# Fileset

[s43246-024-00633-x.pdf](https://mdr.nims.go.jp/filesets/cfa6bff4-3cf0-4c36-bda9-47c2be08fda8/download)

## Creator

[Oleg Makarovsky](https://orcid.org/0000-0002-8625-5084), Richard J. A. Hill, Tin S. Cheng, [Alex Summerfield](https://orcid.org/0000-0001-6091-3969), [Takeshi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Christopher J. Mellor](https://orcid.org/0000-0001-5987-7876), [Amalia Patanè](https://orcid.org/0000-0003-3015-9496), [Laurence Eaves](https://orcid.org/0000-0002-5334-0987), [Sergei V. Novikov](https://orcid.org/0000-0002-3725-2565), [Peter H. Beton](https://orcid.org/0000-0002-2120-8033)

## Rights

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

## Other metadata

[High-temperature Brown-Zak oscillations in graphene/hBN moiré field effect transistor fabricated using molecular beam epitaxy](https://mdr.nims.go.jp/datasets/8be49dbf-34e1-48d3-b339-52d5d1eb64bf)

## Fulltext

High-temperature Brown-Zak oscillations in graphene/hBN moiré field effect transistor fabricated using molecular beam epitaxycommunicationsmaterials Articlehttps://doi.org/10.1038/s43246-024-00633-xHigh-temperature Brown-Zak oscillationsin graphene/hBN moiré field effecttransistor fabricated using molecularbeam epitaxyCheck for updatesOleg Makarovsky 1 , Richard J. A. Hill1, Tin S. Cheng1, Alex Summerfield 1, Takeshi Taniguchi 2,Kenji Watanabe 2, Christopher J. Mellor 1, Amalia Patanè 1, Laurence Eaves 1,Sergei V. Novikov 1 & Peter H. Beton 1Grapheneplaced on hexagonal boron nitride (hBN) has received significant interest due to its excellentelectrical performance and physics phenomena, such as superlattice Dirac points. Direct molecularbeam epitaxy growth of graphene on hBN offers an alternative fabrication route for hBN/graphenedevices. Here, we investigate the electronic transport of moiré field effect transistors (FETs) in whichthe conducting channel ismonolayer graphene grownonhexagonal boron nitride by high temperaturemolecular beam epitaxy (HT-MBE). Alignment between hBN and HT-MBE graphene crystal latticesgives rise to a moiré-fringed hexagonal superlattice pattern. Its electronic band structure takes theform of a “Hofstadter butterfly”. When a strong magnetic field B is applied perpendicular to thegraphene layer, the electrical conductance displaysmagneto-oscillations, periodic inB−1, over a widerange of gate voltages and temperatures up to 350 K.Weattribute this behaviour to the quantisation ofelectronic charge and magnetic flux within each unit cell of the superlattice, which gives rise to so-called Brown-Zak oscillations, previously reported only in high-mobility exfoliated graphene. Thus,this HT-MBE graphene/hBN heterostructure provides a platform for observation of room temperaturequantum effects and device applications.Single layer graphene1 has unique electronic properties, including recordhigh room temperature carrier mobility2–4, for fundamental studies ofquantum phenomena in novel quantum transport devices, such as moirésuperlattices5–7 andmoiré field effect transistors (FETs)8. A large number ofgrowth and fabrication techniques have been developed in the last 20 yearsto improve graphene quality and scalability for applications in electronicdevices. At present, the best performance is achieved with exfoliated gra-phene encapsulated by another remarkable material, hexagonal boronnitride, hBN9. FETs fabricated from hBN-encapsulated graphene using theexfoliation-stamping technique exhibit record high carrier mobility,reaching 500,000 cm2/Vs3. However, attempts to adapt hBN/graphene FETtechnology for large scale fabrication and epitaxial growth have so far metwith only limited success. Graphene/hBN FETs fabricated using chemicalvapour deposition (CVD) either require manual hBN encapsulationof individual flakes4 or demonstrate rather moderate mobility of about10,000 cm2/Vs10. High temperature molecular beam epitaxy (HT-MBE)growthof single layergraphenedirectly on anhBNsubstrate11–13 provides analternative route for making hBN/graphene devices. Despite significantinterest in the growth ofMBE graphene and hBN14–16, we believe that this isthe first report on the transport properties of an HT-MBE hBN/grapheneFET device.An opportunity to combine 2Dmaterials in a “LEGO building-block”way has led to a new class of functional materials, van der Waals (vdW)heterostructures17–19. One of the simplest vdW heterostructure consists of alayer of exfoliated graphene placed on the atomically flat surface of an hBNcrystal. These twomaterials have lattice constants that differ by only ~1.8%.When their crystalline axes are carefully aligned to within an angle of ~1o,atomic force microscopy (AFM) reveals a hexagonal moiré pattern on thesurface of the graphene layer with a period of typically ~14 nm for aligned,unstrained graphene20,21. This periodic pattern generates a superlattice1School of Physics and Astronomy, University of Nottingham, Nottingham, NG7 2RD, UK. 2The National Institute for Materials Science, Advances MaterialsLaboratory, 1-1 Namiki, Tsukuba, Ibraki, 305-0044, Japan. e-mail: oleg.makarovsky@nottingham.ac.ukCommunications Materials |           (2024) 5:189 11234567890():,;1234567890():,;http://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00633-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00633-x&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s43246-024-00633-x&domain=pdfhttp://orcid.org/0000-0002-8625-5084http://orcid.org/0000-0002-8625-5084http://orcid.org/0000-0002-8625-5084http://orcid.org/0000-0002-8625-5084http://orcid.org/0000-0002-8625-5084http://orcid.org/0000-0001-6091-3969http://orcid.org/0000-0001-6091-3969http://orcid.org/0000-0001-6091-3969http://orcid.org/0000-0001-6091-3969http://orcid.org/0000-0001-6091-3969http://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/0000-0003-3701-8119http://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/0000-0001-5987-7876http://orcid.org/0000-0001-5987-7876http://orcid.org/0000-0001-5987-7876http://orcid.org/0000-0001-5987-7876http://orcid.org/0000-0001-5987-7876http://orcid.org/0000-0003-3015-9496http://orcid.org/0000-0003-3015-9496http://orcid.org/0000-0003-3015-9496http://orcid.org/0000-0003-3015-9496http://orcid.org/0000-0003-3015-9496http://orcid.org/0000-0002-5334-0987http://orcid.org/0000-0002-5334-0987http://orcid.org/0000-0002-5334-0987http://orcid.org/0000-0002-5334-0987http://orcid.org/0000-0002-5334-0987http://orcid.org/0000-0002-3725-2565http://orcid.org/0000-0002-3725-2565http://orcid.org/0000-0002-3725-2565http://orcid.org/0000-0002-3725-2565http://orcid.org/0000-0002-3725-2565http://orcid.org/0000-0002-2120-8033http://orcid.org/0000-0002-2120-8033http://orcid.org/0000-0002-2120-8033http://orcid.org/0000-0002-2120-8033http://orcid.org/0000-0002-2120-8033mailto:oleg.makarovsky@nottingham.ac.ukwww.nature.com/commsmatpotential landscape in the graphene layer, which significantly changes itselectronic band structure5,6,20,21.In an earlier article, we reported that moiré-fringed superlatticeswith periodicities greater than 14 nm can be formed when graphene isgrown by HT-MBE on exfoliated hBN crystals with excellent alignmentof the crystal lattices11. In some cases, at substrate temperatures above1600 °C, the pattern is found to diverge towards “infinity”, indicating alattice matching condition between the graphene and hBN12, which hasnot been achieved using other growth or processing techniques. Ramanspectroscopy measurements on these heterostructures reveal a sig-nificant splitting and shifting of the G and 2D peaks of graphene, whichconfirm that the moiré fringing arises from the presence of large strainsof up to ~1.8% for the case of lattice-matched graphene. The large moirépattern resulting from these strains is an intrinsic feature of graphenegrown on hBN by MBE at these temperatures; it is not observed ingraphene grown on hBN by CVD. Conductive AFMmeasurements havealso revealed moire-́modulated current through the hBN tunnelbarriers13.ResultsHere we investigate the electrical properties of a planar FET based on aHT-MBE-graphene-hBN heterostructure and mounted on the oxidised surfaceof a silicon substrate. By applying a gate voltage, it is possible to change thepolarity and sheet density of the carriers andmeasure carrier concentrationandmobility.We find that the very low (<1011 cm−2) doping level producedby unintentional impurities in our devices is similar to that reported forhigh-quality hBN/graphene heterostructures produced by exfoliation2,3.However, the carrier mobility in our devices is temperature-independentand much lower (about 1000 cm2/Vs) than in exfoliated graphene. Thissuggests a different type of dominant scattering mechanism in the HT-MBE-grown hBN/graphene heterostructures. We also investigate the effectof an appliedmagneticfield,B, on the electrical properties of the devices.Weobserve a large linear magnetoresistance upon which are superimposedmagneto-oscillations, periodic in 1/B. We attribute these magneto-oscillations to the formation of Brown-Zak minibands when a unit cell ofthe superlattice is threaded by a unit fraction of a magnetic flux quantum,1/p, where p is an integer22,23.Our MBE graphene layers are grown at high substrate temperatures(1500 oC) on hBN flakes. Details of the layer growth and device fabri-cation processes are given in theMethods section. Schematic diagrams ofthe graphene-hBN FET with a bias voltage, Vb, and a gate voltage, Vg,applied between the graphene channel and the boron-doped p-Si sub-strate and its transfer characteristic at T = 273 K are shown in Fig. 1a, b.Figure 1c shows the Raman spectrum of HT-MBE graphene layer withhBN, G, 2D and Dag peaks discussed below. Figure 1d, e show optical andAFM images of the centre of the device, following fabrication togetherwith the contact electrodes and etched MBE graphene surface. Figure 1fpresents a typical tapping mode (AC-mode) AFM image of a monolayerof graphene on hBN grown under these conditions, prior to flake transferand device fabrication. It reveals a moiré pattern with a periodicity, a,of ~14 nm.The resistance maximum at Vg =+1.1 V in Fig. 1c indicates that thepolarity of the ungated graphene layer is weakly p-type, with a hole con-centration, p = 8.2 × 1010 cm−2 at Vg = 0. The very small hysteresis of R(Vg)measured atdifferentdirectionsof theVg-sweep (blackarrows inFig. 1c) canbe attributed to the high purity (absence of charge traps) in this HT-MBEgraphene. A broader satellite peak in R(Vg) occurs on the hole branch of theplot at Vg ~−40 V.This additional feature has been investigated intensively in moiré-fringed superlattices made from exfoliated graphene crystallographically-Fig. 1 | HT-MBE graphene FET. a Schematic and connection diagrams of the HT-MBE graphene FET used in the electrical measurement of the transport properties.b Raman spectrum of HT-MBE graphene. c Resistance of MBE-graphene FET atT = 273 K and B = 0 as a function of gate voltageVg. Black arrows indicate directionsof the Vg-sweep. d Optical image of the region in the main image showing the hBNflake (green) and Au/Ti contacts (gold). e AFM image of the centre of the graphenedevice following fabrication. fACmodeAFM image of the pristine graphene surfacefollowing HT-MBE growth prior to device fabrication showing a 14 nm periodsuperlattice with the underlying hBN substrate.https://doi.org/10.1038/s43246-024-00633-x ArticleCommunications Materials |           (2024) 5:189 2www.nature.com/commsmataligned on hBN substrates. It is due to the formation of second-generationDirac points in the valence band produced by the superlattice potential5,6.Using a linear fitting of electrical conductivity σ(Vg)24, we estimate the roomtemperature electron and hole mobilities to be µe = 1300 cm2/Vs andµh = 840 cm2/Vs at T = 273 K. They have a very weak (<30%) temperaturedependence over a wide temperature range 2 K < T < 300 K, see Supple-mentary Note 1.The electrical resistance of the device was measured by passing aconstant current of I = 10 µA through the graphene channel, first in theabsence of an applied magnetic field and then in magnetic fields of up to18 T applied at different tilt angles Θ, to the normal of the graphene sheet.Figure 2a shows the two-terminal magnetoresistance of the device, R(B), atVg =+50 Vand atT = 273 K, up tofields of 14 TwithB oriented at differentangles Θ. The large and approximately linear magnetoresistance for Θ = 0decreases as cos(Θ) when the tilt angle is increased. Inspection of the R(B)curves indicates the presence of magneto-oscillations, which are periodic in1/B and are superimposed upon the large monotonic increase of R(B). Theoscillations are shownmore clearly in Fig. 2b, in which a linear (R ~ B) termis subtracted from the R(BcosðΘÞ) plots. These measurements demonstratethat the period of the magneto-oscillations depends only on the perpendi-cular component of B, B? ¼ B cosðΘÞ, confirming that they arise from thetwo-dimensional electron system. These oscillations are observed over awide range of the applied gate voltages (Fig. 2c) and high temperaturesT > 300 K (Fig. 2d.Figure 3a, b show themagnetoresistance of the device atT = 210 K andT = 2K respectively, at Θ = 0, and different applied gate voltages. At lowtemperature the structure of the observed oscillations is rather complicated.The magnetic field values of some peaks follow a linear dependence on thegate voltage (black dots in Fig. 3c). The B-values of others are almostindependent of Vg (red triangles in Fig. 3c). We ascribe the first group ofmagneto-oscillations with a linear Vg dependence to the Shubnikov – daHaas effect (SdH) in graphene1. The dashed lines in Fig. 3c represent thepositions of the Landau levels calculated using a capacitance model of theVg-dependent carrier concentration in graphene and carrier theconcentration associated with SdH oscillations1:n ¼ εε0edVg ¼4eBjNjhð1Þwhere ε = 3.9 and d = 300 nmare the dielectric constant and thickness of theSiO2 layer respectively, and N is Landau level index. The second group ofoscillations (red triangles in Fig. 3c) are indicated by red arrows in Fig. 3a.They are periodic in 1/B andmost pronounced forVg > 30 V.Their period isessentially independent of Vg, and hence of the carrier density (Fig. 3c).These oscillations persist over a wide range of temperatures up to about350 K (80 oC), as shown in Fig. 2d. These observations indicate that theycannot be due to the Shubnikov-de Haas effect, which is dependent on thecarrier concentration Eq. (1) and requires that the thermal energy kBT issmall compared to the Landau level separation and the Fermi energy. Thefield-dependence ofVg-independent oscillations can be fitted empirically toan exponentially damped cosine function of the formΔR ¼ R0 exp�γBfB� �cos2πBfBþ φ� �ð2Þwhere Bf ¼ 24 T determines the characteristic period, γ≈ 1:0 is thedamping term andφ≈ π=10 is a phase factor, see SupplementaryNote 2 fordetails of the fit.DiscussionWe now consider the physical mechanism responsible for the Vg-inde-pendent magneto-oscillations. Their characteristic frequency Bf = 24 T isquite similar to the condition for the magnetophonon resonance effect ingraphene25,26. Magnetophonon resonance appears as a series of maxima (orminima) in the magnetoresistance when the condition N_ωc ¼ _ωp issatisfied. Here,N is an integer and _ωp is the energy of the phonon involvedin the scattering process, typically a weakly-dispersed longitudinal optic-mode phonon25,26. These well-established phenomena are not responsibleFig. 2 | Magnetoresistance as a function of tem-perature, gate voltage and field orientation.a Two-terminal residual magnetoresistance of theMBE graphene device at Vg =+50 V and T = 273 Kas a function of the tilt angle, Θ, between the per-pendicular to the graphene plane and the appliedmagnetic field, as shown in the inset. b Same dataplotted as a function of B component perpendicularto the graphene plane (B⊥) after subtraction of thelinear (R ~ B) magnetoresistance background.c Gate-voltage dependence of magneto-oscillationsat T = 273 K. d Temperature dependence above228 K of magneto-oscillations up to 18 T atVg =+50 V. Bup and Bdown curves at T = 275 K wereobtained while sweeping to higher and lower mag-netic field, respectively.https://doi.org/10.1038/s43246-024-00633-x ArticleCommunications Materials |           (2024) 5:189 3www.nature.com/commsmatfor the Vg-independent magneto-oscillations observed in our graphene-hBN heterostructures. Instead, they arise from magneto-oscillations asso-ciated with the Hofstadter butterfly band structure20,21. This phenomenonwas recently observed in crystallographically-aligned layers of exfoliatedgraphene on hBN and has been given the name Brown-Zak22,23 magneto-oscillations, recently reported inhBNencapsulated exfoliated graphenewithhigh electronmobility μ > 10,000 cm2/Vs27–29. The frequency Bf is related tothe area, A, of the unit cell of the moiré superlattice, Bf = h/eA. Ourexperimental value Bf = 24 T implies a moiré periodicity a = 14 nm con-sistent with our AFM images (Fig. 1f).Interestingly, in our samples we observe Brown-Zak oscillations ingraphene layers with relatively low mobility µ ~1000 cm2/Vs, where noBrown-Zak oscillations have been previously reported to our knowledge.We ascribe this behaviour to the high purity of our MBE-grown graphene.The doping level in our graphene layer is Nimp < 1011 cm−2 (Fig. 1c, d).Scattering by ionised impurities is regarded as a major mobility-limitingmechanisms for graphene layers such as CVD graphene on SiO2/Si30,31.However, the impurity density required to reduce electron mobility toµ < 1000 cm2/Vs, is Nimp > 5 × 1012 cm−2 (corresponding to Vg ≈+ 70 V)30,which is about 2 orders of magnitude higher than carrier concentrationmeasured at Vg = 0, p = 8.2 × 1010 cm−2 (Fig. 1c). Other scatteringmechanisms: phonons32, surface corrugations33, sample edges34, are usuallyignored in devices with such a low mobility as their mobility limits aretypically µ > 10,000 cm2/Vs32–34. The presented device does not have thehBN capping layer used in some ultrahigh mobility (µ > 100,000 cm2/Vs)exfoliated35 andCVD4 hBN/graphene/hBNFETs.Without a top hBN layer,FETs made using high-purity (p/n < 1011 cm−2) graphene typicallydemonstrate mobilities much higher than 1000 cm2/Vs24,36, suggesting thatmobility of our HT-MBE graphene is limited by the growth-related pro-cesses rather than post-growth contamination.It is possible that the scattering mechanism responsible for μ ≈1000 cm2/Vs in our HT-MBE-grown graphene/hBN layer is related to thevery high level of strain generated during HT-MBE growth. Previously, insimilarHT-MBE graphene-hBNheterostructurewe reported that the straincan be > 1%11,12. Themoiré pattern periodicity of 14 nm (Fig. 1f) andRamanspectrum (Fig. 1b) indicate that this strain is largely relaxed in the deviceinvestigated here12. The Raman spectrum (Fig. 1b) also differs significantlyfrom the Raman spectra of high mobility (> 100,000 cm2/Vs) graphenelayers4,35. The relative intensity of the 2D and G peaks I(2D)/I(G) ≈ 1.7 issimilar to the ratio observed in high-qualitymonolayer graphene. However,the fullwidth at halfmaximumof the 2Dpeak is large, 54 cm−1, compared tothat (< 20 cm−1) reported for high mobility graphene4,35. The wide 2D peakmay arise from small, nanometre-scale strain35, which can affect electronmobility in high quality hBN/graphene4. Also, we observe an additionalpeak at 1350 cm−1 (Dag peak in Fig. 1c) associated with graphene aggregateson the HT-MBE graphene surface11,12. These aggregates are visible as smallbright spots in the AFM image of the device (Fig. 1e). Previously, we sug-gested that the aggregates provide pinning sites that maintain the strain inthe epitaxial graphene when cooling down from the high growthtemperatures12; however, their role in electron transport and their effect ongraphene mobility have not been studied yet.The specific growth conditions responsible for the low carrier con-centration and mobility in MBE graphene (ultrahigh growth temperature(1500oC), post growth relaxation processes11,12) cannot be achievedin other types of epitaxial or exfoliated graphene making it difficult tocompare the mobility-limiting mechanics in our HT-MBE FET withother graphene FETs. Further theoretical and experimental studies arerequired to reveal details of the electron transport in theHT-MBE grapheneas it can significantly limit its applicability in high mobility electronicapplications.MethodsMBE growth of graphene on hBNOur MBE graphene layers are grown at high substrate temperatures(1500oC) on hBN flakes which are exfoliated from high-temperature- andhigh-pressure-grown bulk hBN crystals and mounted on a sapphire sub-strate. The samples are grown in a custom-designedVeecoGENXplorMBEsystem (base pressure ~10−10 Torr) that is described in our earlierpublications11–13. The carbonflux incident on the hBN is generated by Joule-heating a high-purity graphite filament for ~5 h in order to form a con-tinuous graphene monolayer on hBN. Details of the growth process aregiven in the Supplementary Note 3 and our prior publications11,12.Device fabricationFollowingMBEgrowth, a single graphene-hBNflakewas transferredusing amicromanipulator from the sapphire surface to the Si/SiO2 wafer (300 nmSiO2). The graphene was etched using reactive ion etching (RIE) to definethe device geometry and contacts were fabricated using electron beamlithography. Additional details of the device fabrication process are given inthe Supplementary Note 4.Fig. 3 | Shubnikov-de Haas and Brown-Zak oscillations. a Differential magne-toresistance, dR/dB, of the MBE graphene device at T = 210 K for a range of gatevoltages,Vg, showing Brown-Zak (B-Z)magneto-oscillations (peaks are indicated bythe red arrows). bMagnetoresistance (ΔR = R(B)-R(B = 0)) at T = 2 K showingShubnikov-de Haas (SdH) oscillations (indicated by the black arrows). The plotsare offset for clarity. c Fan-diagram showing positions of the SdH oscillations(black circles) and of B-Z oscillations (red triangles). Dashed lines representLandau levels.https://doi.org/10.1038/s43246-024-00633-x ArticleCommunications Materials |           (2024) 5:189 4www.nature.com/commsmatAFM imagingAFM imaging of the MBE graphene devices was performed in ambientconditions with an Asylum Research Cypher-S AFM in amplitude-modulated tapping mode (AC-mode) using Budget Sensors Al75-G canti-levers tuned to 5% below the free-air amplitude at resonance. All AFMimages were analysed using the Gwyddion37 software package.Transport measurementsTransport andmagneto-transportmeasurementswere conducted inheliumatmosphere using Keithley-2400 source-meters and Keithley-2010 multi-meters. Helium filled magneto-cryostat with maximum magnetic field of14 T (Cryogenic Ltd.) was used for measurements in the temperature range2 K < T < 210K (Fig. 3). A cryogen free magnet with open 50mm bore andmaximum magnetic field of 18 T (Cryogenic Ltd.) was used for the mea-surements in the temperature range 228 K < T < 314 K (Fig. 2d).ConclusionsWe have measured the electrical transport properties of field effecttransistors fabricated by growing a monolayer of graphene on hBN byhigh temperature MBE. Its unique properties include ultra-high purity(doping < 1011 cm−2), relatively low and temperature-independentmobility (µ ≈ 1000 cm2/Vs), and a perfect match of the hBN and gra-phene lattices. We found that high (1500 oC) growth temperature and theorientational alignment of the graphene and hBN lattices give rise to anumber of interesting phenomena, such as a moiré-fringed hexagonalsuperlattice pattern which transforms its electronic band structure intothe form of the “Hofstadter butterfly”. The reported low (~1000 cm2/Vs)carrier mobility in such a clean (doping level < 1011 cm−2) graphene layersis related to the HT-MBE growth and post-growth relaxation processes.In strong magnetic fields we observe Brown-Zak oscillations above roomtemperature previously reported only in high mobility graphene. Ourtransistors based on HT-MBE graphene/hBN heterostructures are auseful platform for observation of room temperature quantum effectsand future device applications.Data availabilityAll data used in this work are available from the correspondent author onreasonable request.Received: 7 May 2024; Accepted: 5 September 2024;References1. Novoselov, K. S. et al. Electric field effect in atomically thin carbonfilms. Science 306, 666–669 (2004).2. Bolotin, K. I. et al. Ultrahigh electronmobility in suspended graphene.Solid State Comm. 146, 351–355 (2008).3. Mayorov, A. S. et al. Micrometer-Scale Ballistic Transport inEncapsulated Graphene at Room Temperature. Nano Lett. 11,2396–2399 (2011).4. Banszerus, L. et al. Ultrahigh-mobility graphene devices fromchemical vapor deposition on reusable copper. Sci. Adv. 1,e1500222 (2015).5. Yankowitz, M. et al. Emergence of superlattice Dirac points ingraphene on hexagonal boron nitride. Nat. Phys. 8, 382–386(2012).6. Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphenesuperlattices. Nature 497, 594–597 (2013).7. Wallbank, J. et al. Generic miniband structure of graphene on ahexagonal substrate. Phys. Rev. B 87, 245408 (2013).8. Yan, X. et al. Moiré synaptic transistor with room temperatureneuromorphic functionality. Nature 624, 551–556 (2023).9. Taniguchi, T. et al. Synthesis of high-purity boron nitride singlecrystals under high pressure by usingBa-BNsolvent. J. Cryst. Growth303, 525–529 (2007).10. Martini, L. et al. Scalable High-Mobility Graphene/hBNHeterostructures. ACS Appl. Mater. Interfaces 15,37794–37801 (2023).11. Summerfield, A. et al. Strain-engineered graphene grown onhexagonal boron nitride by molecular beam epitaxy. Sci. Rep. 6,22440 (2016).12. Davies, A. et al. Lattice-Matched Epitaxial Graphene Grown on BoronNitride. Nano Lett. 18, 498–504 (2018).13. Summerfield, A. et al. Moire-Modulated Conductance of HexagonalBoron Nitride Tunnel Barriers. Nano Lett. 18, 4241–4246 (2018).14. Moreau, E. et al. Graphene growth by molecular beam epitaxy on thecarbon-face of SiC. Appl. Phys. Lett. 97, 241907 (2010).15. Xu, Z. et al. Direct growth of hexagonal boron nitride/grapheneheterostructures on cobalt foil substrates by plasma-assistedmolecular beam epitaxy. Appl. Phys. Lett. 109, 043110 (2016).16. Plaut, A. S. et al. Exceptionally large migration length of carbon andtopographically-facilitated self-limiting molecular beam epitaxialgrowth of graphene on hexagonal boron nitride. Carbon 114,579–584 (2017).17. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures.Nature499, 419–425 (2013).18. Ferrari, A. C. et al. Science and technology roadmap for graphene,related two-dimensional crystals, and hybrid systems. Nanoscale 7,4598–4810 (2015).19. Novoselov, K. S. et al. 2Dmaterials and van derWaals heterostructures.Science 363, 461–474 (2016).20. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Halleffect in moiré superlattices. Nature 497, 598–602 (2013).21. Hunt, B. et al. MassiveDirac fermions andHofstadter butterfly in a vander Waals heterostructure. Science 340, 1427–1430 (2013).22. Brown, E. Bloch electrons in a uniformmagnetic field.Phys. Rev. 133,A1038–A1044 (1964).23. Zak, J. Magnetic translation group. Phys. Rev. 134, A1602–A1606(1964).24. Morozov, S. V. et al. Giant Intrinsic Carrier Mobilities in Graphene andIts Bilayer. Phys. Rev. Lett. 100, 016602 (2008).25. Mori, N. & Ando, T. Magnetophonon resonance in monolayergraphene. J. Phys. Soc. Jpn. 80, 044706 (2011).26. Wang, C. M. & Luan, X. Y. Surface-optical-phonon–inducedmagnetophonon resonance in graphene. Europhys. Lett. 103,37012 (2013).27. Krishna Kumar, R. et al. High-temperature quantum oscillationscaused by recurring Bloch states in graphene superlattices. Science357, 181–184 (2017).28. Krishna Kumar, R. et al. High-order fractal states in graphenesuperlattices”. PNAS 115, 5135–5139 (2018).29. Huber, R. et al. Band conductivity oscillations in a gate-tunablegraphene superlattice. Nat. Comm. 13, 2856 (2022).30. Adam, S. et al. A self-consistent theory for graphene transport. PNAS104, 18392–18397 (2007).31. Xuesong Li. et al. Large-Area Synthesis of High-Quality and UniformGraphene Films on Copper Foils. Science 324, 1312–1314 (2009).32. Hwang, E. H. & Das Sarma, S. Acoustic phonon scattering limitedcarrier mobility in two-dimensional extrinsic graphene. Phys. Rev. B77, 115449 (2008).33. Wang, L. et al.Mobility Enhancement inGrapheneby in situReductionof Random Strain Fluctuations. Phys. Rev. Lett. 124, 157701 (2020).34. Lin, M.-W. et al. Approaching the intrinsic band gap in suspendedhigh-mobility graphene nanoribbons.Phys. Rev. B 84, 125411 (2011).35. Neumann,C. et al. Ramanspectroscopy asprobeof nanometre-scalestrain variations in graphene. Nat. Comm. 6, 8429 (2015).36. Chen, B. et al. How good can CVD-grown monolayer graphene be?Nanoscale 6, 15255 (2014).37. Nečas,D. &Klapetek, P.Gwyddion: anopen-source software for SPMdata analysis. Cent. Eur. J. Phys. 10, 181 (2012).https://doi.org/10.1038/s43246-024-00633-x ArticleCommunications Materials |           (2024) 5:189 5www.nature.com/commsmatAcknowledgementsThis work at Nottingham was supported by the Engineering and PhysicalSciences Research Council UK (Grants No. EP/L013908/1, No. EP/P019080/1, No. EP/V05323X/1, and No. EP/W035510/1).Author contributionsO.M. andR.H. did the transportmeasurements and data analysis. T.Ch. andS.N. grew thematerial. T.T. and K.W. provided hBN crystals. A.S., C.M. andP.B. processed the material into devices, did AFMmeasurements and theiranalysis. A.P. and L.E. participated in discussions and development of themodel. All co-authors contributed to the results analysis and model devel-opment, co-wrote and approved manuscript submission.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s43246-024-00633-x.Correspondence and requests for materials should be addressed toOleg Makarovsky.Peer review information Communications Materials thanks theanonymous reviewer(s) for their contribution to thepeer reviewof thiswork.Apeer review file is available. Primary Handling Editors: SangHoon Bae andAldo Isidori.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/s43246-024-00633-x ArticleCommunications Materials |           (2024) 5:189 6https://doi.org/10.1038/s43246-024-00633-xhttp://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/www.nature.com/commsmat High-temperature Brown-Zak oscillations in graphene/hBN moiré field effect transistor fabricated using molecular beam epitaxy Results Discussion Methods MBE growth of graphene on hBN Device fabrication AFM imaging Transport measurements Conclusions Data availability References Acknowledgements Author contributions Competing interests Additional information