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I. Babich, I. Reznikov, I. Begichev, A. E. Kazantsev, S. Slizovskiy, D. Baranov, M. Šiškins, Z. Zhan, P. A. Pantaleon, M. Trushin, J. Zhao, S. Grebenchuk, K. S. Novoselov, [K. Watanabe](https://orcid.org/0000-0003-3701-8119), [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), V. I. Fal’ko, A. Principi, A. I. Berdyugin

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[Milli-Tesla quantization enabled by tuneable Coulomb screening in large-angle twisted graphene](https://mdr.nims.go.jp/datasets/6adeceb0-1037-4cfc-9bc5-c40694ed4631)

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Milli-Tesla quantization enabled by tuneable Coulomb screening in large-angle twisted grapheneArticle https://doi.org/10.1038/s41467-025-62492-5Milli-Tesla quantization enabled by tuneableCoulomb screening in large-angle twistedgrapheneI. Babich 1,2 , I. Reznikov1,2, I. Begichev1,2, A. E. Kazantsev3, S. Slizovskiy 3,4,D. Baranov2, M. Šiškins 2, Z. Zhan 5, P. A. Pantaleon 5, M. Trushin 1,2,J. Zhao2, S. Grebenchuk2, K. S. Novoselov 1,2, K. Watanabe 6, T. Taniguchi 7,V. I. Fal’ko 3,4, A. Principi 3 & A. I. Berdyugin 1,8The electronic quality of graphene has improved significantly over the pasttwo decades, revealing novel phenomena. However, even state-of-the-artdevices exhibit substantial spatial charge fluctuations originating fromcharged defects inside the encapsulating crystals, limiting their performance.Here, we overcome this issue by assembling devices in which graphene isencapsulated by other graphene layers while remaining electronically decou-pled from them via a large twist angle (~10–30°). Doping of the encapsulatinggraphene layer introduces strong Coulomb screening, maximized by the sub-nanometer distance between the layers, and reduces the inhomogeneity in theadjacent layer to just a few carriers per square micrometre. The enhancedquality manifests in Landau quantization emerging atmagnetic fields as low as~5milli-Tesla and enables resolution of a small energy gap at the Dirac point.Our encapsulation approach can be extended to other two-dimensional sys-tems, enabling further exploration of the electronic properties of ultrapuredevices.Electron mobility is a critical figure of merit for semiconductors,relevant for observation of quantum phenomena and electronicapplications1–8. Recently, graphene was established as a material withthe highest room-temperature mobility9,10 ~150,000 cm2V−1s−1 which istwo orders of magnitude higher than that of traditional semi-conductors. However, the graphene mobility at cryogenic tempera-tures is still lower than that of GaAs two-dimensional electron gases(2DEGs), which electronic quality has been gradually improving overmany decades4–7, and these days can reach8 57 × 106 cm2V−1s−1 underoptimal doping. In contrast, state-of-the-art graphene devices reachmobilities9–24 of only (1–3) × 106 cm2V−1s−1, an order ofmagnitude lower.Potentially, this discrepancy should vanish close to the chargeneutrality point (CNP), where graphene mobility theoretically diver-ges. However, in real devices, the electron transport near the CNP isstrongly affected by the macroscopic spatial charge fluctuations10,21–28,usually referred to as electron-hole puddles28, limiting grapheneperformance.In the first generation of devices, graphene was placed on top ofSi/SiO2 substrate1–3, where itwas influencedby contamination from theenvironment, surface roughness, and impurities, which limited mobi-lity to μ �104 cm2V−1s−1 and caused substantial charge density fluctua-tions of δn � 1011–1012 cm−2. A significant improvement was achievedthrough the encapsulation of graphene with atomically flat hexagonalboron nitride (hBN) dielectric crystals9–24, which reduced chargeReceived: 16 January 2025Accepted: 22 July 2025Check for updates1Department of Materials Science and Engineering, National University of Singapore, Singapore, Singapore. 2Institute for Functional Intelligent Materials,National University of Singapore, Singapore, Singapore. 3Department of Physics and Astronomy, University of Manchester, Manchester, UK. 4NationalGraphene Institute, University of Manchester, Manchester, UK. 5Imdea Nanoscience, Madrid, Spain. 6Research Centre for Electronic and Optical Materials,National Institute for Material Science, Tsukuba, Japan. 7Research Centre for Materials Nanoarchitectonics, National Institute for Material Science,Tsukuba, Japan. 8Department of Physics, National University of Singapore, Singapore, Singapore. e-mail: ian.babich@u.nus.edu; alexey@nus.edu.sgNature Communications |         (2025) 16:7389 11234567890():,;1234567890():,;http://orcid.org/0000-0003-0428-7259http://orcid.org/0000-0003-0428-7259http://orcid.org/0000-0003-0428-7259http://orcid.org/0000-0003-0428-7259http://orcid.org/0000-0003-0428-7259http://orcid.org/0000-0003-0131-0775http://orcid.org/0000-0003-0131-0775http://orcid.org/0000-0003-0131-0775http://orcid.org/0000-0003-0131-0775http://orcid.org/0000-0003-0131-0775http://orcid.org/0000-0003-4295-2221http://orcid.org/0000-0003-4295-2221http://orcid.org/0000-0003-4295-2221http://orcid.org/0000-0003-4295-2221http://orcid.org/0000-0003-4295-2221http://orcid.org/0000-0002-1575-7722http://orcid.org/0000-0002-1575-7722http://orcid.org/0000-0002-1575-7722http://orcid.org/0000-0002-1575-7722http://orcid.org/0000-0002-1575-7722http://orcid.org/0000-0003-1709-7868http://orcid.org/0000-0003-1709-7868http://orcid.org/0000-0003-1709-7868http://orcid.org/0000-0003-1709-7868http://orcid.org/0000-0003-1709-7868http://orcid.org/0000-0002-1407-7194http://orcid.org/0000-0002-1407-7194http://orcid.org/0000-0002-1407-7194http://orcid.org/0000-0002-1407-7194http://orcid.org/0000-0002-1407-7194http://orcid.org/0000-0003-4972-5371http://orcid.org/0000-0003-4972-5371http://orcid.org/0000-0003-4972-5371http://orcid.org/0000-0003-4972-5371http://orcid.org/0000-0003-4972-5371http://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/0000-0003-0828-0310http://orcid.org/0000-0003-0828-0310http://orcid.org/0000-0003-0828-0310http://orcid.org/0000-0003-0828-0310http://orcid.org/0000-0003-0828-0310http://orcid.org/0000-0002-4776-6965http://orcid.org/0000-0002-4776-6965http://orcid.org/0000-0002-4776-6965http://orcid.org/0000-0002-4776-6965http://orcid.org/0000-0002-4776-6965http://orcid.org/0000-0002-7537-6227http://orcid.org/0000-0002-7537-6227http://orcid.org/0000-0002-7537-6227http://orcid.org/0000-0002-7537-6227http://orcid.org/0000-0002-7537-6227http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-62492-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-62492-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-62492-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-62492-5&domain=pdfmailto:ian.babich@u.nus.edumailto:alexey@nus.edu.sgwww.nature.com/naturecommunicationsinhomogeneity to δn �1010 cm−2, and improved mobility to~106 cm2V−1s−1. Further progress was made by using graphite gates16–20instead of silicon, suppressing inhomogeneity to δn �5 × 109cm−2, andestablishing the current benchmark for state-of-the-art devices. Suchdevices enabled electron transport studies at the CNP near the roomtemperature, revealing properties of Dirac plasma10,21–24. However, atcryogenic temperatures, electron-hole puddles continue to dominatethe electronic properties of graphene near the CNP. The better per-formance to date has been achieved in suspended graphene devices,where the dielectric substrate is eliminated, allowing charge inhomo-geneity as low as3,29–31 δn �4 × 108 cm−2 and enabling to approach theDirac point within 1meV. However, such devices are impractical formost applications because of the challenges in fabricating dual-gatedor multilayer freestanding structures.The difference in quality between suspended and hBN-encapsulated devices is typically attributed to charged defects insideencapsulating hBN crystals, which results in charge inhomogeneity ingraphene. While room for further improvement of hBN crystal qualityis limited, this issue could potentially be addressed by employingCoulomb screening. Namely, a layer with a high density of states (DoS)in close proximity to graphene should suppress the electric field fromcharged defects and associated charge inhomogeneity.Previous studies on Coulomb screening have utilized graphite orgraphene as screening layers separated from the studied graphene by3–10 nm thick hBN spacers14,24,32. While those efforts have enabled theobservation of screening-induced Anderson localization32 and sup-pressed particle-particle collisions14,24,33, they didnot result in a notableimprovement of the device quality. As the screening depends expo-nentially on the distance14, it is essential to position the screening layermuch closer to the graphene than the charged defects (see Supple-mentary Note 6). This makes commonly used hBN spacers impracticalfor electron-hole puddle screening, as charged defects, which are alsopresent inside these crystals, are located closer to graphene than thescreening layer.In this work, we address this challenge by stacking graphene lay-ers directly atop one another and intentionally decoupling them usinga large twist angle θ � 10� 30�. The suppressed interlayer tunnelinganddecoupled spectraof graphene layers in suchheterostructures34–40result in significant interlayer resistance34,38. This allowed us to selec-tively charge one of the graphene layers in such devices and use it as acharged screening substrate separated from the test layer by a sub-nanometer vdW gap.ResultsFigure 1a shows one of our large-angle twisted bilayer graphene(LATBG) devices with a twist angle of θ � 20� (See “Methods” for thedetails of the device fabrication). Using gold top and graphite bottomgates we can independently set the out-of-plane displacement field Dand the total charge density ntot.Firstly, we characterized the LATBG device by measuring itsresistance at zero D, as shown in Fig. 1b. Under such conditions, bothlayers have the same doping, and the system behaves similarly tosingle-layer graphene: resistance sharply peaks at zero carrier densityand rapidly drops when doping increases. Using this curve, we esti-mate inhomogeneity of individual layers δn � 7 × 109cm�2, and elec-tron mobility μe =0:5 × 106 cm2=Vs (Supplementary Fig. 1), which isconsistent with that of a typical high-quality encapsulated devicesreported in the literature9–24.Qualitatively, the applied D creates an interlayer potential differ-ence that separates the Dirac cones in energy, whereas ntot moves thecommon Fermi level (see inset Fig. 1b). When the Fermi level crossesthe Dirac points, it is reflected as resistivity wiggles at positive andnegative doping levels, as shown in Fig. 1b. The dual-gatemap in Fig. 1cfurther shows howDirac cone offset evolves upon changingD. Dashedlines mark the expected positions of Dirac points of top and bottomlayerswhich coincidewellwith resistivity features thatweattributed toCNPs earlier.Screening enabled quantization in milli-Tesla magnetic fieldNext, to test the device quality, we measured Landau fan diagramsunder different displacement fields. When D = 0 V/nm (Fig. 1d)LATBG shows a typical Landau fan diagram of single-layer graphene,but with doubled filling factors, as expected for two graphene layerswith equal doping. The applied D significantly alters this picture: inFig. 1e, there are two sets of fan diagrams converging aroundntot = ±0:4× 1012 cm�2, which correspond to the expected positionsof the top and bottom graphene CNPs. These fans can be attributedto the individual quantization of the top and bottom layers, and theirparabolic-like shape originates from the presence of the otherheavily doped layer (see the schematic band structure in Fig. 2aand Supplementary Note 1). If plotted as a function of the chargedensity in top or bottom layer, the fan diagrams restore their line-arity (Supplementary Fig. 2) and become similar to those shownin Fig. 1d.An important difference between the fan diagrams observed inFig. 1d, e is the magnetic field required to resolve the onset of Landauquantization. At D =0V/nm, Landau levels (LLs) become resolvablearound B* � 100mT, while the applied displacement field significantlylowers this onset. To determine the onset of oscillations under anapplied D we have zoomed into a small magnetic field range, asshown in Fig. 2b. In this map, the signatures of Landau fans becomevisible already at B* = 5� 6mT (see Supplementary Fig. 11 and Sup-plementary Note 5), which is an order of magnitude better than themagnetic field required to see the Landau quantisation at zero D inLATBG and in test graphene devices without proximity screening(Supplementary Fig. 8).A reduction of magnetic field required to resolve the onset ofquantization in Figs. 1e and 2b indicates a decrease of charge inho-mogeneity δn under applied D. Qualitatively, to resolve the firstcyclotron gap in graphene, the fluctuations of the Fermi level must besmaller than the size of the first cyclotron gap30. To crosscheck thiscriterion,wemodelledDoSof graphene for given inhomogeneity level,magnetic field and temperature as a function of Fermi level and energyfluctuations δE (see Supplementary Fig. 9 and Supplementary Note 4).When D =0V/nm and B* = 100mT (B* is the smallest magnetic fieldallowing resolution of the first LL), the model suggestsδn � 5 × 109cm�2, which agrees with earlier estimations. Underapplied D (for B* = 5� 6mT) we find that inhomogeneity drops toδn � 2� 3 × 108 cm�2, corresponding to just 2–3 electrons permicrometre area of the Hall bar shown in Fig. 1a. However, at smallmagnetic fields, the cyclotron radius Rc becomes comparable to thewidth of our voltage probesW, which possibly limits the resolution ofquantization onset. To show this, in Fig. 2c, we plotted the W = 2Rccondition, which well describes the onset of Landau quantization inour device, indicating that the quality of the LATBG device likely to beeven better than estimated above. Finally, while quantization becomesapparent already at 5–6mT, we estimate that the quantum Hall effectfully onsets at 13mT (see Supplementary Note 5). However, at low B,zero resistivity within the cyclotron gaps is not observed because ofparallel conduction through the second strongly doped layer, whichremains non-quantized and contributes a significant backgroundsignal.The suppression of δn under applied displacement field origi-nates from the tuneable screening, in agreementwith the design ofourexperiment. The screening of an external electric field by metalliclayers is set by the DoS around the Fermi energy, which drops to zerowhen both layers are simultaneously tuned towards CNP (D =0 case).As a result, any charged impurities within the encapsulating hBNcrystals create substantial spatial fluctuations in carrier density, asillustrated in the top panel of Fig. 2c. On the contrary, the applied DArticle https://doi.org/10.1038/s41467-025-62492-5Nature Communications |         (2025) 16:7389 2www.nature.com/naturecommunicationscreates an energy offset between Dirac cones of different layers whichentails that the double layer device has high DoS even when one ofgraphene layers is tuned towards the CNP. It results in screening ofexternal electric field and improves the homogeneity of graphenelayers, as shown in bottom panel of Fig. 2c. This behavior can bequantitatively described using the Thomas–Fermi model (see Sup-plementary Note 6) and 2D maps in Fig. 2d, which show how thescreening layer suppresses charge inhomogeneity. We also note thatthe analysis above primarily focuses on the energy gap between the0th and 1st Landau levels. This gap is the largest and, due to the lowintrinsic doping of graphene at this filling, is expected to be the mostsensitive to external screening. In contrast, higher Landau level gapstypically emerge only at larger carrier densities, where enhanced self-screening within the quantized graphene layer reduces its suscept-ibility to external screening.Resolving the gap at the CNP of graphene layersAnother notable differencebetween themeasurements at zero and theappliedD is the presenceof twomagneticfield-independent resistancepeaks in the centres of the fan diagrams of each graphene layer inFigs. 1e and 2b. To understand these features, we perform spectro-scopy of the top layer by plotting its fan diagram as a function ofchemical potential in the bottom layer μb, see Fig. 2b. The theoreticalpositions of the first few LLs, indicated by dashed lines, align well withthe resistivity features on this map, except that instead of a singlevertical resistivity peak expected for zero-energy LL, there are twopeaks. This suggests the formation of a gap at the CNPs, estimated tobe Δg = 5 ± 1 meV in both layers. Furthermore, we found that the gap ispresent even at zero magnetic field, as shown in high-resolution fandiagram, magnetic focusing measurements, and bulk-current fan dia-gram (Supplementary Figs. 2 and 4). It is independent of D andbecomes resolvable already at D =0.05 V/nm (see SupplementaryFigs. 3 and 5).To verify the presence of the band gap, we modelled the fandiagramof a double layer graphene system, assuming a gap at the CNPof the quantized layer. Usually, such a gap should produce a localresistance maximum, which is not observed in our devices. To repro-duce the measurements shown in Fig. 2b, we had to additionallyassume valley decoupling in the gapped graphene layer, as discussedin Supplementary Note 7, which leads to the edge conductivity-1 +1 +2 +30- 0+-2-3B=0 TB=0 TD=0 V/nm D=0.6 V/nmt-hBNCr/AuGraphite hBNhBN VtgVbga b cd eb-CNPt-CNPb-CNP t-CNPt-CNPD0.01b-CNP0 40 421- 82022144--28 -203Fig. 1 | Characterization of a large-angle twisted bilayer graphene (LATBG)device. a Top panel: schematic structure of LATBGdevice, utilizing thin hBN flakesas dielectrics for bottom graphite and top metal gates, V tg and Vbg are top andbottom gate voltages; bottom panel: optical image of LATBGHall bar device. Blackline highlights the metallic top gate and electrical contacts. Scale bar is 1μm.b Longitudinal resistivity as a function of total charge density ntot for D =0 V/nm,and D =0.5 V/nm measured at zero magnetic field. Dashed circles indicate thepositions of charge neutrality points of top (t-CNP, black circle) and bottom gra-phene layers (b-CNP, blue circle) calculated using the electrostatic model (seeSupplementary Note 1). Insets schematically show band structure of LATBG underappliedDwhen theFermi level crosses theCNPof one of the graphene layers; here,the red part of the cone represents hole doping, and blue represents electrondoping of graphene. c Longitudinal resistivity atB =0T as a functionofntot andD.Dashed lines indicate expected positions of CNPs. d, e Resistivity as a function ofmagnetic field B and ntot for D =0V/nm (d) and D =0.6 V/nm (e). In (d) dashedlines show the expected position of doubled graphene filling factors. In (e) whitedashed lines are a guide for the eye of the first three Landau levels and CNP gapboundaries in bottom graphene layer. See the text for the further discussion.Further examples of Landau fan measurements are shown in SupplementaryFigs. 2 and 4. The high magnetoresistance observed around ntot =0 can beattributed to the compensated semimetal state, similar to ref. 24, which naturallyforms under applied D when one layer is electron-doped and the other is hole-doped. Measurements were performed at 2 K for all panels.Article https://doi.org/10.1038/s41467-025-62492-5Nature Communications |         (2025) 16:7389 3www.nature.com/naturecommunicationschannels inside the gap. The results of our modelling, Fig. 2e, capturethe measurements shown in Fig. 2b, confirming that the two verticalresistance peaks originate from the gap edges, with their separationset by the gap size. The possible origin of this gap is discussed furtherin the text.Graphene fully encapsulated with screening graphene layersApart from LATBG devices, where graphene serves as a substrate foranother graphene layer, we fabricated large-angle twisted trilayergraphene (LATTG) devices to showcase full encapsulation of themiddle graphene layer. Optical images of fabricated devices are shownin Fig. 3a. See “Methods” for fabrication details.To characterize LATTG, we firstly measured resistance as a func-tion of D and ntot, as shown in Fig. 3b. Similar to bilayer devices,the resistance map reveals features that evolve under an applieddisplacement field. Using an extended electrostatic model (see Sup-plementary Note 1), we identified these features as the CNPs of theindividual graphene layers, indicated by dashed lines in Fig. 3b. Whilesymmetry considerations suggest that the middle-layer CNP (m-CNP)should remain independent of D, the m-CNP in Fig. 3b shifts towardsnegative doping with increasing D. This behavior is reproducibleacross all our devices and can be explained by small energy offsets ofouter graphene layers interfacing hBN39.Next, wemeasured the sameD vs. ntotmap at a smallmagnetic fieldof B= 50mT, as shown in Fig. 3c. At this field, all three layers becomequantized and produce three sets of parallel resistivity lines (labeled bycorresponding LL number). There are single resistivity peaks corre-sponding to zeroth LLs in top and middle layer, while in the bottomlayer, the peak doubles (labeled as 0+ and 0−). This feature, similarly toobservations in LATBG, corresponds to the formation of a gap. How-ever, in this LATTG device, the gap is resolved only in one of the layers.To further assess the quality of our LATTG devices, we measuredfan diagrams under fixed D or ntot, shown in Fig. 3d–g and Supple-mentary Fig. 22. In all LATTGdevices, we observed three sets of Landaufans converging at carrier densities corresponding to the expectedpositions of the CNPs for individual layers, as indicated by the arrows5-6 mT10-1-2bottom SLG top SLGa b D=-0.75V/nmModelling-1 1nt (1011 cm-2)nb=0.5×1012cm-2nb=0c d ehBNhBNFig. 2 | Resolving theonsetofLandauquantization inmilli-Teslamagneticfield.a Schematic illustration of LATBGband structure at lowmagneticfieldB and highDwhenFermi level is tuned close to theCNPof one of graphene layers.b Fandiagrammeasured at D = −0.75 V/nm and 2K shown as a function of chemical potential inthe bottom graphene layer μb. Black parabolic dashed lines indicate the expectedposition for the first five Landau levels (LLs) plotted using a standard graphenesequence EN =ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ℏeBv2FN +Δ2q, where ℏ is the reduced Plank constant, e is theelectron charge, EN is the energy of the Nth LL, and vF is the Fermi velocity ingraphene, 2Δ is a band gapdiscussed further in the text. The horizontal dashed lineand the error bar mark the onset of Landau quantisation. Square root dashed linesindicate the limit of quantization set by the probe width (see SupplementaryNote 5). c Schematic illustrations of electron-hole puddles in LATBG at zero (top)and under applied (bottom) displacement fields. Red and blue shaded regionsrepresent positive and negative doping correspondingly, coloured circles in thehBN illustrate charged defects.d Simulated charge density profiles in top graphenecalculated for hBN with impurity density nimp = 1010 cm�2 at zero doping of thebottom layer nb =0, and for nb =0.5 × 1012 cm−2 (see Supplementary Note 6). Scalebars are 250 nm. e Modelling of LATBG resistance subjected to high D under theassumption of a gapped graphene spectra (see Supplementary Note 7).Article https://doi.org/10.1038/s41467-025-62492-5Nature Communications |         (2025) 16:7389 4www.nature.com/naturecommunicationsin Fig. 3d and f. Notably, in Fig. 3f, the complete lifting of the zerothLandau level degeneracy is resolvable at magnetic fields as low as 1Tesla, while it is not seen in devices without screening at similar fieldranges. The high-resolution fan diagrams at small magnetic fieldsshown in Fig. 3e and g reveal the onset of Landau quantization alreadyat 5–7mT (see Supplementary Note 5 and Supplementary Fig. 12) fortwo different LATTGdevices, showcasing the high electronic quality ofgraphene in such structures.0+0 1m-CNPb-CNP t-CNP5-7 mT5-6 mTCr/AuGraphite hBNhBN VtgVbgDadb cDevice A, D=-0.5 V/nme -10-0.1 0.3 0 110-20 180-0.5 0.50.1 8tb mDevice ADevice BDevice A, B=0 T Device A, B=50 mTDevice ADevice B, D=0.5 V/nm Device Bf g2- 1- 012- 1- 00210+0-1212-12- 1- -0 12- 1-2- 1-2Fig. 3 | High quality of LATTG devices. a Schematic structure of LATTG devices,graphene layers (b, m, and t labels indicate bottom, middle, and top layers,respectively) are twisted by large angles θ12 (the angle between the bottom and themiddle layers) and θ23 (the angle between the middle and the top layers). See“Methods” for further information. Optical images show twomeasured LATTG Hallbar devices A and B, scale bar is 5μm. b Longitudinal resistance at B =0T as afunction of charge density ntot and displacement field D measured in device A.Coloured lines indicate conditions of CNP for top, middle, and bottom layers withblack, red, and yellow correspondingly. Inset band structures illustrate the positionof CNPs of each layer. c Longitudinal resistance at B = 50mT as a function of ntotand D measured in device A. Coloured dashed lines show the calculated CNPpositions for all three layers based on the electrostatic model described in theSupplementary Note 1. We therefore label the nearest Landau levels as ±1, ±2, withthe sign reflecting the charge carrier type in each layer. d–g Magnetoresistancemeasurements for devices A and B. d, f Measured for fixed D = −0.5 V/nm andD =0.5 V/nm correspondingly as a function of ntot, coloured arrows show posi-tions of CNPs. e, g Longitudinal resistancemeasured for fixed ntot as a function ofDwith removed background (see Supplementary Fig. 10 formore details). Onset ofLandau quantisation become resolvable already at B* = 5� 7 mT in (e) and atB* = 5� 6 mT in (g). Measurements were done at 2 K for all panels.Article https://doi.org/10.1038/s41467-025-62492-5Nature Communications |         (2025) 16:7389 5www.nature.com/naturecommunicationsDiscussionWhile both LATBG and LATTG devices exhibit similar onsets of quan-tization in millitesla magnetic field range, LATTG devices demonstratesuperior electronic quality. For instance, at B= 50 mT LATTG deviceallows to resolve up to 20–30 LLs per layer, Fig. 3c, whereas LATBGdevices show only up to 8 LLs, even at higher B= 100mT, Supplemen-tary Fig. 5. However, in LATTG devices, when the Fermi level is tunedtowards the CNP of one of the layers, the other two heavily doped layersact as parallel conduction channels. This obstructs the access to theproperties of the charge neutral layer by introducing significant back-ground signals that can interfere with measurements (see Supplemen-tary Fig. 22). Another difference in performance between LATBG andLATTG devices is that the former shows identical gaps at CNPs of bothlayers (see Fig. 2d), whereas the latter shows a clear gap only in one ofthe layers (see Fig. 3c and Supplementary Fig. 22). Below, we considerseveral possibilities for the gap origin.Multiple theoretical works have predicted a Mott insulator gap atthe CNP of graphene41,42. However, experiments with freestanding gra-phene have shown renormalization of the Fermi velocity instead of agap, which was attributed to the presence of strong long-range Cou-lomb interactions29. A recent study suggests that suppressing the tail ofCoulomb interactions (e.g., with ametallic screening layer)may result ina semimetal-Mott insulator transition42. However, our modelling of suchtransition predicts gap dependence on temperature and D, which arenot observed in the measured devices (see Supplementary Notes 2, 8and Supplementary Figs. 5 and6). This points towards a structural originof the gap, whichmay appear due to the contact between graphene andhBN (G/hBN) or due to the twist between graphene layers.Prior studies on the devices where graphene is aligned withencapsulating hBN crystals report varying gap sizes depending on thegraphene-hBN alignment17,18,43–48; however, this effect is minimized in oursamples, since we intentionally misaligned graphene and hBN duringdevice fabrication. Moreover, in Fig. 2d, the observed gaps in the LATBGdevice are identical in both layers; this symmetry would likely be brokenif misaligned hBN/G interface had a noticeable impact on the bandstructure. Next, in LATTG devices, the presence of a gap in only one ofthe outer layers suggests that any gap due to the graphene/hBN interfacecan indeed be negligible with our intentional misalignment (otherwise, itwould be resolved in the other outer layer) pointing to the possibleintrinsic origin of this gap within the twisted graphene structure.To investigate this hypothesis,we calculated the band structureofLATBG at various high commensurate angles (Supplementary Fig. 23).The calculated band structures revealed a small band gapof a fewmeVopening at the Dirac points of each layer, along with a larger gap at theCNP of the double layer, which was not observed experimentally. It isessential to note that these calculations are influenced by the choice ofthe unit cell origin, which may change due to the lateral shift betweenthe layers (see Supplementary Note 10).It should be noted that existing theories on the band structure ofLATBG mainly focus on commensurate angles49–51 which are challen-ging to achieve in real devices.Moreover, the precise determination ofthe electronic structures is highly sensitive to the actual arrangementof atoms, as determined by the lateral shift and twist angle. Thesechallenges make the systematic study of gaps at the Dirac points quitedifficult and place it beyond the scope of this work.Although it is challenging topinpoint the exactmicroscopic originof the gap, the ability to resolve such small features of the bandstructure highlights the spectroscopic capabilities enabled by encap-sulation with graphene layers. Since resolving gaps below 5meV(δE <2:5meV) at the CNP of Dirac point requires a doping inhomo-geneity level below 2 × 109 cm−2, our samples exceed performanceof the state-of-the-art devices. More than that, tunable Coulombscreening reduces doping inhomogeneities towards 3 × 108 cm−2,which is an order of magnitude improvement and correspondsto δE � 0:5meV.Such high quality allowed to resolve the onset of Landau quanti-zation in our devices at magnetic fields of 5–6mT, corresponding to aquantummobility relevant for the observation of quantumphenomena,μq � (1.5–2) × 106 cm2V−1s−1. Unfortunately, the large-angle twisted mul-tilayer graphene geometry does not allow the direct measurement ofthe transport mobility of individual graphene layers under appliedscreening, as a significant portion of the current always propagatesthrough a heavily doped graphene layer. Nevertheless, our toy model(see Supplementary Note 3 and Supplementary Fig. 7) estimates thatthe transport mobility near CNP in our devices approachesμ �(12–20) × 106 cm2V−1s−1, an order of magnitude higher than μq. Thisdifference is expected as transportmobility is limited by backscattering,whereas quantum mobility is more sensitive to small-angle scattering.Both quantum and transport mobilities in our devices are an order ofmagnitude higher than those in devices without screening.We also notethat the quantum mobility achieved in our devices is higher than thequantum mobility of the best GaAs 2DEGs, where quantum oscillationsonset7 around 35–40mT even at milli-Kelvin temperature, with thequantum mobility6 μq � 1 × 106 cm2V−1s−1. At the same time, our estima-tions give mobility values of the same order as that of the best GaAssamples, highlighting a significant improvement of graphene devices.Finally, we note that the large twist angle approach also intro-duces new capabilities, such as tuneable Coulomb interactions viaadjustable screening, facilitating further exploration of many-bodyeffects in moiré quantum materials52. Our encapsulation method isreadily adaptable to other multilayer and twisted heterostructures,thereby broadening its potential applications.MethodsSample fabricationThe heterostructures studied in this work were assembled using acombination of the tear-and-stack method together with dry transfertechnique9,12,53. Polydimethylsiloxane (PDMS) stamps coated with a thinpolycarbonate (PC) membrane were employed to pick up exfoliatedcrystals from Si/SiO2 substrates. The pick-up process was conducted at100 °C in the following sequence: hBN of 30–40nm thickness (toplayer), a large graphene flake (first segment), the second segment of thesame graphene flake, rotated to a large twist angle, and another hBNlayer (bottom layer, 30–40nm). Our target angle for the HATBG sampleis 20�, for the HATTG devices A and B θ12 � 20�,θ23� �20� andθ12 � 30�,θ23 � 30�, respectively; the device C shown in the Supple-mentary Information had target angles θ12 � 10�, θ23� 10�. The finalvdW stack was released on top of graphite flake at 180°, after which thePDMS stamp was carefully delaminated from the PC membrane. Themelted PC film was subsequently dissolved in dichloromethane, fol-lowed by rinsing in acetone and isopropyl alcohol.Next, we used high-resolution atomic force microscopy to locatebubble-free regions suitable for device fabrication. Standard nanofab-rication techniques were then used to pattern Hall bars in the identifiedclean regions. First, the top gates were fabricated using electron-beamlithography (EBL), followed by chromium/gold (Cr/Au) metal deposi-tion. In a subsequent EBL step, deep reactive ion etching with a CHF3/O2gas mixture was employed to define the Hall bar geometry. Finally, one-dimensional electrical contacts to the twisted bilayer graphene (TBG)were formed by depositing Cr/Au onto the exposed graphene edges.Electronic transport measurementsThe electronic transport measurements were performed using stan-dard low-frequency lock-in techniques with excitation currents below100nA, minimizing heating and non-linear effects; the measurementtemperature was 2K if not specified. Most of the data presented in themain text were acquired under nonzero displacement field, D. Thedual-gated device configuration allowed independent control ofD andthe total carrier density, ntot. The carrier densitywas determined as thesum of the densities induced by the top and bottom gates:Article https://doi.org/10.1038/s41467-025-62492-5Nature Communications |         (2025) 16:7389 6www.nature.com/naturecommunicationsntot =1e CtgV tg +CbgVbg� �, where V tg and Vbg are the voltages appliedon a top and bottom gates, and Ctg and Cbg are the top and bottomgate capacitances per unit area, respectively, found from the Halleffect measurements. The displacement field was calculated as:D= 12ε0CtgV tg � CbgVbg� �, where ε0 is the vacuum permittivity.To characterize our devices, we first measured their resistivity atzero displacement andmagnetic field and defined inhomogeneity as ahalf-width at half-maximum (HWHM) as illustrated in SupplementaryFig. 1a. We note that the inhomogeneity of individual layers is half ofthe HWHM. Next, we calculated mean free path and mobility using astandard expression for the single-layer graphene, but consideringthat we have two graphene sheets instead of one:μ=1ρntoteð1Þlmfp =1ρℏe2ffiffiffiffiffiffiffiffiffiffiffiπ2ntotrð2ÞHere ρ is the resistivity of the whole double layer, ℏ is reduced Plankconstant, and e is an electron charge. The results are shown in Sup-plementary Fig. 1b, c, which indicate that at zero D the mean free pathin our device is approaching device width, and mobility approaching106 cm2V−1s−1 as expected for the high-quality encapsulated devices.At appliedD, we cannot decipher resistivity of the individual layer,however, magnetic focusing measurements allow to claim when thesample is ballistic. In Supplementary Fig. 2, magnetic focusing lineapproaches the boundaries of the gap as close as the measurementaccuracy δn< 2× 109cm�2, and corresponds to the mean free path oflmfp > L=2:7μm, where L is the distance between centers of the con-tacts, and the inequality sign is used because the electronsmove alongcyclotron orbits. Thus, we can set a lower boundary for electronmobility at D = −0.55 V/nm:μ=lmfpeℏffiffiffiffiffiffiffiffiffiffi2πδnr> 7:3× 106cm2=Vs ð3ÞData availabilityRelevant data supporting the key findings of this study are availablewithin the article and the Supplementary Information file. All raw datagenerated during the current study are available from the corre-sponding authors upon request.References1. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nat. Mater. 6,183–191 (2007).2. Yankowitz,M.,Ma,Q., Jarillo-Herrero, P. & LeRoy, B. J. van derWaalsheterostructures combining graphene and hexagonal boronnitride. Nat. Rev. Phys. 1, 112–125 (2019).3. 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Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117,116804 (2016).AcknowledgementsThis work has been supported by the National Research Foundation, Sin-gapore under its NRF Fellowship (NRFF) (NRF-NRFF16-2024-0011), and byA*STAR under its RIE2025 Manufacturing, Trade and Connectivity (MTC)Young Individual Research Grant (M23M7c0126) awarded to A.I.B.; S.S.and V.I.F. acknowledge support from International Science PartnershipsFund (UK), British Council Grant 1185409051, and EPSRC grant EP/V007033/1; M.T. is supported by the Singapore Ministry of EducationResearch Centre of Excellence award to the Institute for Functional Intel-ligent Materials (I-FIM, Project No. EDUNC-33-18-279-V12); A.P. and A.K.acknowledge support from the European Commission under the EU Hor-izon 2020 MSCA-RISE-2019 program (project 873028 HYDROTRONICS)and from the Leverhulme Trust under the grant agreement RPG-2023-253;K.W. and T.T. acknowledge support from the JSPS KAKENHI (Grant Num-bers 21H05233 and 23H02052), the CREST (JPMJCR24A5), JST and WorldPremier International Research Center Initiative (WPI), MEXT, Japan. IMDEANanociencia acknowledges support from the ‘Severo Ochoa’ Programmefor Centres of Excellence in R\&D (CEX2020-001039-S/AEI/10.13039/501100011033); Z.Z. and P.A.P. acknowledge support from NOVMOMAT,project PID2022-142162NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by FEDER, UE as well as financial support through the(MAD2D-CM)-MRR MATERIALES AVANZADOS-IMDEA-NC; Z.Z. acknowl-edges support from the European Union’s Horizon 2020 research andinnovation programme under the Marie–Sklodowska Curie grant agree-ment No 101034431. K.S.N. acknowledges support from the Royal Society(UK, grant no. RSRP\R\190000). This project is supported by the NationalResearch Foundation, Singapore under its AI Singapore Programme (AISGAward No: AISG3-RP-2022-028). Authors are grateful to Kristina Vaklinovafor fabrication advice, to Giovanni Vignale, and Mohammed MohammedEsmail Al-Ezzi for useful discussions.Author contributionsA.I.B. designed and supervised the project. I.B. carried out the projectandperformed the electron transportmeasurements,with contributionsfrom I.Bg. and J.Z. I.B. fabricated and characterized the devices shown inthe main text; I.R. fabricated an additional LATTG device shown in theSupplementary Information. D.B., S.G., and M.S. contributed to samplecharacterization. K.W. and T.T. provided hBN crystals. A.E.K., A.P., S.S.,V.I.F. and M.T. contributed to the theoretical interpretation and per-formed numerical simulations. Z.Z. and P.A.P. performed band structurecalculations for LATBG. I.B. and A.I.B. analysed the data, with contribu-tions fromS.S., V.I.F., K.S.N., A.E.K., A.P. andM.T. I.B. and A.I.B. wrote themanuscript with inputs from A.E.P., A.P., S.S., V.I.F. and M.T. All authorsdiscussed the results and contributed to the final version of themanuscript.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-62492-5.Correspondence and requests for materials should be addressed toI. Babich or A. I. Berdyugin.Peer review information Nature Communications thanks Luca Bans-zerus and the other, anonymous, reviewers for their contribution to thepeer review of this work. 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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/s41467-025-62492-5Nature Communications |         (2025) 16:7389 8https://doi.org/10.1038/s41467-025-62492-5http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Milli-Tesla quantization enabled by tuneable Coulomb screening in large-angle twisted graphene Results Screening enabled quantization in milli-Tesla magnetic field Resolving the gap at the CNP of graphene layers Graphene fully encapsulated with screening graphene layers Discussion Methods Sample fabrication Electronic transport measurements Data availability References Acknowledgements Author contributions Competing interests Additional information