# Fileset

[s41467-024-48166-8.pdf](https://mdr.nims.go.jp/filesets/a581c9f4-35aa-4ed1-bf0b-224396653334/download)

## Creator

Hongyun Zhang, Qian Li, Youngju Park, Yujin Jia, Wanying Chen, Jiaheng Li, Qinxin Liu, Changhua Bao, Nicolas Leconte, Shaohua Zhou, Yuan Wang, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Jose Avila, Pavel Dudin, Pu Yu, Hongming Weng, Wenhui Duan, Quansheng Wu, Jeil Jung, Shuyun Zhou

## Rights

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

## Other metadata

[Observation of dichotomic field-tunable electronic structure in twisted monolayer-bilayer graphene](https://mdr.nims.go.jp/datasets/6d958197-935f-4a44-b8c2-408866c1d1cd)

## Fulltext

Observation of dichotomic field-tunable electronic structure in twisted monolayer-bilayer grapheneArticle https://doi.org/10.1038/s41467-024-48166-8Observation of dichotomic field-tunableelectronic structure in twisted monolayer-bilayer grapheneHongyun Zhang 1,12, Qian Li 1,12, Youngju Park 2, Yujin Jia3,4, Wanying Chen1,Jiaheng Li3,4, Qinxin Liu1, Changhua Bao1, Nicolas Leconte 2, Shaohua Zhou 1,Yuan Wang1, Kenji Watanabe 5, Takashi Taniguchi 6, Jose Avila 7,Pavel Dudin 7, Pu Yu 1,8, Hongming Weng 3,4,9, Wenhui Duan 1,8,10,Quansheng Wu 3,4, Jeil Jung 2,11 & Shuyun Zhou 1,8Twisted bilayer graphene (tBLG) provides a fascinating platform for engi-neering flat bands and inducing correlated phenomena. By designing thestacking architecture of graphene layers, twisted multilayer graphene canexhibit different symmetries with rich tunability. For example, in twistedmonolayer-bilayer graphene (tMBG)which breaks the C2z symmetry, transportmeasurements reveal an asymmetric phase diagram under an out-of-planeelectric field, exhibiting correlated insulating state and ferromagnetic staterespectively when reversing the field direction. Revealing how the electronicstructure evolves with electric field is critical for providing a better under-standing of such asymmetric field-tunable properties. Here we report theexperimental observation of field-tunable dichotomic electronic structure oftMBG by nanospot angle-resolved photoemission spectroscopy (NanoARPES)with operando gating. Interestingly, selective enhancement of the relativespectral weight contributions from monolayer and bilayer graphene isobserved when switching the polarity of the bias voltage. Combining experi-mental results with theoretical calculations, the origin of such field-tunableelectronic structure, resembling either tBLG or twisted double-bilayer gra-phene (tDBG), is attributed to the selectively enhanced contribution fromdifferent stacking graphene layers with a strong electron-hole asymmetry. Ourwork provides electronic structure insights for understanding the rich field-tunable physics of tMBG.Magic angle twisted bilayer graphene (tBLG) has attracted extensiveresearch interests due to the flat band1 near the Fermi energy EF withemergent correlated phenomena, such as superconductivity2, Mottinsulating state3, and ferromagnetism4,5. By increasing the number ofgraphene layers, twistedmultilayer graphene (tMLG) can exhibit a richspectrum of stacking configurations with distinct symmetries6–9, pro-viding additional controlling knobs for tailoring the physicalproperties. For example, tunable spin-polarized correlated states havebeen reported in twisted double-bilayer graphene (tDBG)10–13, andcorrelated states with non-trivial band topology have been reported inrhombohedral trilayer graphene14–16.Among various structures of tMLG, twisted monolayer-bilayergraphene (tMBG) with a lower symmetry is particularly fascinating17–22.Unlike tBLG and tDBGwhich have symmetric stacking, the asymmetricReceived: 29 August 2023Accepted: 22 April 2024Check for updatesA full list of affiliations appears at the end of the paper. e-mail: syzhou@mail.tsinghua.edu.cnNature Communications |         (2024) 15:3737 11234567890():,;1234567890():,;http://orcid.org/0000-0002-0993-8949http://orcid.org/0000-0002-0993-8949http://orcid.org/0000-0002-0993-8949http://orcid.org/0000-0002-0993-8949http://orcid.org/0000-0002-0993-8949http://orcid.org/0000-0003-1452-7121http://orcid.org/0000-0003-1452-7121http://orcid.org/0000-0003-1452-7121http://orcid.org/0000-0003-1452-7121http://orcid.org/0000-0003-1452-7121http://orcid.org/0000-0001-7671-6142http://orcid.org/0000-0001-7671-6142http://orcid.org/0000-0001-7671-6142http://orcid.org/0000-0001-7671-6142http://orcid.org/0000-0001-7671-6142http://orcid.org/0000-0002-1209-9656http://orcid.org/0000-0002-1209-9656http://orcid.org/0000-0002-1209-9656http://orcid.org/0000-0002-1209-9656http://orcid.org/0000-0002-1209-9656http://orcid.org/0000-0002-1820-5245http://orcid.org/0000-0002-1820-5245http://orcid.org/0000-0002-1820-5245http://orcid.org/0000-0002-1820-5245http://orcid.org/0000-0002-1820-5245http://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/0000-0003-1027-5676http://orcid.org/0000-0003-1027-5676http://orcid.org/0000-0003-1027-5676http://orcid.org/0000-0003-1027-5676http://orcid.org/0000-0003-1027-5676http://orcid.org/0000-0002-5971-0395http://orcid.org/0000-0002-5971-0395http://orcid.org/0000-0002-5971-0395http://orcid.org/0000-0002-5971-0395http://orcid.org/0000-0002-5971-0395http://orcid.org/0000-0002-5513-7632http://orcid.org/0000-0002-5513-7632http://orcid.org/0000-0002-5513-7632http://orcid.org/0000-0002-5513-7632http://orcid.org/0000-0002-5513-7632http://orcid.org/0000-0001-8021-9413http://orcid.org/0000-0001-8021-9413http://orcid.org/0000-0001-8021-9413http://orcid.org/0000-0001-8021-9413http://orcid.org/0000-0001-8021-9413http://orcid.org/0000-0001-9685-2547http://orcid.org/0000-0001-9685-2547http://orcid.org/0000-0001-9685-2547http://orcid.org/0000-0001-9685-2547http://orcid.org/0000-0001-9685-2547http://orcid.org/0000-0002-9154-4489http://orcid.org/0000-0002-9154-4489http://orcid.org/0000-0002-9154-4489http://orcid.org/0000-0002-9154-4489http://orcid.org/0000-0002-9154-4489http://orcid.org/0000-0003-2523-0905http://orcid.org/0000-0003-2523-0905http://orcid.org/0000-0003-2523-0905http://orcid.org/0000-0003-2523-0905http://orcid.org/0000-0003-2523-0905http://orcid.org/0000-0002-9841-8610http://orcid.org/0000-0002-9841-8610http://orcid.org/0000-0002-9841-8610http://orcid.org/0000-0002-9841-8610http://orcid.org/0000-0002-9841-8610http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-48166-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-48166-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-48166-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-48166-8&domain=pdfmailto:syzhou@mail.tsinghua.edu.cnstacking ofmonolayer graphene on Bernal-stacked bilayer graphene intMBG breaks the C2z symmetry (Fig. 1a), making it asymmetric or“polar” along the out-of-plane direction. Applying an out-of-planeelectric field can further enhance the asymmetry, giving rise to a richphase diagram which strongly depends on the field direction. So far,transport measurements have reported an asymmetric field-tunablephase diagram19, which changes from a correlated phase (similar totBLG) to a ferromagnetic phase (reminiscent of tDBG) when reversingthe electric field direction. Such field-tunable correlated phenomenasuggest a strong modification of electronic structure under theapplication of an electric field. Directly probing how the actual elec-tronic structure evolves with electric field is therefore critical forproviding a better understanding of such dichotomic field-tunablephysics.Here, by performing NanoARPES measurements (see schematicillustration in Fig. 1a) on tMBG with a twist angle of 2.2° with operandogating, we report the observation of a dichotomic response of theelectronic structure to the electric field (induced by a bias voltage).The main experimental results are schematically summarized inFig. 1b–d and supported by data shown in Fig. 1e–g. We find that,although the bottom bilayer graphene (2 ML) always has a weakerspectral intensity compared with top monolayer (1 ML) graphene, apositive bias voltage (induced electric field Eind pointing from mono-layer to bilayer) enhances the relative spectral weight contributionfrom 1 ML graphene (pointed by red arrow in Fig. 1e) as well as theconical shaped feature, while a negative bias voltage enhances therelative contribution from 2ML graphene, leading to flatter electronicstructure near the Fermi energy (Fig. 1g). A comparison between theexperimental results with theoretical calculations allows to reveal theorigin of dichotomic field-tunable properties of tMBG from an elec-tronic structure perspective.Identifying the flat band, monolayer and bilayergraphene features in tMBGThe high-quality tMBG sample was prepared by the clean dry transfermethod23,24 (see method and Supplementary Figs. 1, 2 for more details).The twist angle was determined from the moiré period using lateralforce atomic force microscope (L-AFM) measurements and furtherconfirmedbyNanoARPESmeasurements (see Supplementary Figs. 3, 4).Figure 2a–f shows NanoARPES intensity maps measured at energiesfrom EF to −0.5 eVwith twist angle of 2.2°. The Fermi surfacemap showstwo intensity spots at the Brillouin zone (BZ) corners of the top mono-layer graphene (red dot, K1) and the bottom bilayer graphene (blue dot,K2) respectively, with weaker replicas at the moiré superlattice Brillouinzone (mSBZ) corners. Moving down in energy, these spots expand intopockets and hybridize with each other, resulting in a flower-shapedpattern at higher binding energy (Fig. 2d–f). Here the choice of twistangle of 2.2° is ideal for the investigation of the electronic structure andits field tunability, because the slightly larger angle than themagic anglemakes it easier to resolve the contributions frommonolayer and bilayergraphene, meanwhile the flat band can still be observed.The high-quality NanoARPES data allow to resolve the flat bandand identify spectral features from monolayer and bilayer graphene.Figure 2g shows dispersion image measured by cutting through twomSBZ corners as schematically illustrated in the inset. An isolated flatband (pointed by red arrow) is observed with a clear hybridization gap(pointed by black arrow), which separates the flat band from theremote bands at higher binding energy. Similar features are also cap-tured by the calculated spectrum shown in Fig. 2h using an effectivetight-bindingmodel (seeMethod formore details), where red and bluecolors represent projected contributions from the top 1 ML and bot-tom 2 ML graphene layers respectively. From the experimental data,the extracted bandwidth of the flat band is 70 ± 10meV (see Supple-mentary Fig. 5 formore details), which is comparable to the calculatedCoulomb energy3,Ueff = e2/(4πϵ0ϵrλm) = 75meV, where ϵ0 and ϵr are thedielectric constants of the vacuum and the substrate respectively, andλm is the moiré period. The similar energy scales between the band-width and the Coulomb energy suggest that 2.2° tMBG is near thecorrelated regime, in linewith the larger range of twist angle where theflat band exists9,25,26. Figure 2i shows dispersion image measured bycutting through the BZ corners of both monolayer and bilayer gra-phene, and the calculated spectrum is shown in Fig. 2j for comparison.An overall conical dispersion (guided by red dashed curves in Fig. 2i) isobserved around K1 together with their moiré replica bands (brownBNgraphiteEindVga1 ML2 MLθZonePlateNanoARPESTwisted monolayer-bilayer graphene b c de f gVg < 0Vg = 0Vg > 0Vg = -20 VVg = 0Vg = 20 V0.0-0.5-1.0-1.5 0.0-0.2 0.2 0.0-0.2 0.20.0-0.5-1.0-1.50.0-0.5-1.0-1.50.0-0.2 0.21 ML2 ML1 ML2 MLStronger StrongerFig. 1 | Schematic summary of the electric field-tunable electronic structurein tMBG. a Schematic for NanoARPES measurements of tMBG with operandogating capability. The red arrow indicates the induced electric field Eind amongthree graphene layers under positive bias voltage. b–d Schematic summary of thefield-tunable electronic structure. e–gDispersion imagesmeasured under positive,zero, and negative bias voltages, respectively. Colors represent the NanoARPESmeasured intensity as indicated by the colorbar. Themeasurement direction is thatconnecting the BZ corners of the top (red dot, K1) and bottom (blue dot, K2)graphene, as indicated by the black line in the inset of (e).Article https://doi.org/10.1038/s41467-024-48166-8Nature Communications |         (2024) 15:3737 2dashed curves), and two parabolic bands from bilayer graphene (bluedashed curves) are observed near K2. In the region where these bandsoverlap, there is a strong intensity suppression and the flat bandemerges as a result of the interlayer interaction (see SupplementaryFig. 5), similar to the case of tBLG27,28, while here the asymmetricstacking of tMBG provides additional field-tunability. We note thatwhile the hybridization gap (pointed by black arrow in Fig. 2j) is toosmall to be resolved from the experimental data directly, however, asudden change of intensity is observed at the flat band edge (Fig. 2i),suggesting an overall agreement with the calculated spectrum inFig. 2j. The comparison between experimental results and theoreticalcalculations allows to reveal the flat band as well as spectroscopiccontributions from monolayer and bilayer graphene, which lays animportant foundation for further investigating the field-tunable elec-tronic structure.Dichotomic field-tunable electronic structureFigure 3a–j shows anoverviewof dispersion imagesmeasured throughK1 andK2with bias voltages from−20 V to30V.Here thebias voltageVgis applied on the bottom gate, which not only tunes the carrier con-centration n, but also applies an electric field29,30. There are a fewobservations from the evolution of the electronic structure. First of all,a negative bias voltage (Eind pointing from bilayer to monolayer gra-phene) dopes the sample with holes and shifts the bands up, while apositive bias voltage leads to electron doping and shifts the bandsdown, showing the same trend as gated graphene devices29–32. From0V to 30V, the bands shift in energy by 140 ± 30meV (see Supple-mentary Fig. 6), which is consistent with the estimated carrier densityfrom the geometric capacitance (see Supplementary Note 3 for moredetails). Secondly, the flat band near the Fermi energy can be selec-tively tuned to be more extended (flatter) or dispersive by switchingthe bias voltage (see Supplementary Fig. 7 for more details). Fornegative bias voltage, the flat band becomes more extended in themomentum space (red dotted curve in Fig. 3a), while for positive biasvoltage, more pronounced “M-shaped” dispersion with a conicalbehavior is observed (red-to-blue dotted curve in Fig. 3j). Thirdly, therelative spectral weight contributions from monolayer and bilayergraphene can also be selectively enhanced by reversing the bias vol-tage, as indicated by red arrow in Fig. 3j and blue arrow in Fig. 3a (seeSupplementary Fig. 8). This is also evident in the momentum dis-tribution curves (MDCs) measured at a few representative bias vol-tages in Fig. 3k, where the red and blue dashed arrows indicate therelative spectral weight transfer to monolayer and bilayer grapheneunder positive and negative bias voltages respectively. Figure 3qshowsa comparisonbetweenMDCsmeasured atbias voltages of−20V(blue curve) and 30 V (red curve), where a relative spectral weighttransfer from 2ML to 1ML bands is clearly observed when increasingthe bias voltage.The dichotomic field response of the electronic structure is alsorevealed in the calculated spectra in Fig. 3l–p,where a stronger relativespectral weight contribution is observed for monolayer valence bandat positive bias voltage. Interestingly, at negative bias voltage (Fig. 3l),the enhanced relative spectral weight contribution from bilayer gra-phene in the valence band (blue arrow in Fig. 3l) is also accompaniedby a reduced spectral weight contribution from the conduction ofbilayer graphene (light blue arrow in Fig. 3l), suggesting a strongerelectron-hole asymmetry than that at zero bias voltage (Fig. 3n). Inaddition, the application of a bias voltage also leads to flatter disper-sion for bilayer graphene bands, similar to gated bilayer graphene33.Moreover, the calculated spectra show that the valence band at posi-tive bias voltage shows similar dispersion to the conduction band atnegative bias voltage (see Supplementary Fig. 9 for more details),suggesting that reversing the bias voltage can lead to a switchingbetween the electron and hole bands in tMBG.Origin of the field-tunable dichotomic electronicstructureTo reveal the origin of the spectral weight transfer and the field-tunable electronic structureof tMBG,we show inFig. 4 the comparisonof calculated energy contours at −0.2 eV for tBLG, tMBG and tDBGFig. 2 | Fermi surface topology and coexistence of monolayer and bilayergraphene features in the 2.2∘ tMBG. a–f ARPES intensity maps measured atenergies from EF to −0.50 eV. The red and blue lines mark the Brillouin zoneboundaries for topmonolayer graphene andbottombilayer graphene respectively.The black dotted hexagons represent the moiré Brillouin zones. g, h Dispersionimage measured along the black line indicated by the inset of (g), and calculatedspectrum for comparison. Red and blue colors in (h) represent projected con-tributions from the top 1 ML and bottom 2 ML graphene layers, respectively. Redand black arrows point to the flat band and hybridization gap respectively.i, jDispersion imagemeasured along the black line indicated by the inset of (i), andcalculated spectrum for comparison. Red, blue and brown dashed curves indicatethe bands from 1 ML, 2 ML and the moiré replica band.Article https://doi.org/10.1038/s41467-024-48166-8Nature Communications |         (2024) 15:3737 3under positive and negative bias voltages, respectively. For tBLG andtDBG, the energy contours remain similar when reversing the biasvoltage (see comparison between Fig. 4a, d and Fig. 4c, f), except thatthe pattern centering at K1 now switches to K2 and vice versa, which isconsistent with the overall symmetric phase diagram from transportmeasurements of tBLG4,34 and tDBG11–13. In sharp contrast, reversing thebias voltage leads to a dramatic change in the energy contour of tMBG(see Fig. 4b, e). Remarkably, the energy contour of tMBG under posi-tive bias voltage (Fig. 4b) is strikingly similar to that for tBLG (Fig. 4a),while the energy contour under negative bias voltage (Fig. 4e)resembles that of tDBG (Fig. 4f), again supporting the asymmetric or“polar” electric field response.To resolve the puzzle of how tMBG under bias voltage can exhibitelectronic structures similar to tBLG and tDBG, we show in Fig. 4g–lenergy contours at −0.2 eV projected onto each constitute graphenelayers for tBLG, tMBG, and tDBG. For these three different types oftwisted structures, the energy contours for graphene layers above theinterface (L3 and L4) all exhibit clockwise vortex pattern centered at K1(red dot), while the bottom layers (L1 and L2) show counter-clockwisevortex pattern centered at K2 (blue dot). This is consistent with theirrelative rotation directions in the real space, and reflects the chiralproperties of twisted graphene structures35,36. Moreover, for positivebias voltage, the energy contours for the topgraphene layers (L3 and L4)show a larger pocket size with an enhanced spectral weight, suggestingthe enhanced contributions from top graphene layers (Fig. 4g–i), whilefor negative bias voltage, contributions from the bottom layers areenhanced (Fig. 4j–l) (see Supplementary Fig. 10 for the calculated layer-resolved density of states (DOS)). Therefore, although tMBG has onemore layer (bottom layer, L1) than tBLG, the energy contour for tMBGunder positive bias voltage is still similar to that of tBLG due to thesmaller contribution of spectral weight from L1. The energy contour fortDBG, however, is quite different from tMBG, because tMBG lacks thetop layer L4, which has a strong spectral weight. Similarly, for negativebias voltage, the energy contour of tMBG is overall similar to that oftDBG due to the smaller pocket of L4. Although the modulation in thespectral weight contribution of different layers is small, the asymmetricshape of pockets under reversed bias voltage is still significant enoughto explain the origin of the overall asymmetric behavior in the tMBG.The layer-projected electronic structure analysis suggests that thedichotomic field-tunable electronic structure under positive andnegative bias voltages originates from the selectively enhanced con-tributions from different constitute graphene layers, which is alsointrinsically related to the breaking of theC2z symmetry in tMBG.Whilea field-tunable electronic structure has been deduced from the asym-metric phase diagram reported in transportmeasurements19, our workprovides direct electronic structure insights for understanding thefield-tunable physics. In particular, by projecting the spectral con-tribution from each individual layer in themomentum space, our workalso providesmore complete andmicroscopic information onhow theelectric field actually tunes the electronic structure of each individuallayer. We envision that similar strategies can be extended to otherasymmetric twisted bilayer ormultilayer systems,where the crystallinesymmetry can be used as a tuning knob to obtain exotic properties,such as gate-tunable ferroelectricity and nonlinear optical response.MethodsSample preparation with gating capabilityThe tMBG sample was prepared by using the clean dry transfermethod23,24. First, the graphene flake with both monolayer and bilayerparts connected togetherwas exfoliatedonto a clean SiO2/Si substrate.A thin BN flake attached to PVA/PDMS (Polyvinyl Alcohol/Poly-dimethylsiloxane) was then positioned above the graphene under anoptical microscope to pick up the bilayer graphene part. The mono-layer graphene on the SiO2/Si substrate was rotated by the desired(Δ = -100 meV) (Δ = -50 meV) (Δ = 0 meV) (Δ = 50 meV) (Δ = 100 meV)Intensity (arb. units)Intensity (arb. units)Fig. 3 | Dichotomic field response of the electronic structure under negativeand positive bias voltages in a 2.2∘ tMBG. a−j Dispersion images measuredthrough K1 and K2 (indicated by the inset) with bias voltages from -20V to 30V.Dotted red and blue curves in (a–j) are guiding curves. k Representative MDCsextracted at energies indicated by gray dashed arrow in (a) and black tick marks in(c, e, g, h, j) to reveal the selectively enhanced spectral weight from 1ML (pointedby red dashed arrow) and 2ML graphene (pointed by blue dashed arrow) underpositive and negative bias voltages, respectively. Colored marks and curvescorrespond to the experimental results andfitting curves. l–pCalculated spectra atnegative (l,m), zero (n), and positive (o, p) bias voltages, with red and blue colorsrepresenting the contribution from 1ML and 2ML graphene respectively. Thevalues of the interlayer potential difference (Δ) used for the calculations are Δ =−100, −50, 0, 50 and 100 meV respectively. q Comparison of MDCs extracted at−20V and 30V, which shows relatively enhanced 2ML or 1ML bands at negativeand positive bias voltages.Article https://doi.org/10.1038/s41467-024-48166-8Nature Communications |         (2024) 15:3737 4angle and picked up by bilayer-graphene/BN/PVA/PDMS to form thetMBG/BN/PVA/PDMS structure. Subsequently, the tMBG/BN/PVA/PDMS was flipped over, and the tMBG/BN/PVA was picked up byanother PDMS stamp to form PVA/BN/tMBG/PDMS structure. The PVAfilm was dissolved by immersing the entire structure in water for sev-eral hours, and the tMBG/BN was transferred onto a graphite flake,which was in contact with the gold-plated pattern as the bottom gateelectrode. Finally, two narrow pieces of graphite were used to elec-trically connect tMBG and the gold-coated pattern to ensure goodelectrical conductivity for ARPES measurements. The gold-platedpattern was connected to the gating electrode of the sample holder bywire bonding. See Supplementary Figs. 1, 2 for more details.AFM measurementsThe twist angle canbedeterminedby combiningNanoARPES and lateralforceAFM(L-AFM)measurements. For theL-AFMmeasurements, siliconnitride probes were used to obtain the lateral force and topographyimage under the contact mode. We note that L-AFM measurement isparticularly sensitive to themoiré superlattice period because the stick-slip effect would occur at themoiré superlattice scale37. After extractingthe moiré superlattice period λm from L-AFM measurements, the twistangle θ can be further determined by λm=a/(2sin(θ/2)).ARPES measurementsThe tMBG sample was annealed at 150 °C in ultrahigh vacuum (UHV)until sharp dispersions were observed. NanoARPESmeasurements wereperformed at the beamline ANTARES of the synchrotron SOLEIL inFrance with a beam size of 500–700nm and photon energy of 100eV.The incident light is set to p-polarized and the analyzer slit direction ishorizontal (see Supplementary Fig. 12). The overall energy and angularresolution were set to 50meV and 0.1°, respectively. The measurementtemperature was 70K in a working vacuum better than 2 × 10−10mbar.Theoretical calculationsThe electronic structure calculations are performed by using a real-space tight-binding model, where we define the Hamiltonian for tBLG,tMBG, and tDBG asH =Xi,jtijcyi cj +Xiðεi +V ‘2iÞcyi ci ð1Þwhere εi and tij are the on-site potential energy of atom i and thehopping parameter between atom i and j. We use the effective tight-binding model parameters for εi and tij using either the monolayer38version or the Bernal bilayer39 version depending on which part of thesystem is under consideration. We set the effective nearest hoppingterm t0 = − 3.1 eV and the interlayer hopping scaling factor S =0.895 forthe Scaled Hybrid Exponential (SHE) model40, to effectively match theFermi velocity υF ≈ 1 × 106m/s and themagic angle 1.08° of tBLG. In thecalculations, a commensurate superlattice is used, and here we use atwist angle of 2.28° to perform the calculations, which is the closestcommensurate twist angle near 2.2°. Classical structural relaxationusing LAMMPS41,42 hasbeen implemented in the calculation. In order todescribe the electric field effect under applying bias voltages, we labelthegraphene layers from L1 (bottom layer) to L4 (top layer) as indicatedby Fig. 4, and the potential energy for different layers are set to beV1 = − V4 = − 3Δ/2 and V2 = −V3 = −Δ/2. We note that a positive biasvoltage Vg > 0 gives rise to Δ >0, leading to an induced electric fieldFig. 4 | Field-tunable electronic structure from theoretical calculations, andlayer-resolved energy contours for positive and negative bias voltages.a–f Calculated intensity maps at constant energy of -0.2 eV for tBLG, tMBG andtDBG under positive (a–c) and negative (d–f) bias voltages with interlayer potentialdifference of Δ = 100meV and −100meV respectively. The scale bar in (a) is 0.1 Å−1.g–i Schematic illustrations of field-induced selectively enhanced contributionunderpositivebias voltage fromdifferent layersof tBLG, tMBGand tDBG (indicatedby dark and light shaded colors in the top panel schematic), and calculated layer-projected energy contours at −0.2 eV (lower panels, positive bias voltage withΔ = 100meV). j–l Schematic illustrations of field-induced selectively enhancedcontribution from different layers of tBLG, tMBG and tDBG under a negative biasvoltage (top panels), and calculated layer-projected intensity maps at −0.2 eV(lower panels, Δ = −100meV). The dotted rectangles are used to highlight thesimilarity between tBLG and tMBG at positive bias voltage, and tMBG and tDBG atnegative bias voltage.Article https://doi.org/10.1038/s41467-024-48166-8Nature Communications |         (2024) 15:3737 5Eind pointing from monolayer to bilayer graphene, where the totalelectric field contains Etotal = Eext + Eind contains the external electricfield Eext and the induced electric field Eind. An adjustable chemicalpotential μ is used to introduce an overall shift in the tBLG, tMBG andtDBG bands to allow a fair comparison between bands at specificenergy cuts (Fig. 4). To simulate the intensity of the ARPES data, wecalculate the sublattice-resolved spectral functions using a band-unfoldingmethod43–45, which enables to obtain the layer- or sublattice-resolved electronic structure calculation. The bandunfolding code canbe found as WannierTools46 on the GitHub. See Supplementary Fig. 11and more calculation details in the Supplementary Information.Data availabilityAll relevant data of this study are available within the paper and itsSupplementary Information files. Source data are provided withthis paper.References1. Bistritzer, R.&MacDonald, A.H.Moirébands in twisteddouble-layergraphene. Proc. Natl. Acad. Sci. 108, 12233–12237 (2011).2. Cao, Y. et al. Unconventional superconductivity in magic-anglegraphene superlattices. Nature 556, 43–50 (2018).3. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).4. Sharpe, A. L. et al. Emergent ferromagnetism near three-quartersfilling in twisted bilayer graphene. Science 365, 605–608 (2019).5. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiréheterostructure. Science 367, 900–903 (2020).6. Suárez Morell, E., Pacheco, M., Chico, L. & Brey, L. Electronic prop-erties of twisted trilayer graphene. Phys. Rev. B 87, 125414 (2013).7. Khalaf, E., Kruchkov, A. J., Tarnopolsky, G. & Vishwanath, A. Magicangle hierarchy in twisted graphene multilayers. Phys. Rev. B 100,085109 (2019).8. Liu, J., Ma, Z., Gao, J. & Dai, X. Quantum valley hall effect, orbitalmagnetism, and anomalous hall effect in twisted multilayer gra-phene systems. Phys. Rev. X 9, 031021 (2019).9. Ma, Z. et al. Topological flat bands in twisted trilayer graphene. Sci.Bull. 66, 18–22 (2021).10. Burg, G. W. et al. Correlated insulating states in twisted doublebilayer graphene. Phys. Rev. Lett. 16, 520–525 (2020).11. Cao, Y. et al. Tunable correlated states and spin-polarized phases intwisted bilayer-bilayer graphene. Nature 583, 215–220 (2020).12. Liu, X. et al. Tunable spin-polarized correlated states in twisteddouble bilayer graphene. Nature 583, 221–225 (2020).13. Shen, C. et al. Correlated states in twisted double bilayer graphene.Nat. Phys. 16, 520–525 (2020).14. Chen, G. et al. Signatures of tunable superconductivity in a trilayergraphene moiré superlattice. Nature 572, 215–219 (2019).15. Chen, G. et al. Tunable correlated Chern insulator and ferro-magnetism in a moiré superlattice. Nature 579, 56–61 (2019).16. Chen, G. et al. Evidence of a gate-tunableMott insulator in a trilayergraphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).17. Polshyn, H. et al. Electrical switching ofmagnetic order in an orbitalChern insulator. Nature 588, 66–70 (2020).18. Xu, S. et al. Tunable van Hove singularities and correlated states intwisted monolayer-bilayer graphene. Nat. Phys. 17, 619–626 (2021).19. Chen,S. et al. Electrically tunablecorrelatedand topological states intwisted monolayer-bilayer graphene. Nat. Phys. 17, 374–380 (2021).20. He, M. et al. Competing correlated states and abundant orbitalmagnetism in twisted monolayer-bilayer graphene. Nat. Commun.12, 4727 (2021).21. Li, S.-y et al. Imaging topological and correlated insulating states intwistedmonolayer-bilayergraphene.Nat.Commun. 13, 4225 (2022).22. Zhang, C. et al. Local spectroscopy of a gate-switchable moiréquantum anomalous hall insulator. Nat. Commun. 14, 3595 (2023).23. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).24. Cao, Y. et al. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117,116804 (2016).25. Rademaker, L., Protopopov, I. V. & Abanin, D. A. Topological flatbands andcorrelated states in twistedmonolayer-bilayer graphene.Phys. Rev. Res. 2, 033150 (2020).26. Park, Y., Chittari, B. L. & Jung, J. Gate-tunable topologicalflat bands intwistedmonolayer-bilayergraphene.Phys. Rev. B 102, 035411 (2020).27. Utama, M. I. B. et al. Visualization of the flat electronic band intwisted bilayer graphene near the magic angle twist. Nat. Phys. 17,184–188 (2021).28. Lisi, S. et al. Observation of flat bands in twisted bilayer graphene.Nat. Phys. 17, 189–193 (2021).29. Nguyen, P. V. et al. Visualizing electrostatic gating effects in two-dimensional heterostructures. Nature 572, 220–223 (2019).30. Joucken, F. et al. Visualizing the effect of an electrostatic gate withangle-resolved photoemission spectroscopy. Nano Lett. 19,2682–2687 (2019).31. Nunn, J. E. et al. ARPES signatures of few-layer twistronic gra-phenes. Nano Lett. 23, 5201–5208 (2023).32. Dale, N. et al. Layer-dependent interaction effects in the electronicstructure of twisted bilayer graphene devices. Nano Lett. 23,6799–6806 (2023).33. Ohta, T., Bostwick, A., Seyller, T., Horn, K. & Rotenberg, E. Con-trolling the electronic structure of bilayer graphene. Science 313,951–954 (2006).34. Yankowitz, M. et al. Tuning superconductivity in twisted bilayergraphene. Science 363, 1059–1064 (2019).35. Angeli, M. et al. EmergentD6 symmetry in fully relaxedmagic-angletwisted bilayer graphene. Phys. Rev. B 98, 235137 (2018).36. Yananose, K. et al. Chirality-induced spin texture switching intwisted bilayer graphene. Phys. Rev. B 104, 075407 (2021).37. Zhang, S. et al. Dual-scale stick-slip friction on Graphene/h −BNmoiré superlattice structure. Phys. Rev. Lett. 128, 226101 (2022).38. Jung, J. & MacDonald, A. H. Tight-binding model for graphene π-bands frommaximally localized wannier functions. Phys. Rev. B 87,195450 (2013).39. Jung, J. &MacDonald, A. H. Accurate tight-bindingmodels for the πbands of bilayer graphene. Phys. Rev. B 89, 035405 (2014).40. Leconte, N., Javvaji, S., An, J., Samudrala, A. & Jung, J. Relaxationeffects in twisted bilayer graphene: A multiscale approach. Phys.Rev. B 106, 115410 (2022).41. Plimpton, S. Fast parallel algorithms for short-range moleculardynamics. J. Comput. Phys. 117, 1–19 (1995).42. Thompson, A. P. et al. LAMMPS - a flexible simulation tool forparticle-based materials modeling at the atomic, meso, and con-tinuum scales. Comput. Phys. Commun. 271, 108171 (2022).43. Ku, W., Berlijn, T. & Lee, C.-C. Unfolding first-principles bandstructures. Phys. Rev. Lett. 104, 216401 (2010).44. Lee, C.-C., Yamada-Takamura, Y. & Ozaki, T. Unfolding method forfirst-principles LCAO electronic structure calculations. J. Phys.Condens. Matter 25, 345501 (2013).45. Nishi, H., Matsushita, Y.-i & Oshiyama, A. Band-unfolding approachto moiré-induced band-gap opening and Fermi level velocityreduction in twisted bilayer graphene. Phys. Rev. B 95,085420 (2017).46. Wu, Q. et al. Wanniertools: An open-source software package fornovel topologicalmaterials.Comput. Phys. Commun.224, 405–416(2018).AcknowledgementsThis work ismainly supported by theNational Key R&DProgramofChina(Grant No. 2021YFA1400100, 2022YFA1403800), the National NaturalArticle https://doi.org/10.1038/s41467-024-48166-8Nature Communications |         (2024) 15:3737 6Science Foundation of China (Grant No. 12234011, 52025024,92250305, 11725418, 52388201, 12274436). H.Z. and C.B. acknowledgesupport from the Shuimu Tsinghua Scholar program, the Project fundedby China Postdoctoral Science Foundation (Grant No. 2022M721887,2022M721886), and the National Natural Science Foundation of China(12304226). K.W. and T.T. acknowledge support from the JSPS KAKENHI(Grant Numbers 20H00354 and 23H02052) and World Premier Inter-national Research Center Initiative (WPI), MEXT, Japan. H.W. and Y.J.acknowledge support from the Informatization Plan of the ChineseAcademy of Sciences (CASWX2021SF-0102). J.J. acknowledges thefunding from the National Research Foundation of Korea (NRF) throughgrant numbers NRF2020R1A2C3009142, the support by the KoreanMinistry of Land, Infrastructure and Transport (MOLIT) from the Innova-tive Talent Education Program for Smart Cities and the computationalsupport from KISTI Grant No. KSC-2022-CRE-0514 and the resources ofUrban Big data and AI Institute (UBAI) at UOS. Y.P. and N.L. were sup-ported by the NRF through grant numbers NRF2020R1A5A1016518and the Korean NRF through Grant RS-2023-00249414. We acknowl-edge SOLEIL for the provision of synchrotron radiation facilities.Author contributionsShuyun Z. conceived the research project. H.Z., Qian L., W.C., J.A., P.D.,Qinxin L., and Shuyun Z. performed the NanoARPESmeasurements andanalyzed the data. C.B., Shaohua Z. and Y.W. contributed to the dataanalysis and discussions. Qian L. prepared the tMBG samples. Qian L.and P.Y. performed the AFM measurements. K.W. and T.T. grew the BNcrystals. Y.P., Y.J., J.L., N.L., Q.W., H.W., W.D., and J.J. performed thecalculations. H.Z., Qian L., and Shuyun Z. wrote the manuscript, and allauthors contributed to the discussions and commented on themanuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-48166-8.Correspondence and requests for materials should be addressed toShuyun Zhou.Peer review information Nature Communications thanks the anon-ymous reviewers for their contribution to the peer review of 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.Open 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) 20241State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, PR China. 2Department ofPhysics, University of Seoul, Seoul 02504, Korea. 3Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy ofSciences, Beijing 100190, PR China. 4University of Chinese Academy of Sciences, Beijing 100049, PR China. 5Research Center for Electronic and OpticalMaterials, National Institute forMaterials Science, 1-1 Namiki, Tsukuba305-0044, Japan. 6ResearchCenter forMaterials Nanoarchitectonics, National Institutefor Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 7Synchrotron SOLEIL, L’Orme des Merisiers, Departamentale 128, 91190 Saint-Aubin, France.8Frontier Science Center for Quantum Information, Beijing 100084, PR China. 9Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, PRChina. 10Institute for Advanced Study, Tsinghua University, Beijing 100084, PR China. 11Department of Smart Cities, University of Seoul, Seoul 02504, Korea.12These authors contributed equally: Hongyun Zhang, Qian Li. e-mail: syzhou@mail.tsinghua.edu.cnArticle https://doi.org/10.1038/s41467-024-48166-8Nature Communications |         (2024) 15:3737 7https://doi.org/10.1038/s41467-024-48166-8http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/mailto:syzhou@mail.tsinghua.edu.cn Observation of dichotomic field-tunable electronic structure in twisted monolayer-bilayer graphene Identifying the flat band, monolayer and bilayer graphene features in�tMBG Dichotomic field-tunable electronic structure Origin of the field-tunable dichotomic electronic structure Methods Sample preparation with gating capability AFM measurements ARPES measurements Theoretical calculations Data availability References Acknowledgements Author contributions Competing interests Additional information