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Rui Pu, Naomi Mizuno, Fernando Camino, Runchen Li, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Dmitri Averin, Xu Du

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[Localizing individual exciton on a quantum Hall antidot](https://mdr.nims.go.jp/datasets/e927e44a-8eda-4fef-8ce2-62ac2de6aef7)

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Localizing individual exciton on a quantum Hall antidotArticle https://doi.org/10.1038/s41467-025-65369-9Localizing individual exciton on a quantumHall antidotRui Pu1, Naomi Mizuno1, Fernando Camino 2, Runchen Li1, Kenji Watanabe 3,Takashi Taniguchi 4, Dmitri Averin 1 & Xu Du 1Excitons are bond states of electron-hole pairs formed through Coulombinteraction. While excitonic phases have been widely studied in semi-conductors and quantumHall double-layers, prior works largely focus on bulksystems with large number of excitons, limiting their applications in quantumdevices. Here, employing the approach of quantum Hall antidot with twospatially separated edge channels, we demonstrate a type of quantum Hallquasiparticle exciton which represents a quantum-coherent bound state of anelectron and a hole situated on their corresponding edges coupled throughintralayer tunneling and Coulomb interaction. This approach allows localiza-tion and electrical tuning of individual quantum Hall excitons. Quantum-coherent dynamics of exciton are observed in the gate-dependence of antidotconductance peaks near the electron-hole resonance, which signifies a quan-tum superposition of vacuum- and electron-hole pairing states. Modeling theelectron-hole pair as a coupled two-level system, semi-quantitative under-standing of experimental observations is achieved. This work opens avenuesfor creating quantum systems of multiple quantum Hall quasiparticles.Solid-state systems have been a major area for the development ofquantum devices and circuits owing to their advantages in scalability,electrical control, and constant progress in size reduction down to thenanoscale level. This combination of characteristics allows manipula-tion of individual quasiparticles associated with the states of charge1–8,spin9–14, magnetic flux and superconducting phase15–21, or more com-plex combined degrees of freedom. In this context, a two-dimensional(2D) electron quantum Hall (QH) system has been a unique platformthat, in addition to the basic integer charge states, hosts the moreexotic quasiparticles associated with fractional QH (FQH) abelian andnon-abelian anyonic states22–26, and excitons in double-layer QHsystems27–32 which exhibit Bose–Einstein condensation (see, e.g.,ref. 33) and unusual quantum solids34. Evidence of the anyonicexchange statistics was obtained in the edgemodes-based Fabry-PerotQH interferometer35–39 and in the anyon collisions40.Another experimental platform that utilizes QH edge modes isQH antidot41–43 in which the edgemodes encircle themaximumof anelectrostatic potential, forming closed orbits. Quantized energylevels obtained in this way can localize individual QH quasiparticles,including those with fractional charge and statistics, and providethe basis for their manipulations. Coulomb-blockade-type correla-tions among the quasiparticles on the antidot, combined with thediscrete antidot energy spectrum, control the number of quasi-particles and minimize the phase space for scattering, henceenhancing quantum coherence. Resonant tunneling through theantidot energy levels has successfully demonstrated the fractionalcharges of FQH quasiparticles44–46. The fractional exchange statis-tics of the anyonic quasiparticles are also theorized to be obser-vable through transport measurement in multi-antidot moleculesystems47. Beyond single antidot atoms, however, while there hasbeen experimental evidence of the double-antidot transport inaccidental48 and defined42 structures, creating controllable andquantum-coherent multiple QH quasiparticle systems remains lim-ited and challenging.Received: 13 May 2025Accepted: 14 October 2025Check for updates1Department of Physics andAstronomy,Stony BrookUniversity, StonyBrook, NY, USA. 2Center for Functional Nanomaterials, BrookhavenNational Laboratory,Upton,NY,USA. 3ResearchCenter for ElectronicandOpticalMaterials, National Institute forMaterials Science, Tsukuba, Japan. 4ResearchCenter forMaterialsNanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan. e-mail: dmitri.averin@stonybrook.edu; xu.du@stonybrook.eduNature Communications |        (2025) 16:10375 11234567890():,;1234567890():,;http://orcid.org/0000-0003-0575-2976http://orcid.org/0000-0003-0575-2976http://orcid.org/0000-0003-0575-2976http://orcid.org/0000-0003-0575-2976http://orcid.org/0000-0003-0575-2976http://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/0000-0001-8782-8369http://orcid.org/0000-0001-8782-8369http://orcid.org/0000-0001-8782-8369http://orcid.org/0000-0001-8782-8369http://orcid.org/0000-0001-8782-8369http://orcid.org/0000-0001-5610-2338http://orcid.org/0000-0001-5610-2338http://orcid.org/0000-0001-5610-2338http://orcid.org/0000-0001-5610-2338http://orcid.org/0000-0001-5610-2338http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65369-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65369-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65369-9&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-65369-9&domain=pdfmailto:dmitri.averin@stonybrook.edumailto:xu.du@stonybrook.eduwww.nature.com/naturecommunicationsOne of the archetypal interacting multi-particle quantum systemsis an exciton, a bound state of an electron-hole pair formed throughCoulomb attraction. In QH double-layers, interlayer Coulomb inter-actions can induce excitonic states from the spatially separated elec-trons and holes on their corresponding layers, forming a bosoniccondensate28–32. QH quasiparticle-associated excitons offer thepotential of creatingquantumstates combining interaction effects andnon-trivial quantum statistics. However, to date, the study on QHexcitons has been largely limited to the bulk systems with a largenumber of excitons.In this work, employing the platform of a quantum Hall antidotwith two spatially separated electron- and hole-edge channels, wedemonstrate a coherent and interacting quantum state of an individuallocalized exciton. Quantum-coherent dynamics of excitons areobserved in the gate dependence of antidot conductance peaks nearthe electron-hole resonance, which signifies a quantum superpositionof vacuum- and electron-hole pairing states. Modeling the electron-hole pair as a coupled two-level system, semi-quantitative agreementwith the experimental observations is achieved.ResultsFigure 1a illustrates the basic principle of such a QH antidot exciton incomparisonwith a conventional exciton. A conventional exciton formsin the free space of a semiconductor by exciting a valence electron.The resultinghole in the valenceband and the excited electron formanexcitonic pair through Coulomb interaction, with energy lower thanthe conduction band edge. A QH antidot exciton, on the other hand,forms in a pair of closely placed QH antidot edge modes hosting anelectron and a hole. The quantum tunneling of an electron from thehole-edge mode to the electron edge mode creates a coherentelectron-hole pair, which, through Coulomb interaction, forms anexcitonic state with reduced ground state energy. In contrast to theinterlayer QH excitons (Fig. 1b), a QH antidot exciton is localizedindividually and created via intralayer Coulomb interaction andtunneling.While Coulomb-blockade transport of individual excitons hasbeen studied in quantum dots49–51 as one of the approaches to thedevelopment of “on-demand” single-photon sources, and continue toattract practical interest up to now (see, e.g., ref. 52 and referencestherein), the distinct element added by our antidot structure to themanipulation of the individual excitons is quantum coherencebetween the electron and the hole parts of the exciton. Such quantumcoherence within the individual excitons is potentially useful forquantum information applications, e.g., as an interface for quantuminformation transfer between the photons and the antidot qubits.From the point of view of qubits, electron-hole attraction within theexciton enhances the energy gap between the qubit states beyond thetypically not-so-large tunnel coupling of these states, something thatwould be beneficial in many different contexts, most directly, in thecase of the ground state quantum computing53.The experimental platform studied in this work is a graphene-hexagonal boron nitride (hBN) heterostructure illustrated in Fig. 1c,with hBN encapsulated monolayer graphene tunable by two graphitegates (see Supplementary Information (SI)). The bottom graphite gatetunes the carrier density uniformly throughout the whole monolayergraphene channel. The top graphite gate is patterned with an antidotand two couplers etched out. The diameter of the antidot here isD ’ 180nm. The couplers point toward the antidot with an edge-edgedistance of ~80 nm at the closest points. Combining the top and bot-tom gates, carrier density and QH filling factor can be separatelyadjusted inside the antidot and coupler region, ν = nheB, and outside,ν0 = n0heB . Here n and n0 are the corresponding local carrier densities, h isQH bilayere-orbith-orbitEpEpEpConven�onalQH-edgeEbuFLGhBNMLGhBNFLGI+V+V-f’fI-f f(a) (b)(c) (d)Fig. 1 | The basic principle of the QH exciton and the experimental scheme. a Aschematic showing the principle of theQHedgemodeexciton formed by intralayerCoulomb interaction, and its comparison with the conventional exciton. The redand theblue arrowedcircles correspond to theorbits of the electron andhole chiraledge modes. b Schematic showing the principle of the QH bilayer exciton, formedby interlayer Coulomb interaction. c A schematic of the sample consists of aheterostructure of patterned few-layer graphite (FLG) top gate, hBN, monolayergraphene (MLG), hBN, and FLG bottom gate. d QH edge modes on a graphenechannel, including the bulk edge modes and the top gate-defined edge modes atthe couplers and the antidot. The edge modes form at the boundaries of differentfilling factors. The red and blue arrowed lines correspond to the electron and hole-edge modes. The dotted arrows indicate where tunneling can happen.Article https://doi.org/10.1038/s41467-025-65369-9Nature Communications |        (2025) 16:10375 2www.nature.com/naturecommunicationsPlanck’s constant, e is the electron charge, and B is the external mag-netic field. When the corresponding numbers of the filled Landaulevels (f and f 0, positive on the electron side and negative on the holeside) are different between the two regions, QH edge modes form atthe boundaries of the antidot and the couplers. As a result of quantumconfinement (particle in a ring), the energy of the QH edge modesencircling the antidot becomes quantized:εj =2ℏvDQHj +ΦΦ0� �ð1Þwith energy level spacing: Δε= 2ℏvQHDQHin a fixed magnetic field43,46 (seeSI). Here, j is an integer which indexes the quantization energy levels,vQH is the QH edge mode velocity, DQH is the effective diameter of theantidot edge mode, Φ is the magnetic flux through the antidot, andΦ0 =he is the magnetic flux quantum. The occupation of the energylevels can be tuned through the gate voltage, while a magnetic fluxshifts the manifold of the levels, manifesting the Aharonov–Bohmeffect.When the distancebetween the couplers’ and the antidot’s edgemodes is sufficiently small, coupling between the bulk edge modesthrough the antidot takes place and lowers the transverse resistanceRT � V +�V�I (I being the electric current flowing through the I+ and I−electrodes) which can be characterized through the transport mea-surement in the configuration shown in Fig. 1d. In the regimewhen thebulk graphene is tuned to a QH plateau with quantized resistance RQH ,the antidot tunneling conductance can be measured from the corre-sponding resistance valley: GAD = 1RT� 1RQH.The basic signature of QH antidot tunneling is illustrated in Fig. 2aunder the simplest configuration where the antidot and the couplersare within the f =0 insulating gap, while the outside bulk is on thef 0 = � 2 QH plateau. Here, consistent with the prior studies on physi-cally etched QH antidots43,46, the emergence of quasi-periodic resis-tance valleys on a QH plateau, associated with tunneling throughdiscrete antidot levels, is observed in our gate-defined QH antidotdevice. Each resistance valley corresponds to adding a single holecharge onto the antidot43. Figure 2b goes beyond the linear con-ductance and demonstrates the top gate voltage and bias voltagedependencies of resistance (charge stability diagram). Thedotted lineshighlight the discernible Coulomb diamonds and excited states. Wenote that compared to typical quantum dots, the Coulomb diamondfeatures are less pronounced in the QH antidot. This may be due to (1)break-down of the quantized plateau resistance under finite bias vol-tages which adds a bias-dependent background; (2) small Coulombenergy due to the relatively large antidot size and screening from thehBNdielectric layers; (3) asymmetric tunneling amplitude between theantidot and the two coupler, which results in nearly invisible resonanttunneling traces at the positive-sloped boundaries of the Coulombdiamonds. From this diagram, the on-site Coulomb repulsion energyand quantization energy spacing on a f 0 = � 2 QH plateau in a 1 Tmagnetic field can be estimated to be U ’ 1meV and Δε ’ 0:7meV,respectively.More examples of charge stability diagrams andCoulombdiamonds showing a similar energy scale can be found in the SI. Basedon the quantization energy, the QH edge mode velocity ofvQH = ΔεDQH2ℏ ’ 105m=s can be estimated, which is in qualitative agree-ment with the previous reports on edge mode velocity in QHinterferometers54,55. The measured on-site Coulomb energy of oneedge state can be understood considering a localized ring of chargedensity with thickness on the order of the magnetic length lB =ffiffiffiffiℏeBq,and partially screened by the nearby gate electrodes:Fig. 2 | Transport characteristics and tuning of QH antidot. a Resistance oscil-lations on the f 0 = � 2 plateau from antidot tunneling, under zero back gate vol-tage. b Charge stability diagram for antidot tunneling on the f 0 = � 2 plateau,showing the bias voltage (Vbias) and VTG dependence of the differential resistance.The dotted lines are guides to the eyes to some of the conductance peaks. Hereback gate voltage is VBG =0:08V. c Tuning antidot tunneling through the dualgates. The colormapshows the ν0 dependenceof transverse resistanceon the lowerdensity side of the f 0 = � 2 plateau over a wide range of ν. The bright-colored dotscorrespond to the resistance valleys on a background of the f 0 = � 2 plateau. Fourcharacteristic regimes are labeled, with their corresponding Landau level energydiagrams illustrated. The Landau level diagrams are across the center of the antidotand couplers, reaching the bulk edges of the graphene channel, as indicated by thedotted line on the device schematic in the colormap inset. In the inset, the blue andthe apricot regions illustrate the antidot/couplers and the bulk regions, respec-tively. In the Landau level diagrams, the red and blue lines correspond to electronand hole Landau levels, respectively. The number on each Landau level indicates itsdegeneracy. Around the antidot, the Landau level energy is quantized into discreteenergy levels due to the quantum confinement effect on the closed edgemodes. Inregimes I and IV, antidot tunneling is suppressed by the large tunneling distancesbetween the edges. Regimes II and III allow antidot tunneling.Article https://doi.org/10.1038/s41467-025-65369-9Nature Communications |        (2025) 16:10375 3www.nature.com/naturecommunicationsU = e22πϵBNϵ0Lln 1 + 4tBN2lB2� �1=2+ 2tBNlB� �(see SI). Here, ϵBN ’ 3:5 ±0:2 is thedielectric constant of hBN, and tBN ’ 10nm is the effective hBNthickness for the screening effect from both graphite gates. Theobserved Coulomb energy of U ’ 1meV suggests an antidot modecircumference of L ’ 600nm, i.e., DQH ’ 190± 10nm. This is con-sistent with the similar but slightly smaller diameter of the antidot inthe top graphite gate (D ’ 180nm).The gate-control of the antidot tunneling is illustrated in Fig. 2c.Themain panel shows the tunneling resistance versus the filling inside(ν) and outside (ν’) the antidot/couplers regions. Sharp bright dots(resistance valleys) signify the antidot tunneling on the QH plateau ofRQH = h2e2 (f0 = � 2), coarsely sampled over a wide range of filling factorν in the antidot/couplers regions that are tuned by the back gate. Fourcharacteristic (f , f 0) combinations are highlighted with their corre-sponding Landau level energy diagrams. The spatial profiles of theLandau level energy (in relation to the chemical potential) are tunedthrough the patterned top gate, while the back gate uniformly shiftsthe chemical potential throughout the whole channel. The QH edgemodes are located where the Landau levels cross the chemicalpotential μ. The edgemode tunneling strength depends sensitively onthe spatial separation between the coupler and antidot edge modes,adjusted by the dual gates. To enable coupler-antidot tunneling, thetunneling distance between the coupler edge mode and the antidotedge mode needs to be near its minimum when the Landau Levelassociatedwith these edgemodes is tuned slightly across the chemicalpotential. Directly relevant to thediscussions belowand for f f 0 ≤0, thiscorresponds to the lower carrier density end of a QH plateau. A moredetaileddiscussionof the edgemode tunneling in these four regimes isgiven in the SI.Having demonstrated the basic principle of QH antidot operation,wenext focuson the symmetry-breaking f 0 = � 1 state in amagneticfieldB=3:3T. Figure 3a shows the top gate voltage dependence of theEVTG 0V1V2e�h�e �ℎ�123123(d)hFig. 3 | Localized QH exciton on an antidot. a Top gate-dependent transverseresistance showing quasi-periodic valleys on the f 0 = � 1 plateau. Inset: shift ofresistance oscillations under varying magnetic fields. The curves are displaced onthe y-axis for clarity.bColor-mappedantidot tunneling conductanceversus dopinginside and outside the antidot. The yellow dotted straight lines trace the randomjumps in conductance peak traces along constant top gate voltages. The blackdotted curves are guides to the eyes for the anti-crossing-like features, which areassociated with tunneling through the electron-hole pairing states. The yellowdotted rectangle highlights a pronounced exciton state, which is discussed quan-titatively in the text. c Antidot tunneling conductance curves inside the yellowdotted rectangle in (b), shifted in the y-axis direction for clarity. The dashed lineshighlight the evolution of the position of the conductance peaks. d Qualitativeschematic showing gate tuning of the antidot levels for the outer (hole) and inner(electron) antidot modes. The red and blue lines correspond to electron- and hole-associated levels, respectively. Bottom right plot: the energy levels spread out withincreasing magnitude of top gate voltage. Due to the energy offset between thef 0 = ± 1 Landau levels (εg ), the electron- and hole- antidot levels can cross eachother, resulting in resonances andpairing. Herewehighlight the shift of an electronlevel and a hole level (thick red and blue lines in the EðVTGÞ plot and the red andblue solid circles in the Landau level diagrams) under changing top gate voltage,with corresponding Landau level diagrams at top gate voltages of 0, V 1 and V2shown in panels ①, ②, and ③. Panel ① inset: device schematic where Landau leveldiagrams are along the dotted line. The blue and the apricot regions illustrate theantidot/couplers and the bulk regions, respectively.Article https://doi.org/10.1038/s41467-025-65369-9Nature Communications |        (2025) 16:10375 4www.nature.com/naturecommunicationstransverse resistance RT , where quasi-periodic resistance valleys asso-ciated with coupler-antidot tunneling of the hole side of the zerothLandau level edgemodes emerge on the plateau backgroundofRQH = he2.Following Eq.(1), the gate voltage positions of these valleys shift withchanging magnetic field at a rate of one resistance valley per magneticflux quantum Φ0 through the effective area of the antidot:δVTGΔVTG= � δΦΦ0= � δBπD2QH4Φ0. Here, δVTG is the shift of a resistance valley intop gate voltage under a changing magnetic field, ΔVTG is the top gatevoltage period of the resistance valleys, δB and δΦ are the changes ofmagnetic field and flux, respectively. From the magnetic shift of theresistance valleys, DQH � 230nm can be estimated, suggestingthe edgemode to situate ~25 nm away from the physical antidot edge ofthe top graphite gate. With this effective diameter, we can also estimatethe number of charges added to the antidot per gate period:ΔN =cTGπD2QH4e ΔVTG = 1:04±0:06 (cTG =ϵ0ϵBNdhBNis the area capacitance ofthe top gate with dhBN = 18nm being the thickness of the hBN layerbetween the graphene can the top graphite gate), consistent with theaddition of single fundamental charges in the integer QH regime46. Allthese observations further confirm the antidot nature of the resistancevalleys.Themain finding of this work is shown in Fig. 3b, which illustratesthe evolution of the antidot tunneling conductance oscillations on thelower density side of the f 0 = � 1 plateau over a range of filling factor νin the antidot/coupler regions. For clarity, the horizontal axis is set toVTG +αADVBG, which directly depicts the electrostatic doping at theoutside vicinity of the antidot, where αAD =0:53 is the effective capa-citance ratio between the bottom and the top gates for antidot char-ging (see SI). The antidot tunneling conductance peaks appear as near-vertical stripes with abrupt jumps. Most interestingly, anti-crossing-like features are observed, highlighted by the black dotted curves inFig. 3b. These features are generally present under the f , f 0  = ð1, � 1Þconfiguration, although the regularity of their locations is disturbed bya few random slides occurring along the yellow dotted straight lines inFig. 3b. The source of these randomslides is identified asquantumdot-like charge trapping centers located near the antidot edge on the topgraphite gate (see SI), which is not the focus of this work. In the dis-cussions below, we focus on the anti-crossing feature highlighted bythe yellow box in Fig. 3b, for which the individual curves of the antidotconductance are shown in Fig. 3c. As will be argued below, afterdeveloping a quantitative model, the anti-crossing-like featuresobserved here originate not from atomic-scale traps, but from theformation of a gate-defined pair of electron-hole edges coupled bothby tunneling amplitude and Coulomb attraction.Anti-crossing features are typically associatedwith level coupling. Inhigh-quality graphene samples, symmetry-breaking interaction effectslift the 4-fold degeneracy of the zeroth Landau level. With a well-developed f 0 = � 1 plateau and insulating behavior at the charge neu-trality, the inner electronand theouterhole-edgemodesare expected tocoexist and be spatially separated by a gapped region. Increasing themagnitude of the top gate voltage, the antidot-defining potential profilebecomes increasingly sharp, resulting in antidot edgemodes with largeredgemode velocities (vQH � dVdr ), hence larger quantization energy levelspacing (Δε= 2ℏvQHDQH). As a result, both the outer hole- and the innerelectron-antidot edge modes have their quantization energy levels fanoutwith increasing topgate voltage. Since themanifolds of hole- and theelectron- quantization energy levels are offset by the charge neutralitygap, the energy levels of the outer- and inner- modes with differentindiceswill havedifferent shifting rates under changing topgate voltage,and will cross each other as illustrated by Fig. 3d. As a result, just fromthe top gate voltage, some of the hole- and electron levels can be tunedto align with and cross each other, creating tuning and detuning of anelectron-hole resonance. With the back gate tuning the chemicalpotential throughout the channel, one can ensure tunneling through theantidot under the conditions of the electron-hole resonance. A moreanalytical discussion of the gate voltage dependence of the resonancecan be found in the SI.To understand the energy spectrum of the coupled electron andhole-edgemodes, we consider a basicmodel of grapheneQH antidot43extended to two coupled co-centric edge modes, shown in Fig. 4a.Here, Γ is the tunneling rate between the couplers and the outer holemode. The inner electronmode is not coupled directly to the couplers,but to the holemodewith a tunneling amplitudeΔ. The energy spectraof the two edge modes are quantized, and therefore, in the mainapproximation, the tunnel coupling between the two modes iscoherent. Besides tunneling, electrons and holes also experienceCoulomb interaction, which can be described in the constant-interaction approximation for each individual mode:U nh,ne  =12Uhnh nh � 1  +12Uene ne � 1  � unhne ð2ÞHere, nh and ne are the numbers of particles in the hole andelectron mode, respectively, Uh, e are the corresponding interactionconstants for the two modes, and u>0 is the magnitude of the Cou-lomb electron-hole attraction between the two edges.Similar to the basic Coulomb-blockade model for tunnelingthrough the quantum dots, Eq.(2) leads to a periodic response of theedges to the two gate voltages that control nh and ne. For the outeredge, this translates into a quasi-periodic sequence of the resonanttunneling peaks of the antidot conductance GAD =dI=dVbiasjVbias =0,with each peakoccurring at the bias conditions atwhich the number ofholes in the edge changes, nh ! nh + 1. On the other hand, the rela-tions among the parameters in Eq. (2): nearly equal repulsion energiesUe and Uh, and a strong attraction constant u close to U, combinedwith the choice of the non-vanishing tunneling terms,make thismodelvery specific to the system we consider: concentric electron-holeedges encircling one antidot. In this case, the inner edge does notaffect the conductance directly, but the number ne of electrons in italso changes periodically by 1 as a sequence of resonances.To describe the antidot transport properties in the vicinity of onecombined electron-hole resonance (where both the electron and holeantidot energy levels align with the chemical potential), we need toconsider four charge states, each labeled by nh and ne: nhne�� �. On thebasis 00j i, 11j i, 01j i, j10if g of these four states, the Hamiltonian of theantidot is:H =0 Δ* 0 t +Δ ξ t 00tt +0� δe00δh0BBB@1CCCA ð3ÞHere, δh is the gate-induced energy deviation of the outer edgestate from the resonance point, δe is the same for the inner edge,ξ = δh � δe � u is the energy of the electron-hole pair occupying theedge states. We include t, t + terms to indicate how the states of theelectron-hole system are coupled to the external charge reservoirs andproduce the incoherent tunneling rates Γ illustrated in Fig. 4a. How-ever, under the limit of weak antidot-reservoir coupling, we do notcalculate these terms. Note that the electron-hole tunnel amplitude Δthat couples 00j i and 11j i states has a somewhat unusual form ofsimultaneously creating or destroying two particles, an electron and ahole, which form an exciton. The reason for this is that it describes thecoupling of the two different edge states, the electron and the hole-edge states. If one reformulates the description of both edges in termsof the same-charge particles, e.g., electrons, it becomes evident thatthe tunnel amplitude Δ corresponds physically to the usual tunnelingArticle https://doi.org/10.1038/s41467-025-65369-9Nature Communications |        (2025) 16:10375 5www.nature.com/naturecommunicationsprocessof transfer of one electronbetween the twoedge states. Such atransfer either adds an electron to the electron edge, leaving a hole inthe hole edge, thus creating an exciton, or, in the reverse process,takes an electron from the electron edge, filling a hole in the hole edge,thus destroying an exciton in the process.From the Hamiltonian, δh and δe-dependent ground states can becalculated as superpositions of the basis states. Tunneling through theantidot occurs when the system is tuned across two degenerateground states with the same electron numbers but with hole numbersdiffering by one. This limits the conductance-contributing tunnelingprocesses to 00j i $ 10j i (empty electron edge mode) and 11j i $ 01j i(filled electron edge mode). Without electron-hole coupling, the basisstates are the eigenstates of the Coulomb energy, and their chargeconfigurations in the ground state depend directly on the energiesδh, δe, as shown in Fig. 4b. 00j i $ 10j i and 11j i $ 01j i lead to thevertical traces of conductance peak along the corresponding phaseboundaries in the (δh,δe) plane. The horizontal shift between the twovertical parts of this boundary (which is also observed experimentally,e.g., in Fig. 3b) is the direct manifestation of electron-hole attractionwithin the exciton. This shift represents the additional magnitude ofthe gate voltage that is needed to overcome the Coulomb attractionenergy u between the individual electron and hole in the two respec-tive edge states of the antidot, after one extra electron was added tothe internal edge of the antidot, when the gate voltages evolved pastthe resonance point.Near electron-hole resonance, the tunnel amplitude Δ mixes thestates 00j i and 11j i along ξ =0, forming a ground state which is thequantum superposition of the two states (see SI). Tunneling con-ductance peak emerges at energy determined by the condition ofdegeneracy between the resonance state and the adjacent groundstates of 01j i and 10j i (see SI):δe =jΔj2δh�u , δh >ujΔj2δh� u, δh <08<: ð4ÞHere, the hyperbolic δe,δh  relations (which, in the absence ofelectron-hole tunneling, correspond to the straight boundariesbetween the states j11〉 and j01〉 and between the states j10〉 and j00〉 inFig. 4b) give rise to the anti-crossing feature in the conductancepeak trace.Near the resonance, the amplitude of the tunneling conductancefrom the 00j i $ 10j i and the 11j i $ 01j i processes is determined bythe composition of the 00j i and 11j i states in the superposition,respectively. The tunneling probability p0 for the 00j i $ 10j i processrapidly decays as the superposition evolves into pure 11j i state undernegative ξ; and the tunneling probability p1 for the 11j i $ 01j i processrapidly decays as the superposition evolves into pure 00j i state underpositive ξ (see SI):p0, 1 =12 1 + ξ=2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiξ2=4+ jΔj2p� �12 1� ξ=2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiξ2=4 + jΔj2p� �8>>><>>>:ð5ÞHence, deviation from the resonance condition drives the systemout of the electron-hole superposition and results in the termination ofthe curvy anti-crossing feature.Applying the model above to our experimental system, we simu-late the doping dependence of the antidot tunneling conductance asFig. 4 |Modeling the coherent electron-hole pair state. a Transportmodel of theantidotmade of two coupled electron andhole-edgemodes.bDiagramof chargingphases with different electron-hole configurations as the ground states, repre-sented by different colors. The dashed line corresponds to ξ =0, along which 00j iand 11j i are degenerate and therefore aremixed stronglyby the tunnel amplitudeΔ.(c) and (d) illustrate color-coded tunneling conductance versus top and back gatevoltages, computed with the transport model with u=0:7meV and Δ= 1meV,and with u=0:7meV and Δ=0:4meV, respectively. Correspondingly, the insetsillustrate the real space separation of the twomodes under these parameters. In (c),the labeled gray arrows indicate tunneling processes illustrated in (e). Processes iand iv are between states with electron and hole levels detuned. Processes ii and iiiinvolve tunneling through the excitonic state, which is a superposition of 00j i and11j i, with dotted ovals indicating the components that contribute to the tunnelingconductance. f Ground state energy reduction from that of the non-interactingisolated electron-hole pair.Article https://doi.org/10.1038/s41467-025-65369-9Nature Communications |        (2025) 16:10375 6www.nature.com/naturecommunicationsshown in Fig. 4c. Here, we assume Lorentzian-shaped tunneling con-ductance peaks46 with an energy broadening of 0.2meV to match thebroadening of the measured conductance peaks. The energy (δe, δh)dependences of the peak position and peak amplitude are calculatedfromEqs.(4) and (5). The gate voltage-tuning of energy at ~0.5meV/mVis obtained from the ratio between the top gate voltage period and thecorresponding charging energy measured in Fig. 2a, b. Semi-quantitative agreement with the experimental observations (Fig. 3b,c) is achieved with an electron-hole Coulomb energy of u=0:8meVand tunneling amplitude ofΔ=0:3meV, reproducing the anti-crossing-like gate-dependent peak position as well as the tunneling con-ductance peak amplitude. In Fig. 4c, the arrows highlight tunnelingprocesses thatgive rise to conductancepeaks, both faroff-resonance (iand iv) and near resonance (ii and iii). The corresponding electron andhole energy level configurations of the tunneling states are depicted inFig. 4e. In processes ii and iii, exciton states are the superposition ofthe 00j i and 11j i states.For the Coulomb interaction between the electron and the holeQH antidot edges, we estimate u = e22πϵBNϵ0Lln 1 + 4tBN2deh2� �1=2+ 2tBNdeh� �(seeSI). Here, deh is the radial separation between the electron and holeedges, which should roughly be equal to deh ’ 35nm to produceu=0:8meV, in agreement with the observations. A theoretical esti-mation of deh requires detailed information on the ν =0 energy gapand the gate-dependent edge mode velocity, and is beyond the scopeof this study. Our QH antidot exciton estimates, nevertheless, areconsistent with the most natural model of concentric electron andhole-edge modes with similar diameters and significant tunnelingbetween them. The order-of-magnitude of these estimates for u and Δare consistent with the assumed geometry of our exciton model withtunnel-coupled, roughly concentric electron and hole edges. Indeed,the inter-mode Coulomb attraction energy u is close to and slightlysmaller than the on-site Coulomb energy measured from the chargestability diagrams, consistent with the fact that the effective distancebetween the edges is slightly larger than the characteristic distancebetween the charges on the same edge. At the same time, the tunnelcoupling Δ is significant, which implies closely spaced electron andhole edges. If an electron were localized on an atomic-scale impuritytrap at such a small distance from the hole edge, it would producemore complex scattering of the hole instead of the observed coherenttunneling with amplitude Δ.Reducing the inter-mode coupling Δ, the model suggests that thehyperbola part of the anti-crossing feature around the resonance isreduced (Fig. 4d). This is consistent with the observations at smallerfilling factor ν, as shown in Fig. 3b (more discussion canbe found in theSI). At small ν, the inner electron edgemode just starts to emerge nearthe center of the antidot and hence is physically distant from the outerhole-edgemode. As a result, the tunneling amplitude between the twomodes is small, and the hyperbola feature in the gate dependence ofthe conductance peaks is largely reduced.Similar to the conventional exciton, the localizedQHexciton stateis stabilized by reducing the ground state energy of an electron-holepair. Compared to the non-interacting (u=0) and isolated (Δ=0)electron-hole states, the excitonic state has its ground state energylowered by finite interaction and finite inter-mode tunneling:Eg u,Δð Þ � Eg 0, 0ð Þ<0. This gate-dependent energy reduction can beconsidered as the equivalent of the exciton binding energy. In parti-cular, for the neutrally biased electron-hole state (δh = δe), we haveEg 0, 0ð Þ � Eg u,Δð Þ= u2 +ffiffiffiffiffiffiffiffiffiffiffiffiffiffiu24 +Δ2q. Interestingly, and different fromconventional excitons, the binding energy of the localized QH excitonis not only affected by the Coulomb energy but also by the tunnelingamplitude between the electron and the holemodes. Finite inter-modetunneling leads to a ground state energy reduction in comparison tothe decoupled interacting electron-hole pair:Eg u,Δð Þ � Eg u, 0ð Þ= ξ2��� ����ffiffiffiffiffiffiffiffiffiffiffiffiffiffiξ24 +Δ2q, with maximum reduction of Δoccurring at ξ =0 (see Fig. 4f).We note that a unique characteristic of the electron-hole systemstudied here is the combination of Coulomb repulsion on-site andCoulombattractionbetween the twoedges, which is different from themore familiar multi-quantum dot systems with Coulomb repulsiononly. The electron-hole attraction u in the exciton breaks one con-tinuous trace of the external hole-edgemode tunneling peakwhen theinner electron edge changes from being empty ( 10j i $ 00j i) to filled( 11j i $ 01j i). Since the inter-edge Coulomb attraction effectivelyreduces the on-site Coulomb blockade, the shift of the off-resonancetunneling conductance peaks is toward a smaller magnitude of gatevoltages with increasing number of electrons on the inner antidotedge. Classically, the two segments of the conductance peak would beconnected and smoothly shifted by an energy of u, reflecting thegradual increase of the averageoccupationof the electron state from0to 1 with the gate voltage. Quantum mechanically, on the other hand,strong tunneling couples the vacuum state 00j i and electron-hole pairstate 11j i, creating a coherent quantumsuperposition of the twostates.Hole tunneling through the vacuum-pair superposition, as discussedthrough our model, leads to the anti-crossing-like gate voltagedependence of the conductance peaks with diminishing amplitudeaway from the electron-hole resonance.In conclusion, we have demonstrated a localization of individualquantum-coherentQHexcitons in a grapheneQHantidot. Compared tothe conventional excitons on semiconductors, the QH exciton allowselectrical tuning of the electron and hole states, and shows a groundstate energy, which is determined both by Coulomb interaction andinter-mode tunneling. This work paves the way to a series of scientifictasks and technical developments. For example, excitonic statesmay bestudied in more complex and versatile many-antidot systems for exci-tonicmolecules. Time-dependentmeasurementsmay be performed onthe excitonic state to explicitly study the quantum coherence. The QHantidot exciton scheme can potentially be extended to study the indi-vidual anyonic excitons in the FQH regime by tuning the bulk fillinginside and outside the antidot to the fractional fillings of the zerothLandau level. This implements a coupled state of the two fractionalquasiparticles with opposite charges. The interaction energy of suchfractional excitons, togetherwith the tunnel coupling between the edgestates of these quasiparticles, would be significantly smaller than in theinteger regime, requiring much lower temperatures to observe theexcitonic state. In the case of a single antidot, which can accommodateat most one exciton at a time, fractional exchange statistics may man-ifest itself indirectly, via the shape of the tunneling conductance peaksthrough the antidot. Beyond a single antidot, potential direct observa-tion of the exchange statistics may be possible through exciton trans-port in the inter-coupled multi-antidot structures.MethodsSample fabricationGraphite-hBN encapsulated graphene stack was assembled usingstandard van der Waals dry pickup technique, where top hBN, topgraphite gate, middle hBN, monolayer graphene, bottom hBN, andbottom graphite gate are picked up sequentially following Fig. 1b witha polycarbonate (PC) stamp. All flakes were mechanically exfoliatedonto precleaned (sonication in isopropanol followed by UV ozonecleaning for 2min and 350 °C baking for 1min) SiO2 substrates andwere scanned using an atomic force microscope (AFM) to ensurecontamination-free and atomically flat surfaces. The stamp base was adroplet-shaped polydimethylsiloxane (PDMS) to take advantage of itsnatural curvature. The PC solution at 6%was then spin-coated onto thedroplet-like PDMS base at 1000 rpm and left to dry on a hot plate at100 °C for a total of 20min.Article https://doi.org/10.1038/s41467-025-65369-9Nature Communications |        (2025) 16:10375 7www.nature.com/naturecommunicationsThe assembly process started with picking up the top hBN layer.The substrate carrying the hBN flake, preheated to 70 °C, was carefullyraised until touching the lowest point of the PC stamp. The substratewas then further raised manually until the touch area expanded to theclose vicinity of the destination hBN flake. The final contact was madeusing thermal expansion by heating the stage slowly to 110 °C at ~3 °C/min. The following separation process was done by cooling the stage/substrate back to 65 °C, at which the hBN flake got picked up from thesubstrate with the thermal contraction of the substrate stage as well asthe PC stamp. The subsequent layers of graphite gates, hBN dielectriclayers, and graphene were picked up in a similar manner. With all thelayers designed in order and orientation on the PC stamp, the stackwas then pressed onto a precleaned SiO2 substrate at 160 °C andheated up to 180 °C. Upon separation, the PC was detached from thePDMS stampand transferred onto the SiO2 substrate together with theheterostructure stack. As the final step, we soaked the stack inchloroform for at least 10 h to dissolve PC. The stack was then trans-ferred to isopropanol to remove chloroform before being blow-driedwith nitrogen gas. The sample was then thermally annealed in forminggas (5% hydrogen in argon) at 400 °C for 2 h to thoroughly removepolymer residue on the top surface. The completed stack consisted of,from top to bottom, hBN (8nm), top graphite(~2 nm), middlehBN(18 nm), monolayer graphene, bottom hBN (36 nm), and backgraphite(~2 nm).After assembly, the heterostack was scanned with an AFM for sur-face topography, andabubble-free areawas identified for the active areaof the sample. The overall device outline was patterned into van derPauwgeometrywith standarde-beam lithographyandetched into shapewith reactive ion etch (RIE) in CHF3/O2 plasma (40 sccm/4 sccm,30mTorr, 60W). The four edge-contacts to the encapsulated graphenechannel weremade using the same etchingmethod followedby thermalevaporation of 5 nm Cr and 50nm Au. Similar edge-contact was fabri-cated on the top graphite gate. To prevent shorting top graphite to thegraphene channel underneath the top gate lead at the edge of thechannel, a crosslinkedPMMAblockwas fabricated covering the exposedgraphene edge, and themetal lead toward the top graphite gate contactwas deposited over this block. In the final step, the two couplers and theantidot were etched out of the top graphite layer, together with fouradditional cutsmade just outside the four side contacts to isolate the topgraphite gate from the graphene channel. A scanning electron micro-scopy image of the device is shown in the SI.Sample measurementTransportmeasurement of the devicewas performed inside anOxfordVTI with a 12 Tesla superconductingmagnet andHe-III cryogenic insertwith a base temperature of 300mK. All electrical cables that enter thesample chamber go through low-pass pi-filters at room temperatureand RC filters at 2 K, to minimize the high-frequency noise and thesample’s electron temperature. The high quality of the sample isconfirmed by the quantum Hall (QH) plateaus, which start to form invery low magnetic fields (see S1).All electrical measurements were carried out with the standardlock-in technique. Current excitation of 5–10 nA was provided by aKeithley 6221 current source at a frequency of 23Hz. In the chargestability diagram measurements, the current course also provided acontrollable DC bias. The AC component of the voltage response wasmeasuredby a StanfordResearch SR830 lock-in amplifier,while theDCvoltage biaswasmeasuredby a Keithley 2182A nanovoltmeter. The topgraphite gate, bottom graphite gate, and Si gate voltages were pro-vided by a Keithley 2450, a Keithley 2400, and a Keithley 6487,respectively.Several segments of the patterned monolayer graphene acting asa contact to the channel are not covered by the graphite gates. Whenthese segments are near charge neutral and under a strong magneticfield, large contact resistance can emerge and result in poormeasurement results. To solve this problem, a Si back gate voltagewasapplied to electrostatically dope the segmentwith the same polarity asthe graphene channel to avoid the highly resistive zero-filling gap at ap-n junction in a strong magnetic field.Data availabilityThe data represented in Figs. 2–4 are available at the Figshare data-base: https://doi.org/10.6084/m9.figshare.29042864. All other datathat support the findings of this study are available from the corre-sponding authors upon request. Any questions regarding the data canbe addressed to the corresponding authors.Code availabilityThe code underlying this study is available at at Figshare database:https://doi.org/10.6084/m9.figshare.29042864. Any questionsregarding the code can be addressed to the corresponding authors.References1. Pashkin, Y. A. et al. Josephson charge qubits: a brief review.Quantum Inf. Process. 8, 55–80 (2009).2. Bouchiat, V. et al. Quantum Coherence with a single cooper pair.Phys. Scr. T76, 165 (1998).3. 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Rev. Mod.Phys. 90, 015002 (2018).54. Déprez, C. et al. A tunable Fabry–Pérot quantumHall interferometerin graphene. Nat. Nanotechnol. 16, 555–562 (2021).55. Ronen, Y. et al. Aharonov–Bohm effect in graphene-basedFabry–Pérot quantum Hall interferometers. Nat. Nanotechnol. 16,563–569 (2021).AcknowledgementsX.D. and D.A. acknowledge support from NSF award under Grant No.DMR-2104781. K.W. and T.T. acknowledge support from the JSPSKAKENHI (Grant Numbers 21H05233 and 23H02052), the CREST(JPMJCR24A5), JST, and World Premier International Research CenterInitiative (WPI),MEXT, Japan. This researchused theElectronMicroscopyfacility of the Center for Functional Nanomaterials (CFN), which is a U.S.Department of Energy Office of Science User Facility, at BrookhavenNational Laboratory, under Contract No. DESC0012704.Author contributionsR.P., N.M., F.C., and R.L. contributed to the sample fabrication. R.P. andX.D. carried out sample measurements. K.W. and T.T. synthesized thehBNcrystals used in this experiment. X.D. designed the experiment. D.A.and X.D. performed modeling and data analysis. X.D., D.A., R.P., N.M.,and F.C. wrote the manuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-65369-9.Correspondence and requests for materials should be addressed toDmitri Averin or Xu Du.Peer review information Nature Communications thanks U. Chandni,who co-reviewed with Suvronil Datta, Masaya Kataoka, and the otheranonymous reviewer(s) for their contribution to the peer review of thiswork. 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The images or other thirdparty material in this article are included in the article’s CreativeCommons licence, unless indicated otherwise in a credit line to thematerial. If material is not included in the article’s Creative Commonslicence and your intended use is not permitted by statutory regulation orexceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-65369-9Nature Communications |        (2025) 16:10375 10http://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Localizing individual exciton on a quantum Hall antidot Results Methods Sample fabrication Sample measurement Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information