# Fileset

[s42005-024-01887-0.pdf](https://mdr.nims.go.jp/filesets/652335a2-e0e4-410f-88fa-25b480916273/download)

## Creator

[Alex Boschi](https://orcid.org/0000-0001-7562-7340), Zewdu M. Gebeyehu, [Sergey Slizovskiy](https://orcid.org/0000-0003-0131-0775), [Vaidotas Mišeikis](https://orcid.org/0000-0001-6263-4250), [Stiven Forti](https://orcid.org/0000-0002-8939-3175), [Antonio Rossi](https://orcid.org/0000-0003-4574-7215), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Fabio Beltram, [Vladimir I. Fal’ko](https://orcid.org/0000-0003-0828-0310), [Camilla Coletti](https://orcid.org/0000-0002-8134-7633), [Sergio Pezzini](https://orcid.org/0000-0003-4289-907X)

## Rights

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

## Other metadata

[Built-in Bernal gap in large-angle-twisted monolayer-bilayer graphene](https://mdr.nims.go.jp/datasets/d56c4b80-cefd-4a9b-bce3-8d854ada0049)

## Fulltext

Built-in Bernal gap in large-angle-twisted monolayer-bilayer graphenecommunications physics Articlehttps://doi.org/10.1038/s42005-024-01887-0Built-in Bernal gap in large-angle-twistedmonolayer-bilayer grapheneCheck for updatesAlex Boschi 1, Zewdu M. Gebeyehu1,2, Sergey Slizovskiy 3,4, Vaidotas Mišeikis 1,2, Stiven Forti 1,2,Antonio Rossi 1,2, Kenji Watanabe 5, Takashi Taniguchi 6, Fabio Beltram7, Vladimir I. Fal’ko 3,4,8,Camilla Coletti 1,2 & Sergio Pezzini 7Atomically thin materials offer multiple opportunities for layer-by-layer control of their electronicproperties. While monolayer graphene (MLG) is a zero-gap system, Bernal-stacked bilayer graphene(BLG) acquires a finite band gap when the symmetry between the layers’ potential energy is broken,usually, via a displacement electric field applied in double-gate devices. Here, we introduce atwistronic stack comprising both MLG and BLG, synthesized via chemical vapor deposition, showinga Bernal gap in the absence of external fields. Although a large (~30°) twist angle decouples the MLGand BLG electronic bands near Fermi level, proximity-induced energy shifts in the outermost layersresult in a built-in asymmetry, which requires a displacement field of 0.14 V/nm to be compensated.The latter corresponds to a ~10meV intrinsic BLG gap, a value confirmed by our thermal-activationmeasurements. The present results highlight the role of structural asymmetry and encapsulatingenvironment, expanding the engineering toolbox for monolithically-grown graphene multilayers.The electronic properties of few-layer graphenes are sensitive to layernumber1, stacking order2,3, lack or presence of inversion symmetry4,5,external electromagnetic fields6, as well as to the twist angle between con-secutive layers (their relative crystallographic orientations)7. Based on thislast tuning parameter, the band hybridization between contiguous sheetscanbe artificiallymodulated, resulting in spectacular emergent behaviors forsmall-angle values associated to specific periodicities of the interlayermoiré8. This paradigm, initially demonstrated in twisted bilayer graphene(TBG)9,10, has now been extended to a plethora of related moiré systems11,including twisted MLG-BLG (TMBG). For twist angles ~1°, TMBG hasbeen shown to support flat bands promoting correlated and topologicalphases, including insulators12,13, orbital magnets14–16 and charge densitywaves17. The lack of inversion symmetry makes the electronic response ofsmall-angle TMBG strongly dependent on the direction of an externaldisplacement field (D) that can be controlled by top and bottom gateelectrodes12–15,17. In the limit of large twist angle (where moiré effects arenegligible), TMBG is expected to decompose into two low-energy sub-systems that retain unperturbed MLG and BLG character, mimicking theindependent-MLGs behavior found in large-angle TBG18–23. However, acomplete picture of large-angle TMBG needs to account for its structuralasymmetry, which can have a subtle (yetmeasurable) influence on the exactband structure close to Fermi level. Specifically, not only BLG is sensitive toD – which drives band-gap opening24–26 exploitable for quantumconfinement27–29 and multiple phase transitions30–32 – but also, whenembedded in stacks, to environment-induced interlayer asymmetry5,24, asdemonstrated by the observation of a mini-gap in large-angle-twisteddouble BLG (TDBG)33. Building on these findings, Agarwal et al. recentlyreported optoelectronic properties widely beyond the independent-subsystems scenario of TDBG34. These results motivate further explora-tion of BLG-containing stacks – such as large-angle TMBG – as well as thedevelopment of scalable synthesis methods for these systems – such aschemical vapor deposition (CVD) growth of single crystals35.In this work, we provide experimental evidence (supported bydetailed mesoscale modelling) for a built-in band gap in a BLG studied asa part of an hBN-encapsulated large-angle TMBG. Key to our observa-tions is the ability to directly grow monolithic TMBG crystals via low-pressure CVD (LP-CVD) and integrate them into high-quality van derWaals (vdW) devices.1Center for Nanotechnology Innovation @NEST, Istituto Italiano di Tecnologia, Piazza San Silvestro 12, I-56127 Pisa, Italy. 2Graphene Labs, Istituto Italiano diTecnologia, Via Morego 30, 16163 Genova, Italy. 3National Graphene Institute, The University of Manchester, Manchester, M13 9PL, UK. 4School of Physics &Astronomy, The University of Manchester, Oxford Rd., Manchester, M13 9PL, UK. 5Research Center for Electronic and Optical Materials, National Institute forMaterials Science, 1-1Namiki, Tsukuba, 305-0044, Japan. 6ResearchCenter forMaterialsNanoarchitectonics, National Institute forMaterials Science, 1-1Namiki,Tsukuba, 305-0044, Japan. 7NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Piazza San Silvestro 12, I-56127 Pisa, Italy. 8Henry Royce Institutefor Advanced Materials, Manchester, M13 9PL, UK. e-mail: camilla.coletti@iit.it; sergio.pezzini@nano.cnr.itCommunications Physics |           (2024) 7:391 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s42005-024-01887-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s42005-024-01887-0&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s42005-024-01887-0&domain=pdfhttp://orcid.org/0000-0001-7562-7340http://orcid.org/0000-0001-7562-7340http://orcid.org/0000-0001-7562-7340http://orcid.org/0000-0001-7562-7340http://orcid.org/0000-0001-7562-7340http://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/0000-0001-6263-4250http://orcid.org/0000-0001-6263-4250http://orcid.org/0000-0001-6263-4250http://orcid.org/0000-0001-6263-4250http://orcid.org/0000-0001-6263-4250http://orcid.org/0000-0002-8939-3175http://orcid.org/0000-0002-8939-3175http://orcid.org/0000-0002-8939-3175http://orcid.org/0000-0002-8939-3175http://orcid.org/0000-0002-8939-3175http://orcid.org/0000-0003-4574-7215http://orcid.org/0000-0003-4574-7215http://orcid.org/0000-0003-4574-7215http://orcid.org/0000-0003-4574-7215http://orcid.org/0000-0003-4574-7215http://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/0000-0002-8134-7633http://orcid.org/0000-0002-8134-7633http://orcid.org/0000-0002-8134-7633http://orcid.org/0000-0002-8134-7633http://orcid.org/0000-0002-8134-7633http://orcid.org/0000-0003-4289-907Xhttp://orcid.org/0000-0003-4289-907Xhttp://orcid.org/0000-0003-4289-907Xhttp://orcid.org/0000-0003-4289-907Xhttp://orcid.org/0000-0003-4289-907Xmailto:camilla.coletti@iit.itmailto:sergio.pezzini@nano.cnr.itwww.nature.com/commsphysResults and discussionA side-view sketch of the studied devices is shown in Fig. 1a. We employ adual-gate configuration to perform transport measurements with inde-pendent control of gate-induced charge density (ntot) and D (defined inMethods; optical microscopy images of the two TMBG devices investigatedare shown in Supplementary Note 1, Figure S1). The trilayer graphenestructure, encapsulated in hexagonal boron nitride (hBN), can be separatedinto aMLG(blue) rotated by~30°with respect to twoaligned layers forminga BLG (red and orange). In analogywith 30°-TBG21, we expect the lattices ofthe two subsystems to arrange into an incommensurate configurationlacking translational symmetry (i.e., with nomoiré superlattice), as sketchedin Fig. 1b. The real-space twist leads to a large momentum mismatchbetween theMLG and BLG bands located at the Brillouin zone corners (seeFig. 1c), effectively leading to their decoupling at low energy. Based onprevious results for 30°-TBG, the features of real-space quasicrystallineregistry could appear only at high energies (few eV)36,37, inaccessible in solid-state transport devices. The TMBG crystals are synthesized via the LP-CVDprocess introduced for 30°-TBG in ref. 21, in which the graphene-Cuinteraction locks the possible interlayer twist angles to either 0° or 30°38, withincreased growth times (here, 60min) favoring the formation of concentricmultilayer structures, sharing a single nucleation point (see Methods forexperimental details). In these samples, the hexagonal shape of the layersreflects their relative crystallographic orientation, making TMBG easilyrecognizable after transfer to SiO2/Si substrates (see Fig. 1d) among othercrystals with varied 0° or 30° rotation and layer number. Our growthapproach replaces the tear-and-stack procedure ubiquitously employed fortwisted graphene devices39,40, including small-angle TMBG12–16 and large-angle TDBG33,34, highlighting a possible path towards scalability of this classof materials.A first experimental indication of the composite MLG-BLG bandstructure of our TMBG41 is obtained from the 2D Raman mode, whichcouples to the electronic degrees of freedom in graphene multilayers42. Asshown in Fig. 1e (black continuous line), we observe a narrowpeak centeredat ~2690 cm−1 with two asymmetric shoulders, suggesting the convolutionof a single-Lorentzian peak (resulting from the Dirac dispersion of MLG)with a broadmulti-Lorentzian peak (resulting from the four-band parabolicdispersion of BLG). The measured TMBG 2D mode can be quantitativelyreconstructed as the sum (grey continuous line) of two Raman spectraseparately acquired on 30°-TBG (blue dotted line) and BLG (grey dottedline, multiplied by a factor two) crystals from the same growth batch (fullspectra are shown in Supplementary Note 2, Figure S2). We recall that the2D peak of 30°-TBG is indistinguishable from that of MLG, apart from ablueshift attributable to the modified dielectric environment21, which alsoapplies to the MLG subsystem within TMBG.Before discussing the results of electrical transport experiments, wediscuss the expected spectral properties of electrically-biased TMBG, at zeroand quantizing magnetic fields. This analysis is based on a self-consistentsolution for charge and potential distribution in vertically biased few-layergraphene, taking into account the out-of-plane dielectric polarizability ofeach layer, using a model developed and tested in ref. 22. For TMBG inquantizing magnetic fields, the charge distribution is determined by theLandau-level (LL) pinning between its monolayer and bilayer components,stemming from the quantum-capacitance effect22,43 (see SupplementaryNote 3 and Fig. S3 for details). In this analysis we take into accountproximity-induced energy shifts (δ) on the graphene layers interfacingencapsulating hBN, relative to the on-layer electrostatic potential of themiddle one (interfacing carbon layers on both sides). Such energy shifts arein line with the recent model developed by Tseng and Chou for free-standing (i.e., interfaced with vacuum) small-angle TMBG44. While theactual magnitude of δ is not known (would depend on the encapsulatingmaterial), we find that it can be determined from the comparison of thecomputed (in)compressibility maps, Fig. 1g, h, with experimentallyFig. 1 | Device concept, CVD-grown twisted graphene crystals and effect ofproximity energy shifts. a Side-view sketch of the studied devices. The gatingscheme is indicated on the lefthand side. The three graphene layers are represented,from top to bottom, as a blue, red and orange line. b Real-space arrangement of theTMBG crystals: MLG (blue lattice) is superimposed to BLG (red and orange lattices,following the color scheme of panel (a)) with a 30° twist angle. c Sketch of thereciprocal-space configuration, with the MLG (blue) and BLG (black) Brillouinzones and low-energy bands at K. d Optical microscopy image of a representativeCVD-grown trilayer graphene crystal transferred on SiO2/Si. The three hexagonsmark the concentric graphene layers formingTMBG (the color scheme follows panel(a)). The scale bar is 40 µm. e 2D Raman mode measured on TMBG on SiO2/Si(black). The grey continuous curve is the sum of aMLG-like (dotted blue line) and aBLG (dotted grey line) component. f BLG band gap as a function of displacementfield, without including proximity energy shifts (δ = 0, black line), and consideringthe shifts (δ = 18meV, dark cyan line). Inset: gap-closing displacement field as afunction of δ. (g,h) DOS of TMBGatB = 1 T calculated without including proximityenergy shifts (δ = 0) (g) and considering the shifts (δ = 18meV) (h). The dark redcircle indicates the BLG gap closing. The sketch above each graph shows the TMBGlayers (following the color scheme of panel (a)), the arrow indicates the direction ofpositive D-field. Dark cyan shadows highlight the graphene layers interfacingencapsulating hBN, hence affected by δ.https://doi.org/10.1038/s42005-024-01887-0 ArticleCommunications Physics |           (2024) 7:391 2www.nature.com/commsphysmeasured quantum Hall (QH) maps in Fig. 2e. In Fig. 1g, h we plot thedensity of states (DOS) of TMBG as a function of ntot andD for the cases ofδ = 0 and δ = 18meV, respectively. The color-coding is chosen to indicatewhen the chemical potential of electrons is pinned at the LLs (bright color)and when it crosses the inter-LL gaps (dark color). Diagonal (vertical) linestraceMLG (BLG) LLs, and their crossings correspond tomutual pinning ofMLG and BLG LLs. The simulation of DOSmaps was iterated for differentvalues of δ, until best matching the experimental QH data.The influence of proximity shift, δ, can be appreciated from the relativeshift of compressibility maps in Fig. 1g, h. Its influence is also illustrated inFig. 1f, where we plot the magnitude of the band gap in the BLG subsystem(Δ) as a function ofD, self-consistently calculated for δ = 0 (black line) andδ = 18meV (dark cyan line). In particular, the proximity shifts induce afinite Δ even in the absence of an external D-field. Furthermore, for eachvalue of δ, one can identify a displacement field,Dc (see inset in Fig. 1f), thatcompensates the proximitized interlayer asymmetry and closes the BLGgap, suggesting a practical tool for precise measurements of the energy shifton graphene under different encapsulating environments.In Fig. 2we present gate-dependent electrical-transportmeasurementsperformed at T = 0.36K on TMBG device D1 (analogous data fromD2 areshown in Supplementary Note 4, Fig. S4). Figure 2a shows the longitudinalresistivity ρxx as a function of the top and bottom gate bias (Vtg andVbg). Atlarge carrier density (top right and bottom left corners), ρxx exhibits lowvalues (<20Ω) that indicate high carrier mobility, as typically observed inhBN-encapsulated graphene stacks. At low carrier density, we observe twointersecting features, with a region of high resistivity (ρxx up to ~10 kΩ)departing from Vtg = Vbg = 0 and extending only in the lower-right quad-rant. To better discern the origin of the different transport contributions, inFig. 2b we show ρxx data acquiredwithin the dotted rectangle in Fig. 2a, as afunction ntot and D. Two split features, attributable to the charge neutralitypoints (CNPs) for the two subsystems, are visible. The first one, dispersingalmost vertically along ntot = 0, is associated to the subsystem with largerDOS, i.e., BLG. The second one, following a diagonal trajectory due toscreening of the gate potentials by BLG, tracks theMLGCNP.We observe amarked slope change of the MLG CNP in the vicinity of D = 0 – signalingdecreased screening and hence suppressed DOS in BLG – accompanied bylarge resistivity. At large negative D, the MLG CNP reverts to the originalslope and, at the same time, resistivity is suppressed, indicating restoredDOS in the BLG subsystem. This behavior is fully consistent with theMLGCNP crossing a band gap in BLG33 and can be reproduced by calculationsshown in Fig. 2c, inset (see Supplementary Note 3 for details). Overall, wenotice the pronounced asymmetry with respect to the displacement fieldwhich reflects the structural asymmetry of TMBG (as opposed to mea-surements on structurally symmetric 30°-twisted MLG-BLG-MLG, shownin Supplementary Note 5, Fig. S5). This characteristic is highlighted by ρxxcurves at selected D values, shown in Fig. 2c. At D = 0 we observe a clearFig. 2 | Low-temperature (magneto)transport of large-angle-twisted monolayer-bilayer graphene. a Longitudinal resistivity as a function of the gate potentials.b Longitudinal resistivity as a function of carrier density and displacement field,acquired within the dotted rectangle in panel (a). c Resistivity as a function of carrierdensity at selected displacement fields, as marked in (b). Inset: calculated resistivityof TMBG, as a function of carrier density and displacement field (the color scale isthe same used in panel (b)). d Longitudinal conductivity at B = 1 T as a function ofthe gate potentials (same ranges as in (a)). e Longitudinal conductivity at B = 1 T, asa function of carrier density and displacement field (same ranges as in (b)). The darkred circle indicates the position of gap closing in BLG, which identifies thedisplacement field Dc compensating the intrinsic BLG polarization. f Longitudinal(black) and Hall (grey) conductivity as a function of the total filling factor vtot =ntoth/eB at D =−0.072 V/nm at B = 1 T (see marker in panel (e)). The inset shows asketch of the alignment of LLs from the two subsystems (blue for MLG, black forBLG). The MLG 0-LL lies within the BLG gap, leading to a MLG-like ± 2 e2/h QHsequence at small fillings. 8 e2/h steps in the Hall conductivity signal coincidence ofLLs from the two subsystems (4 e2/h steps are measured otherwise). All measure-ments are performed at T = 0.36 K on device D1. A logarithmic color scale is used inpanels (a), (b), (d), (e).https://doi.org/10.1038/s42005-024-01887-0 ArticleCommunications Physics |           (2024) 7:391 3www.nature.com/commsphysresistivity peak, which increases (and slightly shifts) at D =−0.1 V/nm;upon reversing displacement field (D =+0.1 V/nm), the resistivity peakdisappears.We then apply a moderate magnetic field (B = 1 T, Fig. 2d–f) per-pendicular to the TMBG device, that reveals the independent Landauquantization of the two subsystems. In Fig. 2d, the longitudinal conductivityσxx (obtained by combining longitudinal and Hall resistivity data via theclassical tensorial relation) shows two separated sets of oscillations, withdifferent slope and frequency. The low-frequency oscillations are associatedto the subsystemwith smallerDOS, i.e., toMLG.TheMLGoscillations showan uneven spacing, reflecting the energy separations between the LLs ofmassless Dirac Fermions, as previously observed in capacitively-coupledgraphene layers, either spaced by dielectrics45 or twisted by a large angle23.The high-frequency oscillations are associated to BLG and are absent in anextended region showing vanishing σxx (dark blue in Fig. 2d), which signalsthe BLGgap. Figure 2e (σxx as a function ofntot andD) clearly shows that thegapped region collapses under a displacement field Dc = 0.14 V/nm (andreopens for D >Dc), which compensates the built-in BLG asymmetry. Themeasured pattern of LLs is best matched by DOS calculations shown inFig. 1h, which include an energy shift δ = 18meV. The sign of Dc indicatesthat the intrinsic BLGpolarizationpoints from top to bottom, in accordancewith ref. 44. Based on the magnitude of Dc, we estimate a correspondingBLG band gap Δ ~ 10meV, comparable to the one reported for TDBG33,34.Although spontaneous, few-meV gaps due to strong electron-electroninteractions weremeasured in suspended BLG devices46–48, those gaps showdistinctive D-symmetric gap closing and reopening, ruling out a possiblerelationwith the observed phenomenology.When theMLGzero-energy LL(0-LL) crosses the BLG gap, we clearly detect MLG-like QH states at fillingfactor vtot = ±2, as shown by σxx and σxy curves in Fig. 2f. Outside of the BLGgap, we observe quantized steps in σxy with the expected amplitude 4 e2/h(due to spin and valley degeneracy), with 8 e2/h steps in case of coincidenceof LLs from the two subsystems.Having identified the experimental signatures expected for an intrinsic~10meV Bernal gap in dual-gated TMBG, we now proceed to its quanti-tative estimate. In Fig. 3a, we present isotherms of ρxx as a function of ntot,measured at D =−0.075 V/nm on device D1 (analogous data from D2 arepresented in SupplementaryNote 6, Fig. S6).We observe thermal activationof the resistivity for T < 100 K, confirming the presence of an energy gap.This behavior is consistently observed at different D values, within thepreviously identified high-resistivity region (where the MLG CNP lieswithin the BLG gap). To appreciate changes in the conductivity of the BLGsubsystem as a function of temperature, we minimize the conductivitycontribution of the other subsystem, i.e.MLG, by considering the resistancemaximum corresponding to MLG CNP. As shown in Fig. 3b, we find anArrhenius-typedependence for themaximumof the resistivity peak ρxxmax∝exp[Δ/(2kBT)] (where Δ is the band gap and kB is the Boltzmann constant).The extracted gap reaches amaximumofΔ = 15meV atD =−0.075 V/nm,in linewith calculations shown inFig. 1f for δ = 18meV.TheD-dependenceshown Fig. 3b inset is influenced by MLG CNP crossing the BLG gap as afunctionof the gate voltages (see trajectory in Supplementary Fig. S3g), sincethe thermal activation gap reflects the distance betweenMLGCNP and theBLG band edges. As the displacement field becomes increasingly negative,the BLG gap widens (see Fig. 1f, dark cyan line), however MLG CNPapproaches one of the BLG band edges, leading to a lower carrier activationenergy and thus to a decrease of measuredΔ. The band gapmeasured fromthermal activation isfinite even atD = 0, confirming that no external electricfield is required for BLG gap opening within TMBG.We further investigate the transport properties of TMBG under largeperpendicular magnetic fields, which allows us to investigate the evolutionof the multicomponent LLs of the two subsystems promoted by Coulombinteractions49. In Fig. 4a, b, we show σxx and σxy data atB = 4 T, as a functionof vtot and D (the measurements span the usual ntot and D ranges). For theMLG subsystem we observe only the 0-LL, which splits into four branches(boundingQHgaps at vMLG = 0,+1,−1) due to complete lifting of the spinand valley degeneracy. The trajectories of the four MLG components aremodulated by multiple crossings with LLs from the BLG subsystem, whichalso clearly showdegeneracy lifting. Inparticular, theBLG0-LLpossesses anextra two-fold degeneracy associated with the orbital degree of freedom,making the multicomponent QH effect even richer and D-tunable50. Weobserve a clear symmetry of the BLG pattern with respect to the gap closingpoint at D =Dc, further confirming the intrinsic BLG polarization and itscompensation by a positive displacement field. At B = 8 T (Fig. 4c, d) weobserve multiple D-driven phase transitions in the BLG 0-LL aroundD =Dc, which reproduce recent results on BLG samples around D = 051.These observations indicate that: (i) the quality of our CVD-based devices isfully comparable with samples based on mechanically exfoliated graphenelayers; (ii) once the intrinsic polarization is compensated, the physics of theBLG subsystem embedded in TMBG is essentially indistinguishable fromthat of a stand-alone BLG. In Fig. 4e, f we show σxx and σxy curves at B = 8 Tand selected values of displacement field. Figure 4e shows the full brokensymmetry of the MLG 0-LL within the BLG band gap, while Fig. 4f high-lights the full broken symmetry in of the BLG0-LL (note that in this case theplateau sequence is shifted by a factor−2e2/h due to the contribution of twoparallel-conducting edge channels from hole-doped MLG).Fig. 3 | Thermal activation across the Bernal gap. a Longitudinal resistivity iso-therms as a function of the carrier density, measured on sampleD1 atD =−0.075 V/nm for 0.36 K < T < 104 K. bArrhenius plot of the resistivity peakmaxima fromdatain (a) (blue dots). The fit to ρxxmax∝ exp[Δ/(2kBT)] is shown as a blue continuous line.Inset: activation gaps obtained from the Arrhenius fit at different displacementfields. Error bars correspond to ± one standard error from the fits.https://doi.org/10.1038/s42005-024-01887-0 ArticleCommunications Physics |           (2024) 7:391 4www.nature.com/commsphysConclusionsIn conclusion, we established the presence of a built-in BLG band gap inlarge-angle TMBG. The gap is induced by the lack of inversion symmetry,combinedwith proximity energy shifts on the outmost graphene layers. TheBLG gap leads to specific signatures in electrical-transport properties, bothunder zero and quantizing magnetic fields that can be employed for itsquantitative estimate.Analogous featureshave alsobeenreported in a recentpre-print52, where TMBG was obtained from exfoliated graphene flakes.Although our samples are encapsulated in hBN (as now ubiquitous ingraphene research), we note that the observed effects are expected to occuralso in free-standing TMBG, where even larger gaps are predicted44, and inTMBG encapsulated with other dielectrics, which should modify the gapmagnitude. Along this line, we can anticipate the use of TMBG and mea-surements of the BLG gap closing atDc in dual-gated devices as ametrologyplatform for determiningproximity-induced energy shifts causedbyvariousencapsulating materials or insulating substrates (such as transition metaldichalcogenides). Moreover, the built-in BLG gap could be leveraged forbroadband detection in the THz window (following recent findings onTDBG34), with tunable absorption properties depending on the encapsu-lating environment. Finally, let us remind the high interest in BLG gap forthe definition of quantum point contacts27 and dots28,29, which might bedesigned with approaches beyond the current paradigm of local gating. Theapplicative potential of TMBG-based (opto)electronic andquantumdevicesis reinforced by the large-scale growth method employed in the fabricationof devices used in the reported studies.MethodsGate induced carrier density and displacement fieldWe adopt the relations ntot = 1/e x (CtgVtg+CbgVbg) and D/ε0 = (CbgVbg-CtgVtg)/218, where Cbg and Ctg are the capacitances per unit-area of thebottom and top gate,Vbg andVtg are voltage bias applied to the bottom andtop gate electrodes, e is the electron charge, ε0 is the vacuum dielectricpermittivity. Both the top and bottom hBN crystals used in the devices are~30 nm thick (as determined by atomic force microscopy, AFM). Weemploy εr = 3 for the out-of plane dielectric constant of hBN53,54, givingCbg=Ctg = 8.85 × 10−8 Fcm−2.CVD growth of multilayer graphene with 0°/30° twistTMBG crystals are grown by chemical vapor deposition in a Aixtron BlackMagic reactor (Aixtron 4” BM-Pro) on electropolished Cu foil at a pressureof 25mbar and a temperature of 1065 °C. After electropolishing, the Cu foilis heated in air on a hot plate at 250 °C for 15min to oxidize the Cu surface.The Cu foil is then loaded in the CVD reactor and annealed in Ar atmo-sphere at 1065 °C for 10mins, followed by 60min of graphene growth in amixture ofAr,H2 andCH4with aflow ratio of 900:40:0.8 sccm, respectively.Then the CVD reactor is cooled down to 100 °C in an Ar atmosphere. Aftergrowth, the shape of graphene crystals shows a deviation from perfecthexagons due to diffusion-limited growth mechanisms, as typical foroxygen-rich Cu foil55 and low partial pressure of H256. Crystals obtainedunder these conditions show regular electron diffraction patterns21 and lowstrain57 ( < 1%after transfer to SiO2/Si; though strain influences details of theBLG dispersion, the system is expected to remain gapless at such values58).We observe concentric multilayers with different interlayer rotations, eachone locked to either 0° or 30° (with a preponderance of aligned layers,attesting at ~60–70%). Among the trilayer crystals, a ~ 30% fraction showsthe stacking configuration targeted for this study.vdW assembly and device fabricationBefore vdW assembly, CVD-grown TMBG crystals are transferred to aSiO2/Si substrate using a semi-dry technique involving electrochemicaldelamination with a PMMA/PPC carrier membrane57. We first prepare acrystalline bottom gate by picking-up a graphite flake (~5 nm thick) usingFig. 4 | Multicomponent Landau levels in the two subsystems. Longitudinal andHall conductivity measured on device D1 at B = 4 T (a, b) and B = 8 T (c, d). Curvesat selected displacement field (indicated by the grey and red marks in panel (d)) areshown in (e) and (f), respectively; insets: sketches of the alignment of LLs from thetwo subsystems (blue for MLG, black for BLG), with degeneracy lifting in MLG (e)and BLG (f). Data acquired at T = 0.36 K on device D1.https://doi.org/10.1038/s42005-024-01887-0 ArticleCommunications Physics |           (2024) 7:391 5www.nature.com/commsphysan hBN flake carried by a PC/PDMS stamp59. The graphite back-gatescreens disorder from the underlying SiO2, yielding clean transport prop-erties in gapped BLGdevices60. After release and cleaning in chloroform, weuse contact-mode AFM to mechanically clean the hBN surface61. A secondhBN flake is used to pick-up a portion of the TMBG crystal. The hBN/TMBG is subsequently released at 180 °C on top of the cleaned hBN/gra-phite. The devices are processed combining electron-beam lithography,reactive ion etching and thermal evaporation of Cr/Au edge contacts andtop-gates.Raman spectroscopyA commercial Renishaw “InVia” system is used for Raman character-ization. Spectra are acquired employing a 532 nm wavelength and with a100x objective, producing a fluence ~350 µW/ µm2 on the sample, using a1800 l/mm grating. Calibration of the system is performed using the SiRaman peak at 520 cm−1.Electrical transport measurementsThe electrical transportmeasurements are performed in a dry “ICE 300mKHe-3 Continuos” cryostat equipped with an 8 T superconducting magnet(sample D1) and in a dry “ICE 3 K INV” cryostat (sample D2). Four-probemeasurements are performed with low-frequency (~13Hz) lock-in detec-tion, either in a constant current (~100 nA), or constant voltage config-uration (0.1 mV). The source-drain current and longitudinal and Hallvoltagedrops are simultaneously recorded,while biasing the top andbottomgates using a dc source-meter.Data availabilityThe data presented in this study are available at https://doi.org/10.5281/zenodo.14178601.Received: 25 July 2024; Accepted: 22 November 2024;References1. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. &Geim, A. K. The Electronic Properties of Graphene. Rev. Mod. Phys.81, 109–162 (2009).2. Slizovskiy, S., McCann, E., Koshino, M. & Fal’ko, V. I. Films ofRhombohedral Graphite as Two-Dimensional TopologicalSemimetals. Commun. Phys. 2, 1–10 (2019).3. Garcia-Ruiz, A., Slizovskiy, S. & Fal’ko, V. I. Flat Bands for Electrons inRhombohedral Graphene Multilayers with a Twin Boundary. Adv.Mater. Interfaces 10, 2202221 (2023).4. Garcia-Ruiz, A., Enaldiev, V., McEllistrim, A. & Fal’ko, V. I. Mixed-Stacking Few-Layer Graphene as an Elemental Weak FerroelectricMaterial. Nano Lett. 23, 4120–4125 (2023).5. McCann, E. & Fal’ko, V. I. Landau-Level Degeneracy and QuantumHall Effect in a Graphite Bilayer. Phys. Rev. Lett. 96, 086805 (2006).6. Ge, Z. et al. Control of Giant TopologicalMagneticMoment and ValleySplitting in Trilayer Graphene. Phys. Rev. Lett. 127, 136402 (2021).7. Carr, S. et al. Twistronics: Manipulating the Electronic Properties ofTwo-Dimensional Layered Structures through Their Twist Angle.Phys. Rev. B 95, 075420 (2017).8. Bistritzer, R. & MacDonald, A. H. Moiré Bands in Twisted Double-Layer Graphene. Proc. Natl. Acad. Sci. 108, 12233–12237 (2011).9. Cao, Y. et al. Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices. Nature 556, 80–84 (2018).10. Cao, Y. et al. Unconventional Superconductivity in Magic-AngleGraphene Superlattices. Nature 556, 43–50 (2018).11. Andrei, E. Y. et al. The Marvels of Moiré Materials. Nat. Rev. Mater. 6,201–206 (2021).12. Chen, S. et al. Electrically Tunable Correlated and Topological Statesin Twisted Monolayer–Bilayer Graphene. Nat. Phys. 17, 374–380(2021).13. Xu, S. et al. Tunable van Hove Singularities and Correlated States inTwistedMonolayer–Bilayer Graphene.Nat. Phys. 17, 619–626 (2021).14. Polshyn, H. et al. Electrical Switching of Magnetic Order in an OrbitalChern Insulator. Nature 588, 66–70 (2020).15. He, M. et al. Competing Correlated States and Abundant OrbitalMagnetism in Twisted Monolayer-Bilayer Graphene. Nat. Commun.12, 4727 (2021).16. Zhang, C. et al. Local Spectroscopy of a Gate-Switchable MoiréQuantum Anomalous Hall Insulator. Nat. Commun. 14, 3595 (2023).17. Polshyn, H. et al. Topological Charge Density Waves at Half-IntegerFilling of a Moiré Superlattice. Nat. Phys. 18, 42–47 (2022).18. Sanchez-Yamagishi, J. D. et al. Quantum Hall Effect, Screening, andLayer-Polarized Insulating States in Twisted Bilayer Graphene. Phys.Rev. Lett. 108, 076601 (2012).19. Sanchez-Yamagishi, J. D. et al. Helical Edge States and FractionalQuantum Hall Effect in a Graphene Electron–Hole Bilayer. Nat.Nanotech 12, 118–122 (2017).20. Rickhaus, P. et al. The Electronic Thickness of Graphene. Sci. Adv. 6,eaay8409 (2020).21. Pezzini, S. et al. 30°-Twisted Bilayer Graphene Quasicrystals fromChemical Vapor Deposition. Nano Lett. 20, 3313–3319 (2020).22. Slizovskiy, S. et al. Out-of-Plane Dielectric Susceptibility of Graphenein Twistronic and Bernal Bilayers. Nano Lett. 21, 6678–6683 (2021).23. Piccinini, G. et al. Parallel Transport and Layer-ResolvedThermodynamic Measurements in Twisted Bilayer Graphene. Phys.Rev. B 104, L241410 (2021).24. McCann, E. Asymmetry Gap in the Electronic Band Structure ofBilayer Graphene. Phys. Rev. B 74, 161403 (2006).25. Oostinga, J. B., Heersche, H. B., Liu, X., Morpurgo, A. F. &Vandersypen, L. M. K. Gate-Induced Insulating State in BilayerGraphene Devices. Nat. Mater. 7, 151–157 (2008).26. Zhang, Y. et al. Direct Observation of a Widely Tunable Bandgap inBilayer Graphene. Nature 459, 820–823 (2009).27. Overweg, H. et al. Electrostatically Induced Quantum Point Contactsin Bilayer Graphene. Nano Lett. 18, 553–559 (2018).28. Banszerus, L. et al. Gate-Defined Electron–Hole Double Dots inBilayer Graphene. Nano Lett. 18, 4785–4790 (2018).29. Eich,M. et al. CoupledQuantumDots in Bilayer Graphene.Nano Lett.18, 5042–5048 (2018).30. Zhou, H. et al. IsospinMagnetism and Spin-Polarized Superconductivityin Bernal Bilayer Graphene. Science 375, 774–778 (2022).31. de la Barrera, S. C. et al. Cascade of Isospin Phase Transitions inBernal-Stacked Bilayer Graphene at Zero Magnetic Field. Nat. Phys.18, 771–775 (2022).32. Seiler, A. M. et al. Quantum Cascade of Correlated Phases inTrigonally Warped Bilayer Graphene. Nature 608, 298–302 (2022).33. Rickhaus, P. et al. Gap Opening in Twisted Double Bilayer Grapheneby Crystal Fields. Nano Lett. 19, 8821–8828 (2019).34. Agarwal, H. et al Ultra-Broadband Photoconductivity in TwistedGraphene Heterostructures with Large Responsivity. Nat. Photon.1–7, https://doi.org/10.1038/s41566-023-01291-0 (2023).35. Zhang, Z. et al. Growth and Applications of Two-Dimensional SingleCrystals. 2D Mater. 10, 032001 (2023).36. Ahn, S. J. et al. Dirac Electrons in a Dodecagonal GrapheneQuasicrystal. Science 361, 782–786 (2018).37. Moon,P., Koshino,M.&Son,Y.-W.QuasicrystallineElectronicStates in30° Rotated Twisted BilayerGraphene.Phys. Rev. B 99, 165430 (2019).38. Yan, Z. et al. Large Hexagonal Bi- and Trilayer Graphene SingleCrystals with Varied Interlayer Rotations. Angew. Chem. Int. Ed. 53,1565–1569 (2014).39. Kim, K. et al. Van Der Waals Heterostructures with High AccuracyRotational Alignment. Nano Lett. 16, 1989–1995 (2016).40. Cao, Y. et al. Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene. Phys. Rev. Lett. 117,116804 (2016).https://doi.org/10.1038/s42005-024-01887-0 ArticleCommunications Physics |           (2024) 7:391 6https://doi.org/10.5281/zenodo.14178601https://doi.org/10.5281/zenodo.14178601https://doi.org/10.1038/s41566-023-01291-0https://doi.org/10.1038/s41566-023-01291-0www.nature.com/commsphys41. SuárezMorell, E.,Pacheco,M.,Chico, L.&Brey,L.ElectronicPropertiesof Twisted Trilayer Graphene. Phys. Rev. B 87, 125414 (2013).42. Ferrari, A. C. et al. Raman Spectrum of Graphene and GrapheneLayers. Phys. Rev. Lett. 97, 187401 (2006).43. Ando, T., Fowler, A. B. & Stern, F. Electronic Properties of Two-Dimensional Systems. Rev. Mod. Phys. 54, 437–672 (1982).44. Tseng, W.-E., Chou, M.-Y. Electrically Tunable Flat Bands with Layer-Resolved Charge Distribution in TwistedMonolayer-Bilayer Graphene.arXiv December 4, https://doi.org/10.48550/arXiv.2312.01820 (2023).45. Kim, S. et al. Direct Measurement of the Fermi Energy in GrapheneUsing a Double-Layer Heterostructure. Phys. Rev. Lett. 108, 116404(2012).46. Weitz, R. T., Allen, M. T., Feldman, B. E., Martin, J. & Yacoby, A.Broken-Symmetry States in Doubly Gated Suspended BilayerGraphene. Science 330, 812–816 (2010).47. Velasco, J. et al. Transport Spectroscopy of Symmetry-BrokenInsulatingStates inBilayerGraphene.Nat.Nanotech 7, 156–160 (2012).48. Freitag, F., Trbovic, J.,Weiss,M. &Schönenberger, C. SpontaneouslyGapped Ground State in Suspended Bilayer Graphene. Phys. Rev.Lett. 108, 076602 (2012).49. Young, A. F. et al. Spin and Valley Quantum Hall Ferromagnetism inGraphene. Nat. Phys. 8, 550–556 (2012).50. Lee, K. et al. Chemical Potential andQuantumHall Ferromagnetism inBilayer Graphene. Science 345, 58–61 (2014).51. Xiang, F. et al. Intra-Zero-Energy Landau Level Crossings in BilayerGraphene at High Electric Fields. Nano Lett. 23, 9683–9689 (2023).52. Jiang, J. et al. Featuring Nuanced Electronic Band Structure inGapped Multilayer Graphene. arXiv https://doi.org/10.48550/arXiv.2405.12885 (2024).53. Yang, F. et al. Experimental Determination of theEnergy per Particle inPartially Filled Landau Levels. Phys. Rev. Lett. 126, 156802 (2021).54. Ferreira, F., Enaldiev, V. V. & Fal’ko, V. I. Scaleability of DielectricSusceptibility εzz with the Number of Layers and Additivity ofFerroelectric Polarization in van Der Waals Semiconductors. Phys.Rev. B 106, 125408 (2022).55. Hao, Y. et al. The Role of Surface Oxygen in the Growth of LargeSingle-Crystal Graphene on Copper. Science 342, 720–723 (2013).56. Wu, B. et al. Self-Organized Graphene Crystal Patterns. NPG AsiaMater. 5, e36 (2013).57. Giambra, M. A. et al. Wafer-Scale Integration of Graphene-BasedPhotonic Devices. ACS Nano 15, 3171–3187 (2021).58. Mucha-Kruczyński, M., Aleiner, I. L. & Fal’ko, V. I. Strained BilayerGraphene: Band Structure Topology and Landau Level Spectrum.Phys. Rev. B 84, 041404 (2011).59. Purdie, D. G. et al. Cleaning Interfaces in Layered MaterialsHeterostructures. Nat. Commun. 9, 5387 (2018).60. Icking, E. et al. Transport Spectroscopy of Ultraclean Tunable BandGaps in Bilayer Graphene. Adv. Electron. Mater. 8, 2200510 (2022).61. Goossens, A. M. et al. Mechanical Cleaning of Graphene. Appl. Phys.Lett. 100, 073110 (2012).AcknowledgementsThis work has received funding from: PNRR MUR project PE00000023 –NQSTI and the European Union’s Horizon 2020 Research and InnovationProgramme under Grant Agreement No. 881603 Graphene Flagship. Weacknowledge funding from theEuropeanUnion through theGraPh-Xproject(Grant agreement ID: 101070482). K.W. and T.T. acknowledge support fromthe JSPSKAKENHI (Grant Numbers 21H05233 and 23H02052), the CREST(JPMJCR24A5), JST and World Premier International Research CenterInitiative (WPI), MEXT, Japan. V.F. and S.S. acknowledge support fromEPSRC grant EP/V007033/1, British Council and International SciencePartnerships Fund Grant 1185409051 for Research Collaboration betweenUK and Japan.Author contributionsS.P. conceivedanddesigned the experiments. Z.M.G. andV.M. synthesizedthe TMBG crystals and transferred them toSiO2/Si. A.B. and S.P. fabricatedthe devices and performed the transport measurements. A.B. and S.P.performed the data analysis, with support from A.R. and S.F. S.S. and V.I.F.performed the theoretical modelling. K.W. and T.T. provided hexagonalboron nitride crystals. F.B. and C.C. supported the experiments andcoordinated the collaboration together with V.I.F and S.P. A.B. and S.P. co-wrote the manuscript with input from all co-authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s42005-024-01887-0.Correspondence and requests for materials should be addressed toCamilla Coletti or Sergio Pezzini.Peer review information Communications Physics thanks Julien Barrierand the other, anonymous, reviewer(s) for their contribution to the peerreview of this work.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard tojurisdictional 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 anymedium or format, as longas you give appropriate credit to the original author(s) and the source,provide a link to the Creative Commons licence, and indicate if changeswere made. The images or other third party material in this article areincluded in the article’s Creative Commons licence, unless indicatedotherwise in a credit line to the material. If material is not included in thearticle’sCreativeCommons licence and your intended use is not permittedby statutory regulation or exceeds the permitted use, you will need toobtain permission directly from the copyright holder. To view a copy of thislicence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2024https://doi.org/10.1038/s42005-024-01887-0 ArticleCommunications Physics |           (2024) 7:391 7https://doi.org/10.48550/arXiv.2312.01820https://doi.org/10.48550/arXiv.2312.01820https://doi.org/10.48550/arXiv.2405.12885https://doi.org/10.48550/arXiv.2405.12885https://doi.org/10.48550/arXiv.2405.12885https://doi.org/10.1038/s42005-024-01887-0http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/www.nature.com/commsphys Built-in Bernal gap in large-angle-twisted monolayer-bilayer graphene Results and discussion Conclusions Methods Gate induced carrier density and displacement field CVD growth of multilayer graphene with 0°/30° twist vdW assembly and device fabrication Raman spectroscopy Electrical transport measurements Data availability References Acknowledgements Author contributions Competing interests Additional information