11. Taychatanapat, T., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P.Electrically tunable transversemagnetic focusing in graphene.Nat.Phys. 9, 225–229 (2013).12. Milovanović, S. P., Masir, M. R. & Peeters, F. M. Magnetic electronfocusing and tuning of the electron current with a pn-junction. J.Appl. Phys. 7, 043719 (2014).13. Wilmart, Q. et al. A Klein-tunneling transistor with ballistic gra-phene. 2D Mater. 1, 011006 (2014).14. Spector, J., Stormer, H. L., Baldwin, K.W., Pfeiffer, L. N. &West, K.W.Electron focusing in two‐dimensional systems by means of anelectrostatic lens. Appl. Phys. Lett. 56, 1290–1292 (1990).n1 (1011 cm-2)n 2(1011 cm-2)0100ΔR(Ω)0-100100100ΔR(Ω)Δn (1011 cm-2)I DC(nA)1.5-1.5-5005000de fa0100ΔR(Ω)B(T)1.5-1.500.50Δn (1011 cm-2)T(K)1.5-1.54120Δn (1011 cm-2)0100ΔR(Ω)gbcFig. 4 | Enhancing collimation with second-order Veselago interference.a Device diagram demonstrating the collimation of small-incident-angle electronswith Veselago interference. Carriers are injected from the source contact and firstcollimated (ineffectively) by the cavity wall. b When |n1| < |n2|, the uncollimated car-riers that escape the cavity predominantly reach voltage probe B, while Veselagointerference further localizes uncollimated carriers in the cavity at 4|n1| = |n2|. Thisleads to d a near-zero measured transverse voltage at 4|n1| = |n2| in the midst of highresistance background. c When |n1|≥ |n2|, the collimation efficiency is not character-ized by transverse voltages. e Weak bias dependence is observed for the zero trans-verse resistance dip. f As a perpendicular magnetic field is applied beyond 0.3 T, themeasured transverse voltage increases both due to the destruction of Veselagointerference.gNo significant temperature dependence is recorded from T=4K ~ 12K.Article https://doi.org/10.1038/s41467-022-34347-wNature Communications |         (2022) 13:6711 5https://github.com/X1Zhang123/Source-Data-Gate-tunable-Veselago-Interference-in-a-Bipolar-Graphene-Microcavity-https://github.com/X1Zhang123/Source-Data-Gate-tunable-Veselago-Interference-in-a-Bipolar-Graphene-Microcavity-https://github.com/X1Zhang123/Source-Data-Gate-tunable-Veselago-Interference-in-a-Bipolar-Graphene-Microcavity-https://github.com/X1Zhang123/Source-Data-Gate-tunable-Veselago-Interference-in-a-Bipolar-Graphene-Microcavity-15. 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ACS Nano 2, 2301–2305 (2008).AcknowledgementsWe thank Boris Shklovskii and Alex Kamenev for useful discussions. Thework at UMNwas supported by the National Science FoundationCAREERAward NSF-1944498. Portions of the UMN work were conducted in theMinnesota Nano Center, which is supported by the National ScienceFoundation through the National Nano Coordinated Infrastructure Net-work (NNCI) under Award Number ECCS-1542202. The band structurecalculation by Z.Z., M.L. and E.K. is supported by STC Center for Inte-gratedQuantumMaterials, NSFGrant No. DMR-1231319, AROMURI GrantNo. W911NF14-0247, and NSF DMREF Grant No. 1922165. Calculationswere performed on theOdyssey cluster supported by the FAS Division ofScience, Research Computing Group at Harvard University and theNational Energy Research Scientific Computing Center (NERSC), a U.S.Department of EnergyOfficeof ScienceUser Facility located at LawrenceBerkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231. Portions of the hexagonal boron nitride material used in thiswork were provided by K.W. and T.T. K.W. and T.T. acknowledge supportfrom the Elemental Strategy Initiative conducted by the MEXT, Japan(Grant Number JPMXP0112101001) and JSPS KAKENHI (Grant Numbers19H05790, 20H00354 and 21H05233).Author contributionsK.W. designed the experiment and device architecture. Data presentedin this work were taken by X.Z. and W.R. Device fabrication, measure-ment and data analysis was performed by X.Z. and W.R. with supportfrom E.B., K.T. and Y.L. under the supervision of K.W. The band structurecalculation for strained graphene was performed by Z.Z. under thesupervision of E.K. and M.L. A portion of the hexagonal boron nitrideused in this work was provided by T.T. and K.W. X.Z., W.R., E.B. and K.W.wrote the paper. All authors discussed the results and provided com-ments on the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-022-34347-w.Correspondence and requests for materials should be addressed to KeWang.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of thiswork. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022Article https://doi.org/10.1038/s41467-022-34347-wNature Communications |         (2022) 13:6711 6https://doi.org/10.1038/s41467-022-34347-whttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Gate-tunable Veselago interference in a bipolar graphene microcavity Results and discussion Sample preparation Observation of Veselago interference Magnetic field, bias and temperature dependence Improving collimation via Veselago interference Methods Gate fabrication Device fabrication Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information