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Biswajit Datta, Santanu Dey, Abhisek Samanta, Hitesh Agarwal, Abhinandan Borah, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Rajdeep Sensarma, Mandar M. Deshmukh

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[Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer graphene](https://mdr.nims.go.jp/datasets/252004a3-04c6-4660-8be6-2ee3c3792d3e)

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Strong electronic interaction and multiple quantum Hall ferromagnetic phases in trilayer grapheneARTICLEReceived 17 Aug 2016 | Accepted 6 Jan 2017 | Published 20 Feb 2017Strong electronic interaction and multiple quantumHall ferromagnetic phases in trilayer grapheneBiswajit Datta1, Santanu Dey2, Abhisek Samanta3, Hitesh Agarwal1, Abhinandan Borah1, Kenji Watanabe4,Takashi Taniguchi4, Rajdeep Sensarma3 & Mandar M. Deshmukh1Quantum Hall effect provides a simple way to study the competition between single particlephysics and electronic interaction. However, electronic interaction becomes important only invery clean graphene samples and so far the trilayer graphene experiments are understoodwithin non-interacting electron picture. Here, we report evidence of strong electronic inter-actions and quantum Hall ferromagnetism seen in Bernal-stacked trilayer graphene. Due tohigh mobility B500,000 cm2 V� 1 s� 1 in our device compared to previous studies, we find allsymmetry broken states and that Landau-level gaps are enhanced by interactions; an aspectexplained by our self-consistent Hartree–Fock calculations. Moreover, we observe hysteresisas a function of filling factor and spikes in the longitudinal resistance which, together, signalthe formation of quantum Hall ferromagnetic states at low magnetic field.DOI: 10.1038/ncomms14518 OPEN1 Department of Condensed Matter Physics and Materials Science, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India.2 Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India. 3 Department of TheoreticalPhysics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India. 4 Advanced Materials Laboratory, National Institute for MaterialsScience, 1-1 Namiki, Tsukuba 305-0044, Japan. Correspondence and requests for materials should be addressed to R.S. (email: sensarma@theory.tifr.res.in)or to M.M.D. (email: deshmukh@tifr.res.in).NATURE COMMUNICATIONS | 8:14518 | DOI: 10.1038/ncomms14518 | www.nature.com/naturecommunications 1mailto:sensarma@theory.tifr.res.inmailto:deshmukh@tifr.res.inhttp://www.nature.com/naturecommunicationsMesoscopic experiments tuning the relative importance ofelectronic interactions to observe complex orderedphases have a rich past1. While one class of experi-ments were conducted on bilayer two-dimensional electronsystems (2DES) realized in semiconductor heterostructures, theother class of experiments focussed on probing multipleinteracting sub-bands in quantum well structures2. There is anincreasing interest in the electronic properties of few-layergraphene3–13 as it offers a platform to study electronic inter-actions because the dispersion of bands can be tuned withnumber and stacking of layers in combination with electric field.Bernal/ABA-stacked trilayer graphene (ABA-TLG) provides anatural platform to observe such multi-subband physics as theband structure gives rise to monolayer-like (ML) and bilayer-like(BL) bands. The presence of the multiple bands and their Diracnature lead to the possibility of observing an interesting interplayof electronic interactions in different channels leading to novelphases of the quantum Hall state.Here we study the Landau-level (LL) spectrum on edgecontacted ABA-TLG samples encapsulated in hexagonal boronnitride (hBN) flakes. We observe the coexistence of both masslessand massive Dirac fermions in the form of parabolically dispersedLL crossing points at low magnetic field. At intermediatemagnetic field we show that the LL fan diagram indicates thatthe electron-electron interactions lead to formation of symmetrybroken spin and valley-polarized states. Our self-consistentHartree–Fock calculation supports the observed interactionenhanced LL gaps at the symmetry broken states. We alsoobserve hysteretic transport showing the formation of quantumHall ferromagnetic (QHF) states.ResultsMagnetotransport in ABA-trilayer graphene. Figure 1a showsthe lattice structure of ABA-TLG with all the hopping parameters.We use Slonczewski–Weiss–McClure (SWMcC) parametrizationof the tight binding model for ABA-TLG14,15 (with hoppingparameters g0, g1, g2, g5 and d) to calculate its low energy bandstructure. Definitions of all the hopping parameters are evidentfrom Fig. 1a, and d is the onsite energy difference of twoinequivalent carbon atoms on the same layer. Its band structure,shown in Fig. 1b consists of both ML linear and BL quadraticbands16,17.Figure 1c shows an optical image of the device where theABA-TLG graphene is encapsulated between two hBN flakes18.�2�3�5�1�4�0E (meV)40a bc d200–20–40ka (10–3)–60 –30 0 30 60Vbg (V)–30 –15 0 15 30250150501.5 K50 K300 K Resistivity (Ω)Figure 1 | ABA-stacked trilayer graphene device and its electrical transport. (a) Schematic of the crystal structure of ABA-TLG with all hoppingparameters. (b) Low energy band structure of ABA-TLG around k� point (� 4p3 , 0) in the Brillouin zone. The wave vector is normalized with the inverse ofthe lattice constant (a¼ 2.46 Å) of graphene. Black and blue lines denote the BL bands along kx and ky direction in the Brillouin zone whereas the red linedenotes the ML band along both kx and ky. ML bands are separated by � dþ g22 �g52 ¼ 2 meV and BL bands are separated by � g2j j2 ¼ 14 meV. However,there is no band gap in total, semi-metallic nature of ABA-TLG is clear from the band overlap. (c) Optical image of the hBN encapsulated trilayer graphenedevice; Scale bar, 20mm. White dashed line indicates the boundary of the ABA-TLG. The graphene sample is a slightly distorted rectangle, but theelectrodes are designed in a Hall bar geometry. Length and breadth wise distance between furthest electrodes are 9.3 mm and 7.8 mm respectively. Thismakes the aspect ratio to be 1.19. Substrate consists of 30 nm thick hBN and 300 nm thick Silicon dioxide (SiO2) coated highly p-doped silicon, which alsoserves as a global back gate. (d) Room temperature and low temperature four-probe resistivity of the device as a function of Vbg.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms145182 NATURE COMMUNICATIONS | 8:14518 | DOI: 10.1038/ncomms14518 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsFour-probe resistivity (r) of the device is shown in Fig. 1d. Thelow disorder in the device is reflected in high mobilityB500,000 cm2 V� 1 s� 1 on electron side and B800,000 cm2V� 1 s� 1 on hole side; this leads to carrier mean free path inexcess of 7 mm (see Supplementary Fig. 1 and SupplementaryNote 1 for mobility and mean free path calculation). Wemeasured one single gated device and one dual gated device onwhich we studied the effect of electric field. We found that theelectron side data is relatively insensitive for low electricfield range (o0.01 Vnm� 1) (see Supplementary Fig. 2and Supplementary Note 2 for dual gate device data). Due tothe better quality of the single gated device we show themeasurements done on the single gated device throughout thepaper.We next consider the magnetotransport in ABA-TLG thatreveals the presence of LLs arising from both ML and BL bands.The LLs are characterized by the following quantum numbers:NM (NB) defines the LL index with M (B) indicating monolayer(bilayer)-like LLs, þ (� ) denotes the valley index of the LLs andm (k) denotes the spin quantum number of the electrons. All thedata shown in this paper, are taken at 1.5 K. Figure 2a shows themeasured longitudinal resistance (Rxx) as a function of gatevoltage (Vbg) and magnetic field (B) in the low B regime (seeSupplementary Fig. 3 and Supplementary Note 3 for more data atlow magnetic field). Observation of LLs up to very high fillingfactor n¼ 118 confirms the high quality of the device. Along withthe usual straight lines in the fan diagram, we find additionalinteresting parabolic lines which arise because of LL crossings.Figure 2b shows the calculated non-interacting density of states(DOS) in the same parameter range which matches very well withthe measured resistance. We find that the low B data can be wellunderstood in terms of non-interacting picture and it allowsdetermination of the band parameters.We now consider the LL fan diagram for a larger range of Vbgand B. Figure 3a shows the calculated14–16 energy dispersion ofthe spin degenerate LLs with B. All the band parameters ofmultilayer graphene are not known precisely, so, we refinerelatively smaller band parameters g2, g5 and d a little over theknown values for bulk graphite19 to understand our experimentaldata (see Supplementary Table 1 and Supplementary Note 3 forestimation of band parameters from experimental LL crossingpoints). We find g0¼ 3.1 eV, g1¼ 0.39 eV, g2¼ � 0.028 eV,g5¼ 0.01 eV and d¼ 0.021 eV best describe our data. Figure 3bshows the main fan diagram where the measured longitudinalconductance (Gxx) is plotted as a function of Vbg and B. Due tolack of inversion symmetry, valley degeneracy is not protected inABA-TLG, it breaks up with increasing B and reveals all thesymmetry broken filling factors as seen in Fig. 3b.Figure 3c shows measured Gxx focusing on the n¼ 0 state,which shows a dip right at the charge neutrality point, evident forB46 T. Corresponding Hall conductance (Gxy) shows a plateauat zero indicating the occurrence of the n¼ 0 state (seeSupplementary Fig. 4 and Supplementary Note 4 for longitudinaland Hall resistance data showing n¼ 0 state). While, the n¼ 0plateau has been observed in monolayer graphene20 and inbilayer graphene21 (for B more than B15–25 T), this is the firstobservation of n¼ 0 state in trilayer graphene at such low B.A marked reduction in disorder allows observation of the n¼ 0state in our device.Focusing on the electron side, Fig. 3d,e show the experimen-tally measured LL fan diagram and labelled LLs, respectively. Wesee that the presence of NM¼ 0 LL gives rise to a series of verticalcrossings along the B axis as is expected from the LL energydiagram (Fig. 3a). The highest crossing along the B axis appearswhen NM¼ 0 crosses with NB¼ 2 LL at B5 T.From the complex fan diagram, seen in Fig. 3d,e, we can seeboth above and below the topmost LL crossing (VbgB10 V andBB5 T), NM¼ 0 LL is completely symmetry broken and NB¼ 2LL quartet, on the other hand, becomes two-fold split at B3.5 T.The crossing between NM¼ 0 and NB¼ 2 LLs gives rise to threering-like structures. Calculated LL energy spectra near thetopmost crossing (Fig. 3e, inset) shows that spin splitting isa bHighLowDensity of states (EF)1.51.00.5B (T)15 30 45NM = 1NM = 2NM = 3NM = 05 50Rxx  (Ω)15 30 45Vbg (V) Vbg (V)B (T)6650 584234� = 26 74 82 901.51.00.50.0Figure 2 | Low magnetic field fan diagram. (a) Colour plot of Rxx as a function of Vbg and B up to 1.5 T. The LL crossings arising from ML bands and BLbands are clearly seen. Each parabola is formed by the repetitive crossings of a particular ML LL with other BL LLs. Crossing between any two LLs shows upas Rxx maxima in transport measurement due to high DOS at the crossing points. The overlaid magenta line shows a line slice at Vbg¼ 50 V. (b) DOScorresponding to a. NM¼ 1 labelled parabola refers to all the crossing points arising from the crossings of NM¼ 1 LL with other BL LLs. Other labels have asimilar meaning. NM¼0 LL does not disperse with B, hence the crossings form a straight line parallel to B axis. Minimum B is taken as 0.5 T to keep finitenumber of LLs in the calculation. The horizontal axis is converted from charge density to an equivalent Vbg after normalizing it by the capacitance per unitarea (Cbg) for the ease of comparison with experimental fan diagram. Cbg is determined from the high B quantum Hall data which matches well with thegeometrical capacitance per unit area of 30 nm hBN and 300 nm SiO2: CbgB105mFm� 2.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14518 ARTICLENATURE COMMUNICATIONS | 8:14518 | DOI: 10.1038/ncomms14518 | www.nature.com/naturecommunications 3http://www.nature.com/naturecommunicationslarger than valley splitting for NB¼ 2 LL but valley splittingdominates over spin splitting for NM¼ 0 LL. We note that valleysplitting of NM¼ 0 is very large compared with other ML LLs;which arises because ML bands are gapped in ABA-TLG unlike inmonolayer graphene. As one follows the NM¼ 0 LL downtowards B¼ 0 one observes successive LL crossings of NM¼ 0with NM¼ 2, 3, 4..... The sharp abrupt bends in the fan diagramoccur due to the change of the order of filling up of LLs aftercrossings and the fact that the horizontal axis is charge density(proportional to Vbg and not LL energy). When these crossingsare extrapolated to B¼ 0, we see that NM¼ 0 LL is valley split asexpected from the LL energy diagram Fig. 3a.Role of electronic interaction and theoretical simulation. Wenext discuss experimental signatures that point towards theimportance of interaction. Observation of spin split NM¼ 0 LL atd123432 54 6 85 10 15 202461814� =10Vbg (V)B (T)c0.52.54.5Vbg (V)B (T)–6 –4 –2 0 2 4 612.510.07.55.02.50.010–110� = –1e f8 11 14465464765310987685B (T)+Gxx (e2/h)Gxx (e2/h) Gxx (e2/h)Gxx (e2/h)0.20.61.0a b400–40E (meV)501015B (T)3±2±2±0+ 1+3±0+0–0–1–0.51.52.5I1 2 3 4 5 6–1–2–3–4–5–6� = Vbg (V)B (T)12.510.57.55.02.50.0–30 –15 0 15 305 10 15 20246Vbg (V)Vbg (V)B (T)NM= 0 NB= 2NB= 313.5 E (meV) 16.5B (T)5.46.2↑– +– +↓2234 6 104 5 6 8 10Figure 3 | LL crossings and resulting QHF ground states. (a) Calculated low energy spectra using SWMcC parametrization of the tight binding model forABA-TLG14–16. Red and black lines denote the ML and BL LLs respectively. Solid and dashed lines denote LLs coming from kþ and k� valleys respectively.Labelled numbers represent the LL indices of the corresponding LLs. (b) Colour scale plot of Gxx, showing the LL fan diagram. n¼0 feature is not seen inthis colour scale as the lock-in sensitivity was set to a low value in this measurement to record the low resistance values accurately. The filling factorsmeasured independently from the Gxy are labelled in every plot. As a function of the B, one can observe several crossings on electron and hole side. Thedata shown in Fig. 2a forms a very thin slice of the low B data shown in this panel. (c) Zoomed-in fan diagram around charge neutrality point showing theoccurrence of n¼0 from B6 T: Gxx shows a dip and Gxy shows a plateau at n¼0. The overlaid red line presents Gxy at 13.5 T which shows the occurrence ofn¼ � 1, 0 and 1 plateaus. (d) Zoomed-in recurrent crossings of NM¼0 LL with different BL LLs. (e) The lines indicate the LLs seen in the data shown in dand their crossings. Circled numbers denote the filling factors. (f) A further zoomed-in view of the parameter space showing LL crossing of fourfoldsymmetry broken NM¼0 LL with spin split NB¼ 2 LL.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms145184 NATURE COMMUNICATIONS | 8:14518 | DOI: 10.1038/ncomms14518 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsBB2 T cannot be explained from the non-interacting Zeemansplitting for GB1.5 meV on electron side, estimated from theDingle plot. Also, the large ratio of transport scattering time ttð Þto quantum scattering time ðtqÞðtttq� 49Þ indicates that smallangle scattering is dominant, a signature of the long-range natureof the Coulomb potential22–24 (see Supplementary Fig. 5 andSupplementary Note 5 for Dingle plot analysis). We also measureactivation gap for the symmetry broken states n¼ 2, 3, 4, 5, 7at B¼ 13.5 T, and find significantly higher gaps than thenon-interacting spin-splitting. For n¼ 3 and 5, Fermi energy(EF) lies in spin-polarized gap of NM¼ 0 LL in K� and Kþ valleyrespectively. Measured energy gap at n¼ 3 is B5.1 meV and atn¼ 5 is B2.8 meV, whereas free electron Zeeman splitting isB1.56 meV at B¼ 13.5 T (see Supplementary Fig. 6, Supple-mentary Table 2 and Supplementary Note 6 for determination ofLL energy gaps from Arrhenius plots). We note that typically thetransport gap tends to underestimate the real gap due to the LLbroadening, so actual single particle gap might be even larger.This shows the clear role of interactions even with a conservativeestimate of the LL gap.Interaction results in symmetry broken states at low B that areQHF states. For the data in Fig. 3d, n¼ 2, 3, 4, 5 are QHF statesfor B45.5 T. Similarly, n¼ 7, 8, 9 are also QHF states for5.5 T4B44 T. In fact the LLs associated with n¼ 3, 4, 5 aftercrossing are the same ML LLs which are responsible for n¼ 7, 8, 9before crossing (Fig. 3e). The crossings result in three ring-likestructures marked by plus, triangle and hexagon in Fig. 3f.Now we discuss theoretical calculations to show that electronicinteractions are crucial in obtaining a quantitative understandingof the experimental data. The theoretical calculations focuson the NM¼ 0 and NB¼ 2 LLs, which form the most prominentLL crossing pattern in our data. The effect of disorder isincorporated within a self-consistent Born approximation(SCBA)25,26, while electronic interactions are included byconsidering the exchange corrections to the LL spectrumdue to a statically screened Coulomb interaction27,28 in a self-consistent way. Figure 4a shows the DOS at EF as a function ofVbg and B, which matches with the experimental resultson the Gxx.Our calculations also provide insight about the polarization ofthe states inside the ring-like structures (Fig. 3f). We find thatalthough the filling factor of region D is the same as that ofregions n¼ 6 above and below, electronic configurations of thesestates are different. Figure 4b shows the spin-resolved DOS at EFas a function of Vbg and B. We find total spin polarization(integrated spin DOS) in region D is non-zero (see Supple-mentary Fig. 7 and Supplementary Note 7 for the details oftheoretical calculation), but it vanishes in regions n¼ 6 above andbelow the ring structure. Figure 4b inset shows the calculatedexchange enhanced spin g-factors. This shows a significantincrease over bare value of g in the spin-polarized states—inagreement with the large gap observed at n¼ 3 and 5 in theexperiment.DiscussionThe key role of interactions is also reflected in the hysteresisof Rxx in the vicinity of the symmetry broken QHF states.Though QHF has been extensively studied in 2DES usingsemiconductors2,29 there are only a few reports of studyingQHF in graphene30–33. In our experiment, we vary fillingfactor by changing Vbg at a fixed B (Fig. 5a) and observe thatthe sweep up and down of Vbg shows a hysteresis in Rxx, whichcan be attributed to the occurrence of pseudospin magneticorder at the symmetry broken filling factors34 (see Supple-mentary Fig. 8 and Supplementary Note 8 for more hyste-resis data). Corresponding hysteresis is absent in simultane-ously measured Hall resistance Rxy (Fig. 5b). Hysteresis inRxx with Vbg is also absent without magnetic field (seeSupplementary Fig. 8 and Supplementary Note 8 for moredetail). The pinning, that causes the hysteresis could be due toresidual disorder within the system as the domains of the QHFevolve. Along a constant filling factor n¼ 6 line (Fig. 5c)transport measurements show an appearance of Rxx spikesaround the crossing of NM¼ 0 and NB¼ 2 LLs (Fig. 5d). Onepossible explanation for the spike in Rxx (ref. 35) is the edge statetransport along domain wall boundaries as studied earlier insemiconductors29,36.a bB (T)10.07.55.02.5Vbg (V) Vbg (V)5 10 15 20 25 5 10 15 20 2512840g s -gs0 65432νLow HighDOS (EF) Spin DOS (EF)–1 1B = 10 T3 54 6 7 8� = 2 3 54 6 7 8Figure 4 | Theoretical calculation of DOS and spin polarization. (a) DOS at the Fermi level as a function of Vbg and B. This matches the fan diagram seenin the experiment. (b) The magnetization in the system as a function of Vbg and B, where density is converted to an equivalent Vbg, described in Fig. 2bcaption. The LL crossing regions clearly show the presence of spin polarization in the system. The inset shows calculated enhanced spin g-factor above thebare value 2 for NM¼0 spin and valley split LLs.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14518 ARTICLENATURE COMMUNICATIONS | 8:14518 | DOI: 10.1038/ncomms14518 | www.nature.com/naturecommunications 5http://www.nature.com/naturecommunicationsIn summary, we see interaction plays an important role toenhance the g-factor and favours the formation of QHF states atlow B and at relatively higher temperature. ABA-TLG is thesimplest system that has both massless and massive Diracfermions, giving rise to an intricate and rich pattern of LLs that,through their crossings, can allow a detailed study of the effect ofinteraction at sufficiently low temperature. The ability to imagethese QHF states using modern scanning probe techniques at lowmagnetic fields could provide insight into these states that havenever been imaged previously. In future, experiments on multi-layer graphene, exchange coupled with a ferromagnetic insulatingsubstrate37, can lead to the possibility of observing an excitinginterplay of QHF with the proximity induced ferromagneticorder.MethodsDevice fabrication. Graphene and hBN flakes were exfoliated by scotch tapemethod on 300 nm SiO2 coated highly p-doped Si substrate. hBN flakes of thick-ness B30 nm were located by an optical microscope. ABA-TLG was thentransferred to a suitably chosen hBN, followed by another hBN transfer of similarthickness to complete the hBN-graphene-hBN stack. Electron-beam lithographywas done to define the contacts. Then the stack was etched with mild plasma inArgon and Oxygen (1:1 ratio) environment to expose the graphene edge. Metal(3 nm Chromium, 15 nm Palladium, 30 nm Gold) was thermally evaporated tomake the contacts immediately after etching without breaking the vacuum.Characterization. After exfoliation on Silicon substrate potential ABA-TLGgraphene flakes were chosen by the optical colour contrast and then confirmed bythe Raman spectroscopy. Atomic force microscopy was also done on the completestack to image the topography of the surface and to find out the thickness of the tophBN which is required to calculate the plasma etching time before metallization.Measurement. All the low-temperature measurements were done in a liquid He4flow cryostat at base temperature T¼ 1.5 K. Standard low frequency lock-intechnique was used to do all current biased four-probe resistance measurements.Excitation current was 100 nA for most of the measurements but sometimesincreased to a higher value of 400 nA to measure low resistances at low magneticfields.Data availability. The data that support the findings of this study are availablefrom the corresponding author upon request.References1. Girvin, S. M. Spin and isospin: exotic order in quantum Hall ferromagnets.Phys. 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Rev.X 2, 011004 (2012).B (T)1.00.60.265432B (T)Vbg (V)–45 –30 –15 0 15 30131145Rxx (Ω)Rxy (KΩ)Rxx (kΩ)800a bc d6004002000B =13.5 T B =13.5 TFilling factor (ν) Filling factor (ν)65 9 10432 7 8121086465 9 10432 7 85 10 15 20246Vbg (V)B (T)1 2 3 4Gxx (e2/h)Figure 5 | Hysteresis in the longitudinal resistance as a function of the filling factor and observation of resistance spikes. (a) Measurement of Rxx as afunction of Vbg at B¼ 13.5 T in the two directions as shown in (inset) the measurement parameter space. Largest hysteresis is seen for the spin and valley-polarized NM¼0 LL. We have done gate sweep as slow as 3 mVs� 1 to check if the hysteresis goes away, however, it stays. Nature of hysteresis does notchange. The sweep up and sweep down rates were same. (b) Simultaneously measured Rxy that exhibits clear quantization plateaus in the two sweepdirections. (c) The laid white dashed line on the fan diagram shows the parameter space along which the Rxx is plotted in the next panel. 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We acknowledge Swarnajayanthi Fellowship of Department ofScience and Technology (for M.M.D.) and Department of Atomic Energy of Governmentof India for support. Preparation of hBN single crystals is supported by the ElementalStrategy Initiative conducted by the MEXT, Japan and a Grant-in-Aid for ScientificResearch on Innovative Areas ‘Science of Atomic Layers’ from JSPS.Author contributionsB.D. fabricated the device, conceived the experiments and analysed the data. M.M.D.,A.B. and B.D. contributed to the development of the device fabrication process. H.A.helped in the fabrication and in the measurements. K.W. and T.T. grew the hBN crystals.S.D., A.S. and B.D. did the calculations under the supervision of R.S.; B.D., M.M.D. co-wrote the manuscript and R.S. provided input on the manuscript. All authorscommented on the manuscript. M.M.D. supervised the project.Additional informationSupplementary Information accompanies this paper at http://www.nature.com/naturecommunicationsCompeting financial interests: The authors declare no competing financial interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/How to cite this article: Datta, B. et al. Strong electronic interaction and multiplequantum Hall ferromagnetic phases in trilayer graphene. Nat. Commun. 8, 14518doi: 10.1038/ncomms14518 (2017).Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.This work is licensed under a Creative Commons Attribution 4.0International License. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unless indicated otherwisein the credit line; if the material is not included under the Creative Commons license,users will need to obtain permission from the license holder to reproduce the material.To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/r The Author(s) 2017NATURE COMMUNICATIONS | DOI: 10.1038/ncomms14518 ARTICLENATURE COMMUNICATIONS | 8:14518 | DOI: 10.1038/ncomms14518 | www.nature.com/naturecommunications 7http://www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationshttp://npg.nature.com/reprintsandpermissions/http://npg.nature.com/reprintsandpermissions/http://creativecommons.org/licenses/by/4.0/http://www.nature.com/naturecommunications title_link Results Magnetotransport in ABA-trilayer graphene Figure™1ABA-stacked trilayer graphene device and its electrical transport.(a) Schematic of the crystal structure of ABA-TLG with all hopping parameters. (b) Low energy band structure of ABA-TLG around k- point (-4   3, 0) in the Brillouin zone. The wave v Figure™2Low magnetic field fan diagram.(a) Colour plot of Rxx as a function of Vbg and B up to 1.5thinspT. The LL crossings arising from ML bands and BL bands are clearly seen. Each parabola is formed by the repetitive crossings of a particular ML LL with Role of electronic interaction and theoretical simulation Figure™3LL crossings and resulting QHF ground states.(a) Calculated low energy spectra using SWMcC parametrization of the tight binding model for ABA-TLG14-16. Red and black lines denote the ML and BL LLs respectively. Solid and dashed lines denote LLs co Discussion Figure™4Theoretical calculation of DOS and spin polarization.(a) DOS at the Fermi level as a function of Vbg and B. This matches the fan diagram seen in the experiment. (b) The magnetization in the system as a function of Vbg and B, where density is conve Methods Device fabrication Characterization Measurement Data availability GirvinS. M.Spin and isospin: exotic order in quantum Hall ferromagnetsPhys. Today5339452000EomJ.Quantum Hall ferromagnetism in a two-dimensional electron systemScience289232023232000YacobyA.Graphene: Tri and tri againNat. Phys.79259262011TaychatanapatT.Wa Figure™5Hysteresis in the longitudinal resistance as a function of the filling factor and observation of resistance spikes.(a) Measurement of Rxx as a function of Vbg at B=13.5thinspT in the two directions as shown in (inset) the measurement parameter spa We thank Allan MacDonald, Jainendra Jain, Jim Eisenstein, Fengcheng Wu, Vibhor Singh, Shamashis Sengupta and Chandni U. for discussions and comments on the manuscript. We also thank John Mathew, Sameer Grover and Vishakha Gupta for experimental assistance ACKNOWLEDGEMENTS Author contributions Additional information