# Fileset

[s41467-024-53890-2.pdf](https://mdr.nims.go.jp/filesets/e67faa5a-3448-4e3c-984e-f6c336a92a74/download)

## Creator

[Kosuke Noro](https://orcid.org/0009-0001-6532-5792), [Yusuke Kozuka](https://orcid.org/0000-0001-7674-600X), Kazuma Matsumura, Takeshi Kumasaka, Yoshihiro Fujiwara, [Atsushi Tsukazaki](https://orcid.org/0000-0003-0251-063X), [Masashi Kawasaki](https://orcid.org/0000-0001-6397-4812), [Tomohiro Otsuka](https://orcid.org/0000-0003-2532-643X)

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Parity-independent Kondo effect of correlated electrons in electrostatically defined ZnO quantum dots](https://mdr.nims.go.jp/datasets/17b66109-c28b-4a13-8659-ea65034e4b31)

## Fulltext

Parity-independent Kondo effect of correlated electrons in electrostatically defined ZnO quantum dotsArticle https://doi.org/10.1038/s41467-024-53890-2Parity-independent Kondo effect ofcorrelated electrons in electrostaticallydefined ZnO quantum dotsKosuke Noro 1,2, Yusuke Kozuka 3, Kazuma Matsumura1,2, Takeshi Kumasaka1,Yoshihiro Fujiwara1,2, Atsushi Tsukazaki 4,5, Masashi Kawasaki 6,7 &Tomohiro Otsuka 1,2,5,7,8Quantum devices such as spin qubits have been extensively investigated inelectrostatically confined quantum dots using high-quality semiconductorheterostructures like GaAs and Si. Here, we present a demonstration of elec-trostatically forming the quantum dots in ZnO heterostructures. Through thetransport measurement, we uncover the distinctive signature of the Kondoeffect independent of the even-odd electron number parity, which contrastswith the typical behavior of the Kondo effect in GaAs. By analyzing tempera-ture andmagnetic field dependences, wefind that the absence of the even-oddparity in the Kondo effect is not straightforwardly interpreted by the con-siderations developed for conventional semiconductors. We propose that,based on the unique parameters of ZnO, electron correlation likely plays afundamental role in this observation.Our study not only clarifies the physics ofcorrelated electrons in the quantum dot but also holds promise for applica-tions in quantum devices, leveraging the unique features of ZnO.Advances in nanofabrication technology have allowed us to artificiallycreate tiny semiconductor devices. A notable example is the semi-conductor quantum dot, which confines electrons to a nanometer-scale area, enabling the direct control and observation of the quan-tized electronic states1–3. By precisely adjusting voltages on split gates,fundamental electronic properties of semiconductor quantum dotshave been extensively investigated, encompassing orbital1,4,5 and spinstates6–10. Beyond single-particle properties, quantum dots serve as anideal platform for exploring the physics of the quantum many-bodyeffect, involving localized electrons and itinerant electrons surround-ing them, which has unveiled interesting phenomena such as the Fanoeffect11,12 and the Kondo effect13–22. Furthermore, because of the highcontrollability of the quantum states, quantum dots offer excitingprospects for quantum information devices, where electron spins areused as qubits23,24, as highly coherent manipulation25–31 and their inte-gration schemes32–36 have been recently demonstrated.Until now, semiconductor quantum dots have been actively stu-died in heterostructures employing materials like GaAs and Si. How-ever, high-quality heterostructures fabricated from emergentsemiconductors, such as graphene37 and ZnO38, have become availablefollowingprolonged efforts to developmanufacturing technologies. InZnO heterostructures, which are the focus of this study, several intri-guing phenomena resulting from the strong electron correlation havebeen reported, including quantum Hall ferromagnetic state39, Wingercrystallization40,41, and even-denominator fractional quantum Halleffects42,43. Figure 1a summarizes the featureofZnOcompared toothersemiconductor materials in terms of the electron interaction para-meter rS and the transport scattering time τ, where rS is defined as theReceived: 22 January 2024Accepted: 24 October 2024Check for updates1Research Institute of Electrical Communication, Tohoku University, Sendai, Japan. 2Department of Electronic Engineering, Graduate School of Engineering,Tohoku University, Sendai, Japan. 3Research Center for Materials Nanoarchitectonics (MANA), National Institute for Material Science (NIMS), Tsukuba, Japan.4Institute for Materials Research, Tohoku University, Sendai, Japan. 5Center for Science and Innovation in Spintronics, Tohoku University, Sendai, Japan.6Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), University of Tokyo, Bunkyo-ku, Tokyo, Japan. 7Center for Emergent MatterScience, RIKEN, Wako, Saitama, Japan. 8WPI Advanced Institute for Materials Research, Tohoku University, Sendai, Japan.e-mail: tomohiro.otsuka@tohoku.ac.jpNature Communications |         (2024) 15:9556 11234567890():,;1234567890():,;http://orcid.org/0009-0001-6532-5792http://orcid.org/0009-0001-6532-5792http://orcid.org/0009-0001-6532-5792http://orcid.org/0009-0001-6532-5792http://orcid.org/0009-0001-6532-5792http://orcid.org/0000-0001-7674-600Xhttp://orcid.org/0000-0001-7674-600Xhttp://orcid.org/0000-0001-7674-600Xhttp://orcid.org/0000-0001-7674-600Xhttp://orcid.org/0000-0001-7674-600Xhttp://orcid.org/0000-0003-0251-063Xhttp://orcid.org/0000-0003-0251-063Xhttp://orcid.org/0000-0003-0251-063Xhttp://orcid.org/0000-0003-0251-063Xhttp://orcid.org/0000-0003-0251-063Xhttp://orcid.org/0000-0001-6397-4812http://orcid.org/0000-0001-6397-4812http://orcid.org/0000-0001-6397-4812http://orcid.org/0000-0001-6397-4812http://orcid.org/0000-0001-6397-4812http://orcid.org/0000-0003-2532-643Xhttp://orcid.org/0000-0003-2532-643Xhttp://orcid.org/0000-0003-2532-643Xhttp://orcid.org/0000-0003-2532-643Xhttp://orcid.org/0000-0003-2532-643Xhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-53890-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-53890-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-53890-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-53890-2&domain=pdfmailto:tomohiro.otsuka@tohoku.ac.jpwww.nature.com/naturecommunicationsratio of the Coulomb energy to the Kinetic energy, and is expressed asrS =m*e2=4π_2εffiffiffiffiffiffiffinπp(m*: effective mass, e: elementary electric charge,ℏ:Planck constant divided by 2π, ε:dielectric constant, n: sheet carrierdensity). ZnO combines strong electron correlation and clean trans-port, opening a new field of quantum dot research in strongly corre-lated systems. In addition to the correlation effect, ZnO stands out as aunique material compared to conventional semiconductors, char-acterized by its large band gap (Eg = 3.37 eV)44 with a single electronpocket preventing intervalley carrier scattering, weak spin-orbitinteraction, and low-density nuclear spins (67Zn (4% natural abun-dance) has a I = 5/2 nuclear spin, and 17O (0.04% natural abundance)has a I = 5/2 nuclear spin, while other Zn and O isotopes show zeronuclear spin states.).These features make ZnO suitable for quantumapplications that leverage long spin coherence. Although spin-orbitinteraction can be used for spin manipulation, it also causes deco-herence and the appropriate control of the interaction is crucial. In Sispin qubits, introducing controllableeffective spin interaction inducedby micro-magnets in small spin-orbit materials are widely used28.Because of the small spin-orbit interaction in ZnO, the same approachcan be employed.Here, we demonstrate the electrostatic formation of quantumdots in high-quality ZnO heterostructures. By precisely tuning the splitgate voltages, we observe Coulomb peaks and Coulomb diamonds atdilution temperatures, illustrating well-defined quantized states.Moreover, we identify the Kondo effect, characterized by zero-biasresonance peaks in the Coulomb diamonds. Remarkably, the Kondoeffect proves to be resilient, independent of the even-odd electronnumber parity. This is in contrast to the commonly observed odd-parity Kondo effect in GaAs quantum dots when an unpaired localizedspin is present. Our study shows the demonstration of electrostaticallyformed quantum dots in ZnO, shedding light on the fundamentalproperties of correlated localized electrons in the quantum dots.ResultsDevice structureThe (Mg,Zn)O/ZnOheterostructure is grown on a Zn-polar ZnO (0001)substrate by molecular beam epitaxy, the details of which areexplained in ref. 45 and “Methods”. As shown in Fig. 1b, the two-dimensional electron gas (2DEG) forms at the interface between(Mg,Zn)O and ZnO. The density is modulated by applying the gatevoltages across the AlOx insulator as described in ref. 46,47. Thevalues of electron density and mobility without gate voltages aredetermined by the Hall measurement at 1.8K as n = 4.9 × 1011 cm−2 andμ = 170,000 cm2 V−1 s−1, respectively. Figure 1c shows a false-coloredscanning electron microscope (SEM) image of the planar structure ofthe top gates48. Here, the mean free path is estimated as ~2μm, whichis much larger than the gate structure. A quantum dot is formed byapplying negative gate voltages on the gate electrodes C, L, P, and R,denoted as VC, VL, VP, and VR, respectively.Quantum dot formation and controlWe first measure the electron transport through the device at a cryo-genic temperature of 60mK. Throughout the measurement, we setVC = −4.5 V to fully deplete the electrons under gate C. Figure 2a showsa conductance map (in the unit of 2e2/h, e: elementary electric charge,h: Planck constant) while sweeping VR and VL that are applied to gate Randgate Lwith afixedplunger gate voltage (VP) of −5.0 V and a source-drain bias (Vsd) of 0.24mV, where the electrons under the plunger gate(P) is alsodepleted. ForVL > −4.0 V andVR > −4.4 V (top right in Fig. 2a),relatively high conductance is obtained,meaning that the transmissionof electrons is large through the gaps between gates C and L and gatesC andR. Aswe lowerVR (Fig. 2b) andVL (Fig. 2c) along theorange line attop and the green line at right in Fig. 2a, the conductance decreasesaccompanied with pronounced oscillation patterns. These oscillationscorrespond to Coulomb oscillations associated with forming thequantized states separated by the on-site Coulomb energy plus thesingle-particle orbital energy in the quantum dot. Then, at fixedVL = −4.37 V and VR = −4.79 V (red cross in Fig. 2a), we control thenumber of electrons in the dot by sweeping VP as evidenced by theCoulomb oscillations in Fig. 2d. The width of the Coulomb peaksbecomes wider at higher VP, reflecting the increase of the tunnelcoupling between the dot and the reservoir. The dot states are furtherconfirmed bymeasuring the conductance as functions of VP and Vsd asshown in Fig. 2e. By varying Vsd, we observe low conductance areascorresponding to the Coulomb blockade. The width of the Coulombblockade regime is varied by VP (Fig. 2f), leading to the conductancemap structure known as Coulomb diamonds. These observationsdemonstrate the electrostatic formation and control of the quantumdot. Here, we can estimate the charging energy (EC) and the orbitallevel spacing (Δε) from the nonuniform sizes between the Coulombdiamonds, as EC = 1.3meV and Δε =0.3meV as indicated in Fig. 2e. Δεcan also be estimated by analyzing the signal of cotunneling49, and it isof the same order as the orbital energy mentioned above. In thisexperiment, we cannot unambiguously determine the absolute num-ber of electrons in the dot because a negative VP lower than −5.0 Vsuppresses the current across the dot.200 nmdotCP RLSource DrainVsd202120091989GaAs19902012ZnOCdTeGaNSi/SiGe2009Bilayer graphene2DEGTi/Au electrodesL P RSourceDrainCAlAsFig. 1 | ZnOanddevice structure. aThemapofmaterial parameters in termsof theelectron interaction parameter rS and the transport scattering time τ, comparingZnO and other semiconductors. b Schematic of the ZnO quantum dot device. Two-dimensional electron gas (2DEG) is formed at the (Mg,Zn)O/ZnO interface. Gateelectrodes are fabricated on top of the AlOx gate insulator. c The false-colored SEMimage of the ZnO quantum dot device.Article https://doi.org/10.1038/s41467-024-53890-2Nature Communications |         (2024) 15:9556 2www.nature.com/naturecommunicationsKondo effectNotably, in Fig. 2e, we notice distinct conductance peaks at Vsd = 0V,reminiscent of the Kondo effect in the quantum dot13,15,16. The Kondoeffect occurs when itinerant electrons screen the localized spins in thequantum dot, resulting in a coherent co-tunneling process50. There-fore, the number of electrons in the dot should be odd because anunpaired localized spin is necessary for the appearance of the Kondoeffect(Fig. 2g). In contrast, in the presence of an even number ofelectrons, the Kondo effect is usually absent since the singlet S = 0state is typically stable (Fig. 2h). Experimentally, however, we observezero-bias peaks in the neighboring Coulomb diamonds, meaning thatthe Kondo effect manifests regardless of the even-odd electron parityin the case of our ZnO quantum dot, which will be further discussedlater. Because the tunnel rate changes significantly with the change inplunger gate voltage, the coupling between the QD and the source-drain electrodes changes quickly from strong to weak, which makes ithard to observe Coulomb diamonds in a wide range of gate voltages.We confirmed the absence of even-odd parity in the Kondo effect asobserved in other devices(Supplementary Fig. 1).To verify the Kondo effect, we measure the temperature depen-dence of the conductance as a function of VP as shown in Fig. 3a, attemperatures from 70 to 600mK. The zero-bias conductance atVsd = 0 V is suppressed in the Coulomb-blockaded regions withincreasing temperature. This behavior is more evident in the con-ductance spectra as a function of Vsd at the midpoint of the Coulomb-blockaded regions at VP = −5.04, −4.64, and −4.30V, denoted asN − 1,N, and N + 1, as shown in Fig. 3b, d, and f, respectively. The peakstructure diminishes rapidly with increasing temperature, consistentwith a characteristic feature of the Kondo effect.To delve into the Kondo effect more quantitatively, we plot thetemperature dependence of the zero-bias conductance peak value inFig. 3c, e, and g. These plots exhibit a clear lnðTÞ dependence, aFig. 2 | Characteristics of the quantum dot. a Conductance map measured asfunctions of VR and VL at VP = −5.0 V. Coulomb oscillations appear when tunnelbarriers are balanced to form a dot state. The red marker denotes the point of VLandVR used in (e, f).b, cConductancemeasured as a functionofVR andVL along thelines in (a), respectively. d Conductance measured as a function of VP withVL = −4.37V and VR = −4.79 V. e Conductancemapmeasured as functions of VP andVsd. The dotted lines are the guides to the eyes, indicating the blockade regime. Thecharging energy (EC) and the orbital level spacing (Δε) are also indicated. The blueline shows the observed cotunneling signal. f Conductancemeasured as a functionof Vsd with changing VP from −4.769 to −4.653V. Each trace is vertically shifted by0.45 (2e2/h) for clarity.g,h Schematicdiagramsof spinfilling andKondostate in thecases of odd and even electrons.Article https://doi.org/10.1038/s41467-024-53890-2Nature Communications |         (2024) 15:9556 3www.nature.com/naturecommunicationscharacteristic feature of the Kondo effect, which is known to be pro-nounced around the temperature range of 0.1TK < T < TK (TK: Kondotemperature). Outside of this temperature range, according to thelinear response theory, the conductance (G) follows a temperaturedependenceof� 1=ln2ðT=TKÞ atT≫ TK and asymptotically approachesG0 with a Fermi liquid temperature dependence of � �ðT=TKÞ2 atT≪ TK51. Here, G0 is the conductance in the low-temperature limit andis expressed asG0 =Gs4∣t2Lt2R∣μ� ε0� �2 + ∣t2L∣+ ∣t2R∣� �2 , ð1Þwhere tL and tR are the transmission coefficients from the dot to the leftand right reservoir, respectively, and Gs is the quantum of conductance2e2/h. G0 is maximumwhen tL= tR51. μ and ε0 show Fermi energy and thesingle-partice energy level in the quantum dot. By fitting theCoulomb peak at T= 70mK in Fig. 3a, jt2Lj, jt2Rj are estimated tobe 0.13meV and 0.68meV, respectively. TK is given by TK =ffiffiffiffiffiffiffiffiΓECp=2� �exp πε0 ε0 + EC� �=ΓEC� �16, where Γ= ΓL + ΓR = jt2Lj+jt2Rj, andTK becomes 1.7K. This also supports that the system is in the Kondoregime. Moreover, we calculated TK by using full width at half maximum(FWHM)of thezero-biaspeakatT= 70mK inFig. 3f. In earlier studies, therelationTK = e ⋅ FWHM/kBwas used to estimateTK16. By using this relationTK was calculated to be 1.7K, which is consistent with the calculation byEq. (1) discussed above. For fitting the experimental temperaturedependence, it is convenient to use the following empirical form14,22GðTÞ=G0T 02KT2 +T 02K !s, ð2ÞwhereT 0K =TK21=s � 1� �1=n : ð3ÞThe fitting using Eq. (2) to the case of N+ 1 is shown in Fig. 3h, yieldingG0 =0.475(2e2/h), s=0.125, n=2, TK =2.27K. These fitting parametersprovide valuable insights into the peculiar features of the Kondo effect inZnO. In the simplest case of nondegenerate S= 1/2 (SU(2)), we wouldexpect the exponents around s=0.22 and n=214,52. This discrepancy inthe exponents is unexpected since ZnO has a nondegenerate singleelectron band, similar to GaAs, and therefore SU(2) symmetry would beexpected. Even assuming the presence of doubly degenerate orbitals(SU(4)) as in carbon nanotube or graphene18,21,22, a renormalization groupapproach predicts s=0.20 and n=352, inconsistent with the present caseof ZnO. The fittings constraining s=0.22 or s=0.20 fail to explain theobserved temperature dependence as shown in Fig. 3h, ruling out thepossibilities of the SU(2) and SU(4) Kondo effects with S= 1/2.In the case of ZnO, we need to consider an alternative perspectiveon the peculiarKondo effect. ZnO is recognized for its relatively strongelectron correlation because of a small dielectric constant (ϵ = 8.3ϵ0,ϵ0: vacuumpermittivity) comparedwith conventional semiconductorssuchasGaAs and Si (ϵ(GaAs) = 12.9ϵ0, ϵ(Si) = 11.7ϵ0)47,53. Togetherwith alarge effective mass ofm =0.3m0 (m0: mass of a bare electron), whichresults in relatively small orbital energy splitting, this property hasled to many unconventional phenomena in the two-dimensional39–43and one-dimensional48 electrons in ZnO. Consequently, we couldanticipate an unconventional phenomenon stemming from thecorrelation effect in the ZnO quantum dot as well. One possible sce-nario is thatHund’s coupling energymay exceed the orbital separationenergy, Δε, thereby stabilizing the S ≥ 1/2 Kondo state, regardless ofthe even-odd electron filling. In fact, a numerical calculation forthe S = 1 triplet Kondo state in ref. 54 demonstrates that Eq. (2) bestfits the temperature dependence with s ≈0.15, assuming n = 2, close tothe fitting parameters in our data.Future further measurements invarious conditions and comparison of the results with numericalrenormalization group (NRG) calculations55–57 will contribute tounderstanding the detailed temperature dependence.The triplet S = 1 Kondo effect in the semiconductor quantum dothas been discussed, but the Kondo temperature is predicted to beFig. 3 | Temperature dependence of theKondo effect. a Plunger gate voltage (VP)dependence of conductance measured at T = 70, 123, 176, 229, 282, 335, 388,441, 494, 547, and 600mK. b, d, f Source-drain voltage (Vsd) dependence of con-ductance measured at the same temperature range for VP = −5.04, −4.64, and−4.30V, corresponding to the electron number of N − 1, N, and N + 1, respectively.c, e, g Temperature dependence of zero-bias peak conductance corresponding tothe (b, d, f). h The fitting to the data shown in (g) using Eq. (2).Article https://doi.org/10.1038/s41467-024-53890-2Nature Communications |         (2024) 15:9556 4www.nature.com/naturecommunicationsseveral orders of magnitude lower than that for the S = 1/255,58. Instead,the even-electron Kondo effect is realized at the singlet-triplet leveldegeneracy under a magnetic field17,20. To access this possibility in ourcase, we measure the magnetic field dependence of the conductancefor the cases ofN − 1 andN as shown in Fig. 4a–b and c–d, respectively.In both cases, we observe several field-dependent peak structures inthe Coulomb-blockaded region. The energy scales of the magneticfield dependence are estimated as 0.20mV/T for N − 1 and 0.28mV/Tfor N. This energy scale roughly aligns with the effect of Zeemansplitting for the S = 1/2 Kondo state, 2gμB = 0.22meV/T, with g = 1.94for the ZnO 2DEG59. However, the Kondo peak at the singlet-tripletdegeneracy is known to be much more sensitive to the magnetic fieldthan the Zeeman splitting effect as observed in ref. 17,20, unlikely to bethe origin of our observation. The S = 1 triplet Kondo effect suggestedabove is not plausible either because additional peak splittingequivalent to 4gμBB corresponding to ∣T�i ! ∣T +   is expected inaddition to the splitting of 2gμBB corresponding to ∣T�i ! ∣T0E.However, we cannot completely rule out this possibility if the two-spinflip process (∣T�i ! ∣T +  ) is too weak to observe as in the case ofbilayer graphene22.Having considered these possibilities, we also propose anothermechanism of the observed even-odd independent Kondo effect thatinvolves multiple orbitals strongly hybridized with each other asindicated by the complex peak structures in Fig. 4. Electrons occupyhigher orbitals with remaining unpaired spins (S ≥ 1/2) instead offorming a singlet state due to intra-dot correlations. In this case, eachlocalized spin may be independently coupled to surrounding elec-trons, resulting in multiple scales of the Kondo temperatures (Fig. 4e,f). This makes the interpretation by fitting with Eq. (2) inappropriate.We note that a similar discussion has been presented in ref. 19LeadDotLeadEven electron, S ≥ 1/2, ZnO, B = 0Kondo stateacB = 1.00 TB = 1.80 TB = 1.00 TB = 2.00 TN-1NbdeN-1NfLeadDotLeadEven electron, S ≥ 1/2, ZnO, B ≠ 0Kondo stategµBFig. 4 | Magnetic field dependence of the Kondo effect. a, c Conductancemap asfunctions ofmagnetic field (B) and source-drain voltage (Vsd) forN − 1 (a) andN (b).Multiple peaks exist as indicated by the dotted lines for the eye guide.b, d Conductance measured as a function of Vsd with changing B by 0.08 T setup(0.1 T in d). Each trace is vertically shifted by 0.015 (2e2/h). e, f Schematic diagramsof spin filling and Kondo state in the case of ZnOwithout andwith amagnetic field.Article https://doi.org/10.1038/s41467-024-53890-2Nature Communications |         (2024) 15:9556 5www.nature.com/naturecommunicationsregarding the Kondo effect in the GaAs quantum dot, where even-oddbehavior is absent when energy separation Δε is smaller than theenergy scales of temperature, kBT, or energy broadening due to tunnelcoupling, Γ. However, our observation differs from this case, having arelatively large energy separation of 0.3meV, corresponding to atemperature of 3.5 K. Moreover, this breakdown of even-odd effects iscommonly observed in different devices in the case of ZnO (Seethe Supplementary Information). Nevertheless, we cannot completelyrule out the possibility of the singlet-triplet or S = 1 Kondo effectbecause of the limitation of the detailed state analysis. For a moredetailed understanding, the energy spectrum should be investigatedover a broader range of electron filling, accompanied by a numericalcalculation using the parameters specific to ZnO, which remains to beinvestigated in the future. The observation of quantum dots in ZnOthat can realize clean and correlated electron systems, and the char-acteristic Kondoeffect reflecting theproperties, is expected toprovidecontrollability for future quantum technologies utilizing electroncorrelation different from that of GaAs and Si.In this study, we have successfully demonstrated the electro-statically defined quantum dot device using high-quality ZnO hetero-structures. Transport measurement through the dot exhibitsthe clear Coulomb peaks and Coulomb diamonds, confirming theformation and control of the quantized states. Additionally, zero-biaspeaks, indicative of the Kondo effect, are observed in the Coulombdiamond, which unexpectedly appears independent of the electronnumber parity. Through the measurement of temperature and mag-netic field dependences of the Kondo resonance peaks, we suggestedthatmultiple orbitals in the dotmaybe involveddue to strong electroninteraction. Our results open new avenues for exploring new physicsand applications of quantum dots, leveraging the distinctive proper-ties of ZnO, such as a simple single electron band, a relativelyweak spin-orbit interaction, low-density nuclear spins, and strongcorrelation effects.MethodsSample fabrication(Mg,Zn)O/ZnO heterostructures are grown on Zn-polar ZnO (0001)substrates at 750 °C by molecular beam epitaxy using distilled pureozone as an oxygen source. Mg content in the heterostructure used inthis study is about 2.5 %. The electron density and mobility are mea-suredby theHall effect asn = 4.9 × 1011 cm−2 andμ = 170,000 cm2 V−1 s−1,respectively, at 1.8 K. The Ti/Au ohmic electrodes are fabricated byphotolithography and lift-off process The AlOx gate insulator isdeposited by atomic layer deposition. The standard electron-beamlithography and lift-off techniques are used to form the Ti/Au top splitgate electrodes.Transport measurementThe transport properties are measured in a dilution refrigeratorequipped with a superconducting magnet. The base temperature is56mK. In the temperature-controlled measurements, a heater in therefrigerator is controlled by a PID controller. The gate voltages aresupplied by DC voltage sources, and the values are optimized to formthe confinement potential of the quantumdot. The conductanceof thedevice is measured using a lock-in amplifier with an excitation fre-quency of 210Hz and a voltage of 6μV. The current from the device isamplified by a current amplifier that converts the current to voltage,and the voltage is supplied to the lock-in amplifier.Data availabilityThe data that support the findings of this study are available in thearticle and its Supplementary Information. Additional data related tothis paper may be requested from the authors.References1. Tarucha, S., Austing, D., Honda, T., Van der Hage, R. & Kouwenho-ven, L. P. Shellfilling and spin effects in a fewelectronquantumdot.Phys. Rev. Lett. 77, 3613 (1996).2. Kouwenhoven, L. P., Austing, D. & Tarucha, S. Few-electron quan-tum dots. Rep. Prog. Phys. 64, 701 (2001).3. Ciorga, M. et al. Addition spectrum of a lateral dot from Coulomband spin-blockade spectroscopy. Phys. Rev. B 61, R16315 (2000).4. Kouwenhoven, L. P. et al. Excitation spectra of circular, few-electronquantum dots. Science 278, 1788–1792 (1997).5. Otsuka, T., Abe, E., Iye, Y. & Katsumoto, S. Control of shell fillingwith Coulomb interaction in quantum dots side-coupled to quan-tum wires. Phys. Status Solidi C. 5, 2873–2875 (2008).6. Ono, K., Austing, D., Tokura, Y. & Tarucha, S. Current rectification byPauli exclusion in a weakly coupled double quantum dot system.Science 297, 1313–1317 (2002).7. Elzerman, J. et al. Single-shot read-out of an individual electron spinin a quantum dot. Nature 430, 431–435 (2004).8. Hanson, R. et al. Single-shot readout of electron spin states in aquantumdot using spin-dependent tunnel rates.Phys. Rev. Lett.94,196802 (2005).9. Amasha, S. et al. Electrical control of spin relaxation in a quantumdot. Phys. Rev. Lett. 100, 046803 (2008).10. Morello, A. et al. Single-shot readout of an electron spin in silicon.Nature 467, 687–691 (2010).11. Kobayashi, K., Aikawa, H., Katsumoto, S. & Iye, Y. Tuning of the Fanoeffect through a quantumdot in anAharonov-bohm interferometer.Phys. Rev. Lett. 88, 256806 (2002).12. Otsuka, T. et al. Fano effect in a few-electron quantum dot. J. Phys.Soc. Jpn. 76, 084706 (2007).13. Cronenwett, S. M., Oosterkamp, T. H. & Kouwenhoven, L. P. A tun-able Kondo effect in quantum dots. Science 281, 540–544 (1998).14. Goldhaber-Gordon, D. et al. From the kondo regime to the mixed-valence regime in a single-electron transistor. Phys. Rev. Lett. 81,5225–5228 (1998).15. Goldhaber-Gordon, D. et al. Kondo effect in a single-electrontransistor. Nature 391, 156–159 (1998).16. Van der Wiel, W. et al. The Kondo effect in the unitary limit. Science289, 2105–2108 (2000).17. Sasaki, S. et al. Kondo effect in an integer-spin quantumdot.Nature405, 764–767 (2000).18. Nygård, J., Cobden, D. H. & Lindelof, P. E. Kondo physics in carbonnanotubes. Nature 408, 342–346 (2000).19. Schmid, J., Weis, J., Eberl, K. & Klitzing, K. V. Absence of odd-evenparity behavior for Kondo resonances in quantum dots. Phys. Rev.Lett. 84, 5824–5827 (2000).20. Sasaki, S., Amaha, S., Asakawa, N., Eto, M. & Tarucha, S. EnhancedKondo effect via tuned orbital degeneracy in a spin 1/2 artificialatom. Phys. Rev. Lett. 93, 017205 (2004).21. Jarillo-Herrero, P. et al. Orbital Kondo effect in carbon nanotubes.Nature 434, 484–488 (2005).22. Kurzmann, A. et al. Kondo effect and spin–orbit coupling in gra-phene quantum dots. Nat. Commun. 12, 6004 (2021).23. Loss, D. & DiVincenzo, D. P. Quantum computation with quantumdots. Phys. Rev. A 57, 120 (1998).24. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).25. Petta, J. R. et al. Coherentmanipulation of coupled electron spins insemiconductor quantum dots. Science 309, 2180–2184 (2005).26. Koppens, F. H. et al. Driven coherent oscillations of a single electronspin in a quantum dot. Nature 442, 766–771 (2006).27. Yoneda, J. et al. Fast electrical control of single electron spins inquantum dots with vanishing influence from nuclear spins. Phys.Rev. Lett. 113, 267601 (2014).Article https://doi.org/10.1038/s41467-024-53890-2Nature Communications |         (2024) 15:9556 6www.nature.com/naturecommunications28. Yoneda, J. et al. A quantum-dot spin qubit with coherence limitedby charge noise and fidelity higher than 99.9%. Nat. Nanotechnol.13, 102–106 (2018).29. Noiri, A. et al. Fast universal quantumgate above the fault-tolerancethreshold in silicon. Nature 601, 338–342 (2022).30. Philips, S. G. et al. Universal control of a six-qubit quantum pro-cessor in silicon. Nature 609, 919–924 (2022).31. Takeda, K., Noiri, A., Nakajima, T., Kobayashi, T. & Tarucha, S.Quantum error correction with silicon spin qubits. Nature 608,682–686 (2022).32. Maurand, R. et al. A CMOS silicon spin qubit. Nat. Commun. 7,13575 (2016).33. Vandersypen, L. et al. Interfacing spin qubits in quantum dots anddonors—hot, dense, and coherent. NPJ Quantum Inf. 3, 34 (2017).34. Veldhorst, M., Eenink, H., Yang, C.-H. & Dzurak, A. S. Silicon CMOSarchitecture for a spin-based quantum computer.Nat. Commun. 8,1766 (2017).35. Camenzind, L.C. et al. A hole spinqubit in afinfield-effect transistorabove 4 kelvin. Nat. Electron. 5, 178–183 (2022).36. Zwerver, A. et al. Qubits made by advanced semiconductor man-ufacturing. Nat. Electron. 5, 184–190 (2022).37. Dean, C. R. et al. Multicomponent fractional quantum Hall effect ingraphene. Nat. Phys. 7, 693–696 (2011).38. Falson, J. et al. Electron scattering times in ZnO based polar het-erostructures. Appl. Phys. Lett. 107, 082102 (2015).39. Kozuka, Y. et al. Single-valley quantum hall ferromagnet in a diluteMgxZn1−xO/ZnO strongly correlated two-dimensional electron sys-tem. Phys. Rev. B 85, 075302 (2012).40. Maryenko, D. et al. Composite fermion liquid to Wigner solid tran-sition in the lowest landau level of zinc oxide. Nat. Commun. 9,4356 (2018).41. Falson, J. et al. Competing correlated states around the zero-fieldWigner crystallization transition of electrons in twodimensions.Nat.Mater. 21, 311–316 (2022).42. Falson, J. et al. Even-denominator fractional quantumhall physics inZnO. Nat. Phys. 11, 347–351 (2015).43. Falson, J. et al. A cascade of phase transitions in an orbitally mixedhalf-filled Landau level. Sci. Adv. 4, eaat8742 (2018).44. Özgür, Ü. et al. A comprehensive review of ZnO materials anddevices. J. Appl. Phys. 98, 041301 (2005).45. Falson, J. et al. MgZnO/ZnOheterostructureswith electronmobilityexceeding 1 × 106cm2/Vs. Sci. Rep. 6, 26598 (2016).46. Tsukazaki, A. et al. Low-temperature field-effect and magne-totransport properties in a ZnO based heterostructure withatomic-layer-deposited gate dielectric. Appl. Phys. Lett. 93,241905 (2008).47. Tsukazaki, A. et al. Observation of the fractional quantumhall effectin an oxide. Nat. Mater. 9, 889–893 (2010).48. Hou, H. et al. Quantized conductance of one-dimensional stronglycorrelated electrons in an oxide heterostructure. Phys. Rev. B 99,121302 (2019).49. De Franceschi, S. et al. Electron cotunneling in a semiconductorquantum dot. Phys. Rev. Lett. 86, 878 (2001).50. Wingreen, N. S. & Meir, Y. Anderson model out of equilibrium:noncrossing-approximation approach to transport through aquantum dot. Phys. Rev. B 49, 11040–11052 (1994).51. Pustilnik, M. & Glazman, L. Kondo effect in quantum dots. J. Phys.Condens. Matter 16, R513 (2004).52. Keller, A. J. et al. Emergent SU(4) Kondo physics in a spin–charge-entangled double quantum dot. Nat. Phys. 10, 145–150 (2014).53. Kasahara, Y. et al. Correlation-enhanced effective mass of two-dimensional electrons in MgxZn1−xO/ZnO heterostructures. Phys.Rev. B 109, 246401 (2012).54. Blesio, G. G., Manuel, L. O., Aligia, A. A. & Roura-Bas, P. Fully com-pensated Kondo effect for a two-channel spin S = 1 impurity. Phys.Rev. B 100, 075434 (2019).55. Izumida, W., Sakai, O. & Shimizu, Y. Kondo effect in single quantumdot systems—studywith numerical renormalizationgroupmethod—.J. Phys. Soc. Jpn. 67, 2444–2454 (1998).56. Roch, N., Florens, S., Costi, T. A., Wernsdorfer, W. & Balestro, F.Observation of the underscreened Kondo effect in a moleculartransistor. Phys. Rev. Lett. 103, 197202 (2009).57. Takada, S. et al. Transmissionphase in theKondo regime revealed ina two-path interferometer. Phys. Rev. Lett. 113, 126601 (2014).58. Wan, Y., Phillips, P. & Li, Q. Suppression of the Kondo effect inquantum dots by even-odd asymmetry. Phys. Rev. B 51,14782–14785 (1995).59. Kozuka, Y. et al. Rashba spin-orbit interaction in a MgxZn1−xO/ZnOtwo-dimensional electron gas studied by electrically detectedelectron spin resonance. Phys. Rev. B 87, 205411 (2013).AcknowledgementsThe authors thank M. Eto, R. Sakano, W. Izumida, M. Takeuchi, A. Kurita,RIEC Fundamental Technology Center, and the Laboratory for Nanoe-lectronics and Spintronics for fruitful discussions and technical support.Part of this work was supported by MEXT Leading Initiative for ExcellentYoung Researchers, Grants-in-Aid for Scientific Research (21K18592,22H04958, 23H01789, 23H04490), Tanigawa Foundation ResearchGrant, Maekawa Foundation Research Grant, The Foundation for Tech-nology Promotion of Electronic Circuit Board, Iketani Science andTechnology Foundation Research Grant, The Ebara Hatakeyama Mem-orial Foundation Research Grant, FRiD Tohoku University, and“Advanced Research Infrastructure forMaterials andNanotechnology inJapan (ARIM)” of the Ministry of Education, Culture, Sports, Science andTechnology (MEXT) (Proposal Number JPMXP1223NM5159). AIMR andMANA are supported by World Premier International Research CenterInitiative (WPI), MEXT, Japan.Author contributionsY.K. and T.O. conceived the ideas. K.N., Y.K., and T.O. led the experi-ments. Y.K., T.K., A.T., M.K., and T.O. fabricated the samples. K.N., K.M.,T.K., Y.F., and T.O. performed the transport measurements. K.N., Y.K.,K.M., Y.F., and T.O. analyzed the data and all the authors discussed theresults. K.N., Y.K., and T.O. wrote the paper with inputs and commentsfrom all authors. T.O. supervised the project.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-53890-2.Correspondence and requests for materials should be addressed toTomohiro Otsuka.Peer review information Nature Communications thanks Louis Gau-dreau and Wilfred van der Wiel for their contribution to the peer reviewof this work. A peer review file is available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in published maps and institutional affiliations.Article https://doi.org/10.1038/s41467-024-53890-2Nature Communications |         (2024) 15:9556 7https://doi.org/10.1038/s41467-024-53890-2http://www.nature.com/reprintswww.nature.com/naturecommunicationsOpen Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons licence, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons licence, unlessindicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons licence and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-53890-2Nature Communications |         (2024) 15:9556 8http://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications Parity-independent Kondo effect of correlated electrons in electrostatically defined ZnO quantum dots Results Device structure Quantum dot formation and control Kondo effect Methods Sample fabrication Transport measurement Data availability References Acknowledgements Author contributions Competing interests Additional information