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Tian Xie, Tobias M. Wolf, Siyuan Xu, Zhiyuan Cui, Richen Xiong, Yunbo Ou, Patrick Hays, Ludwig F. Holleis, Yi Guo, Owen I. Sheekey, Caitlin Patterson, Trevor Arp, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Seth Ariel Tongay, Andrea F. Young, Allan H. MacDonald, Chenhao Jin

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[Optical imaging of flavor order in flat band graphene](https://mdr.nims.go.jp/datasets/b7b07da0-6b33-43d4-865c-3fef1cbb807a)

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Optical imaging of flavor order in flat band grapheneArticle https://doi.org/10.1038/s41467-025-60675-8Optical imaging of flavor order in flat bandgrapheneTian Xie 1, Tobias M. Wolf2, Siyuan Xu1, Zhiyuan Cui1, Richen Xiong1,Yunbo Ou 3, Patrick Hays3, Ludwig F. Holleis 1, Yi Guo1, Owen I. Sheekey1,Caitlin Patterson1, Trevor Arp1, Kenji Watanabe 4, Takashi Taniguchi 5,Seth Ariel Tongay 3, Andrea F. Young1, Allan H. MacDonald 2 &Chenhao Jin 1Spin- and valley flavor polarization plays a central role in the many-bodyphysics of flat band graphene, with Fermi surface reconstruction — oftenaccompanied by quantized anomalous Hall and superconducting state —observed in a variety of experimental systems. Here we describe an opticaltechnique that sensitively and selectively detects flavor textures via the exci-ton response of a proximal transition metal dichalcogenide layer. Through asystematic study of rhombohedral and rotationally faulted graphene bilayersand trilayers, we show that when the semiconducting dichalcogenide is indirect contact with the graphene, the exciton response is most sensitive to thelarge momentum rearrangement of the Fermi surface, providing informationthat is distinct from and complementary to electrical compressibility mea-surements. The wide-field imaging capability of optical probes allows us toobtain spatial maps of flavor order with high throughput, and with broadtemperature anddevice compatibility. Ourwork helps pave theway for opticalprobing and imaging of flavor orders in flat band graphene systems.Flatband graphene systems provide a versatile platform for engineer-ing correlated and topological phenomena. While their phase dia-grams vary remarkably with sample configuration parameters such aslayer number and relative alignment1–21, a feature common to all sys-tems is that small changes in the carrier density and other experi-mental tuning parameters drive flavor order transitions (FTs) in whichthe relative occupation of the (nominally degenerate) electron orbitalswith differing spin and valley polarization changes. In both crystallineand twisted graphene systems, these transitions are often accom-panied by superconducting domes, suggesting that flavor symmetrybreaking may play an important role in superconductingpairing9–11,22–24. To refine the understanding of the phase diagram, FTshave been investigated by various experimental techniques includingelectrical transport7–9,15–17, measurements of the thermodynamiccompressibility and magnetization7,9,17,25,26, and scanning tunnelingmicroscopy15,27–29. However, these techniques all comewithdrawbacks:bulk electrical measurements typically fail in the face of spatial inho-mogeneity and become less expressive in superconducting states,while scanning tunneling measurements are incompatible with thecommon dual-gated geometry. Moreover, these measurements areinherently low bandwidth, precluding studies of dynamics.Here we describe an optical technique that addresses some ofthese challenges. Figure 1a illustrates the device scheme, in which aWSe2 sensor layer is placed in direct contact with a target graphenesystem. The short-range interaction between graphene andWSe2 leadsto a shift in the quasi-particle bandgapof theWSe2 that depends on theflavor polarization of the graphene layer; this can be read out opticallyvia reflection contrast (RC) spectra. As we detail below, ourReceived: 13 February 2025Accepted: 29 May 2025Check for updates1Department of Physics, University of California at Santa Barbara, Santa Barbara, CA, USA. 2Department of Physics, University of Texas at Austin, Austin, TX,USA. 3Materials Science and Engineering Program, School of Engineering for Matter, Transport, and Energy, Arizona State University, Tempe, Arizona, USA.4Research Center for Electronic and Optical Materials, National Institute for Materials Science, AZ, Tsukuba, Japan. 5Research Center for MaterialsNanoarchitectonics, National Institute for Materials Science, AZ, Tsukuba, Japan. e-mail: macd@physics.utexas.edu; jinchenhao@ucsb.eduNature Communications |         (2025) 16:5555 11234567890():,;1234567890():,;http://orcid.org/0000-0002-6406-0403http://orcid.org/0000-0002-6406-0403http://orcid.org/0000-0002-6406-0403http://orcid.org/0000-0002-6406-0403http://orcid.org/0000-0002-6406-0403http://orcid.org/0000-0002-9350-8756http://orcid.org/0000-0002-9350-8756http://orcid.org/0000-0002-9350-8756http://orcid.org/0000-0002-9350-8756http://orcid.org/0000-0002-9350-8756http://orcid.org/0000-0001-9718-2477http://orcid.org/0000-0001-9718-2477http://orcid.org/0000-0001-9718-2477http://orcid.org/0000-0001-9718-2477http://orcid.org/0000-0001-9718-2477http://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/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0001-8294-984Xhttp://orcid.org/0000-0003-3561-3379http://orcid.org/0000-0003-3561-3379http://orcid.org/0000-0003-3561-3379http://orcid.org/0000-0003-3561-3379http://orcid.org/0000-0003-3561-3379http://orcid.org/0000-0002-5965-7475http://orcid.org/0000-0002-5965-7475http://orcid.org/0000-0002-5965-7475http://orcid.org/0000-0002-5965-7475http://orcid.org/0000-0002-5965-7475http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-60675-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-60675-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-60675-8&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-025-60675-8&domain=pdfmailto:macd@physics.utexas.edumailto:jinchenhao@ucsb.eduwww.nature.com/naturecommunicationsmeasurement configuration provides information that is distinct fromelectrical compressibility measurements or exciton sensing using aphysically separated WSe2 layer, which detects the small-wavevectorlimit of the polarzibility30,31, and so offers us the capability in identi-fying flavor transitions.ResultsOptical sensing of FTWe first study a rhombohedral trilayer graphene (RTG) device D1.Figure 1b shows the inverse compressibility of the device measured at3 K (see “methods”). The phase diagram features spontaneous forma-tionofflavor orders onboth electron andhole doping sides, consistentwith previous reports7,10. Owing to sample inhomogeneity, two sets ofpatterns can be observed that are offset from each other (see Sup-plementary Fig. 1). Figure 1c showsRC of the same samplemeasured atdisplacement fieldD = 0.673 V/nm (dashed line in Fig. 1b).We focus onthe spectral range near the 2s exciton resonance of WSe2 (see Sup-plementary Fig. 2 for full spectra). The 2s exciton energy shows twoprominent kinks on the hole doping side, reminiscent of the two lowcompressibility lobes in Fig. 1b. The lower panel in Fig. 1c compares thefitted 2s exciton energy and the inverse compressibility (see “meth-ods”). The optical spectrum reproduces all features of compressibilityon the hole-doping side, while the response on the electron side israther weak. This asymmetry is natural. Under the large displacementfield, doped holes and electrons primarily reside in the top and bottomgraphene layers, respectively. The much weaker WSe2 response toelectrons than holes indicates that WSe2 primarily interacts withcharges in the top (closest) layer with an interaction range Δr < 1 nm.Our sensing scheme therefore also provides a sensitive probe of layerpolarization. Figure 1d summarizes the 2s exciton energy over similarparameter range as Fig. 1b (see “methods”). The optical phase diagrammatches well with the electrical one, except that features appear onlyin the top left and bottom right quadrants owing to the layer polar-ization sensitivity.Having demonstrated the ability to detect FT, we now show thatour technique provides distinct information. Figure 1e compares-2 -1 0 1ne (1012 cm-2)420-2 κ(arb. units)-2 -1 0 1ne (1012 cm-2)420-2 κ(arb. units)abWSe2Muti-layergraphenegraphitegraphitecdeD=0.673V/nmB=0TD=0.673V/nmB=0TEnergy (eV)1.811.7851.761.791.78-2 -1 0 1ne (1012 cm-2)∆ R/R-0.015 0.01ν0 0202-κ (arb. units)0.1 1.5D(V/nm)010.5-0.5-1-2 -1 0 1ne (1012 cm-2)2 -2 -1 0 1ne (1012 cm-2)2Energy (eV)1.774 1.789D(V/nm)00.80.4-0.4-0.8Fig. 1 | Optical sensing of FT inRTG. a Schematics of device configuration. AWSe2sensing layer is placed adjacent to flatband graphene without a spacer. The short-range interaction between graphene and WSe2 imprints flavor orders of grapheneinto WSe2 exciton responses. b Displacement-field and carrier-density dependentinverse compressibility of RTG device D1. c Upper panel: RC of device D1 atD =0.673 V/nm and B =0T (white dotted line in (b, d) near WSe2 2s exciton reso-nance. Lower panel: extracted 2s exciton energy (black) and comparison to inversecompressibility (red). The exciton energy shift fully captures FT on the hole side.dDisplacement-field and carrier-density dependent 2s exciton energy of device D1.Features are only observed in the top-left and bottom-right quadrants owing to thesensitivity to layer polarization. e Upper panel: RC of device D1 at D =0V/nm andB = 3 T. Lower panel: extracted 2s exciton energy (black) and comparison to inversecompressibility (red). The prominent inverse compressibility peaks from chargegaps do not show up in optical sensing, in contrast to the FT in (c). All measure-ments are performed at a temperature of 3 K.Article https://doi.org/10.1038/s41467-025-60675-8Nature Communications |         (2025) 16:5555 2www.nature.com/naturecommunicationselectrical capacitance and optical RC measurements under the sameexperimental condition ofD =0V/nm and Bz = 3 T (see SupplementaryFig. 1 for more results). A series of incompressible peaks emerge incapacitance, corresponding to gaps between Landau levels. Surpris-ingly, none of them appear in RC spectra. In capacitance the incom-pressible peaks are quite prominent, several times larger than the FT-induced features (Fig. 1c). If the optical response were effectivelymeasuring compressibility one would expect, in contradiction to ourobservations, similarly strong features.To gain further insight, we apply our sensing technique toalternating-twist magic-angle trilayer graphene (MATTG). Figure 2dshows the four-probe longitudinal resistance of MATTG device D2with twist angle of 1.43° (see “methods”). The phase diagram isqualitatively consistent with previous reports11,14,15,32 in that resistivestates emerge at integer moiré fillings from v = 0 to 4 under largedisplacement fields (v = 1 corresponds to one electron per moiréperiod). At smaller displacement fields, the resistive behaviors atinteger fillings become weaker, suggesting Fermi surface resetsinstead of gaps11,15. Interestingly, optical measurement of the samedevice shows the opposite trend. At zero displacement field (Fig. 2b),the 2s exciton resonance shows prominent cascade features atinteger fillings, which becomes weaker at larger displacement fields(Fig. 2a, c). See Supplementary Fig. 3 for more data. Figure 2e sum-marizes the 2s exciton energy across the entire phase diagram. Whilethe emergence of features around integer fillings is consistent withtransportmeasurement, their displacement field dependencies are insharp contrast. Optical sensing does not weigh the gaps at largedisplacement field heavily but is sensitive to FT-induced Fermi sur-face reconstructions.We have also performed measurements on Bernal bilayer gra-phene (BBG) in the quantum Hall regime. The upper panel in Fig. 3ashows the RC spectra of BBG device D3 under Bz = 3 T and zero dis-placement field. The lower panel shows a comparison between the 2sexciton energy (black) and inverse compressibility (red) under thesame measurement conditions. See Supplementary Figs. 4 and 5 formore results. A series of chemical potential jumps, observed as peaksin inverse compressibility, appear at evenfilling factors ν 2 �4, 4ð Þ andat higher filling factors only at the cyclotron gap filling factors, whicharemultiples of 4 because of spin-valley degeneracy. The peaks withinν 2 �4, 4ð Þ are related to flavor ferromagnetism. The optical mea-surement again shows quite distinct behavior. Instead of having fea-tures at even filling factors, the 2s exciton energy oscillates rapidly inthe ν 2 �4, 4ð Þ interval between minima at odd filling factors andmaxima at even filling factors. No strong features are seen at higherfilling factors, even when the Fermi level lies in a cyclotron gap. Thelack of gap features at high filling factors is consistent with ourobservations in RTG (Fig. 1e) and MATTG (Fig. 2e), and this makes theprominent features when ν 2 �4, 4ð Þ even more surprising.D(V/nm)00.60.3-0.3-0.6-4 -2 0 2ne (1012 cm-2)4-6 6ν-4 20 4-2-2.52.5∆ Energy (meV)Energy (eV)1.811.821.78-4 -2 0 4ne (1012 cm-2)ν-4 4D=0V/nm2- 21.82 6-6a b cd eEnergy (eV)1.811.821.78-4 -2 0 4ne (1012 cm-2)ν-4 40D=0.46V/nm2- 21.82 6-6Energy (eV)1.811.821.78-4 -2 0 4ne (1012 cm-2)ν-4 400D=-0.46V/nm2- 21.82 6-6∆ R/R-0.020.02νD(V/nm)00.60.3-0.3-0.6-4 -2 0 2ne (1012 cm-2)4-6 6-4 20 4-2 R (Ω)0500Fig. 2 | Selective sensing of FT. a−c RC ofMATTG device D2 atD = a 0.46, b 0, andc −0.46V/nm. The 2s exciton resonance shows cascade features at integer fillings,which becomes weaker at larger displacement field.d, e Longitudinal resistance (d)and 2s exciton energy (e) of device D2 as a function of displacement field andcarrier density. The insulating features at integer fillings in transportmeasurementsbecome more prominent at larger displacement field due to the transition fromFermi surface resets to charge gaps. In contrast, the optical sensing is more sen-sitive to FT-induced Fermi surface reconstruction at low displacement field thanthe charge gaps at high displacement field. All measurements are performed at atemperature of 3 K.Article https://doi.org/10.1038/s41467-025-60675-8Nature Communications |         (2025) 16:5555 3www.nature.com/naturecommunicationsSelective detection of FTOur investigations acrossmultiple flat band graphene systems indicatethat the optical sensing technique here provides qualitatively differentinformation from electrical measurements and has unique FT sensi-tivity. Our results also contrast with those from the common exciton-sensing configuration with a thick hBN spacer, which largely repro-duces electrical compressibilitymeasurements, e.g. in the detection ofgraphene Landau levels31. To elucidate the origin of FT sensitivity, it ishelpful to examine the role of an hBN spacer. To this end, we comparethe RC spectra of device D3 and another BBG device D4 with a WSe2sensor layer and a 5 nm hBN spacer, as shown in Fig. 3b, c. Undersimilar measurement conditions, we observe two major differences.First, the 2s exciton without a hBN spacer appears at a much lowerenergy (Fig. 3b), indicating much stronger interaction between WSe2and graphene. Second, at large displacement field, the excitonresponses without a hBN spacer show prominent asymmetry (Fig. 3b)between electron and hole doping while those with a spacer remainlargely symmetric (Fig. 3c). The lack of layer sensitivity in the lattercase suggests that the interaction is long-range in nature, which alsoexplains themuchweaker interaction strength.We therefore concludethat the WSe2-graphene interactions without (with) an hBN spacer aredominated by strong (weak) short- (long-range) interactions.We have formulated a quantitative theoretical interpretation ofour adjacent layer exciton sensing, one that also sheds light on thedistinct information suppliedby exciton sensingwith hBNspacers.Ourstarting point is the successful GW theory of excitons33,34 in TMDs (the“sensing layer”), withinwhich the influenceof a nearby 2Dmaterial (the“target layer”) with negligible hybridization is captured exactly byadding a screening correction to Coulomb interactionsVC ! VC + χ V2D. Here χ is the target layer density-density responsefunction, VD =2πe2e�qd=q is the interlayer Coulomb interaction and dis the layer separation. χ V2D captures the contribution to the interac-tion between two electrons in the sensing layer that is mediated bycharge density response in the target layer. Due mainly to reduceddimensionality, the 2s exciton has a rather small binding energy that isinsensitive in absolute terms to screening35–38 (see SupplementaryNote 1 for a detailed discussion). Its resonance energy is then mainlydetermined by the quasi-particle bandgap of WSe2. Because thecarrier-density dependent part of the target layer response is at longwavelengths compared to the graphene lattice constant, theb ceda ν0 0101-D=0V/nmB=3T5.0 105.0-1-ne (1012 cm-2)Energy (eV)1.8051.7951.7751.7851.791.7886420 κ(arb. units)∆ R/R-0.01 0.01D=0.635V/nmB=0T5.0 105.0-1-ne (1012 cm-2)∆ R/R-0.010.01Energy (eV)1.8051.7951.7751.7851.791.7851.7951.78D=0.612V/nmB=0T∆ R/R-0.09 0.031.871.861.841.851.8531.8541.852Energy (eV)-1 -0.5 0 5.0 1ne (1012 cm-2)= 0,±2, ±4= ±1, ±3× 10−5B=4T, ∆ 01=4.8meV0-(,=0)(−2−1)4321∆Egap=-1.0meV0 0.10.05q·aG0.15e-2qd00.80.60.40.21.21q·aG0 4.0 6.0 8.00.2 1 2.1d=2aGd=5aGd=20aG1/IB(B=3T)2kF (around SC1)Fig. 3 | Probingorbital polarization inBBG. aUpperpanel: RCof BBGdeviceD3atD =0 andBz = 3 T. Lowerpanel: extracted2s exciton energy (black) and comparisonwith inverse compressibility (red). The strong inverse compressibility peaks fromcyclotron gaps do not show up in RC. Instead, an oscillation of 2s exciton energy isobserved between even and oddfillings within the zeroth Landau level. Blue arrowsmark even fillings within the octet of the zeroth Landau level. b, c Comparisonbetween device D3 without an hBN spacer (b) and BBGdeviceD4with a ~ 5 nmhBNspacer (c) under similar measurement configurations. Their distinct behaviorsindicate the dominance of short-range and long-range interactions, respectively, asdetailed in the text. d Momentum-cutoff for three representative interlayerdistances d. aG =0.246 nm is the graphene lattice constant. Vertical dashed linesmark themomentum range of polarizability change from a cyclotron gap atBz = 3 T(inverse magnetic length qB, red) and from a representative FT in RTG (Fermimomentum kF, blue). e Calculated static polarizability Π(q,ω =0) of graphene ateven (red) and odd (blue) Landau level fillings under magnetic field B = 4 T. Thefinite-q part of graphene polarizability is enhanced at odd filling factors when n =0and n = 1 orbitals are alternately occupied, which can be uniquely accessed inadjacent layer exciton sensing as an energy shift ΔEgap. Π(q,ω) ≈ Π(q,0) forω≪Δ01 = 4.8meV, where Δ01 is the orbital splitting.Article https://doi.org/10.1038/s41467-025-60675-8Nature Communications |         (2025) 16:5555 4www.nature.com/naturecommunicationsquasiparticle bandgap change reduces to a simple exchange correc-tion (see Supplementary Note 6). When the GW approximation is usedfor χ, the quasiparticle band gap Egap is given byEgap ! E0 +Zd2q2πð Þ2Π22 q;ω= ℏ2q22m*� �VD qð Þ21� VS qð ÞΠ22 q;ω= ℏ2q22m*� � ð1Þwhere E0 is the quasi-particle bandgap of bare WSe2, Π22 is the single-particle polarization function, m* is the WSe2 valence band effectivemass and VS =2πe2=q: An hBN spacer increases d and decreases themomentum cutoff in the integral to qc < 1=d. Figure 3d illustrates suchmomentum cutoff implied by VD for three representative interlayerdistance that corresponds to the adjacent graphene layer (d =2aG), thedistant graphene layer in RTG (d = 5aG), and the case with a 5 nm hBNspacer (d =20aG), respectively. The small range of relevant momen-tum in the spacer case (green) captures the property that large-qcharge fluctuations do not produce a significant electrical potential ina distant layer. In the limit of thickhBN spacer and large d, qc ! 0. Egapthen depends on the graphene polarizability in the long wavelengthand static limit, which is directly related to its compressibility.Therefore, the exciton sensing scheme with an hBN spacer largelyreproduces results from electrical measurements.The case without an hBN spacer is distinctively different sinced � 0:5nm for the closest graphene layer. Egap senses changes in thelarge-q parts of graphene polarizability, which typically dominate dueto their larger phase space (Fig. 3d). Our sensing scheme thereforemainly probes the large-q polarizability of graphene, which is inac-cessible to electrical measurements. The observed layer sensitivity(Fig. 1) is a direct manifestation, where the bandgap shifts induced bythe adjacent anddistant graphene layers in RTGdiffer by several times.As illustrated in Fig. 3e, the difference between the two cases (blue andred) only becomes prominent at large-q. The much larger bandgapshift from the adjacent layer confirms the dominance of large-q con-tribution. This unique capability allows it to identify physics unrelatedto the appearance of charge gaps, such as a cyclotron gap, thatmainlyaffects the small-q part of polarizability (red dashed line). It alsoexplains its sensitivity to FT since FT involves reconstruction of theentire Fermi surface and modifies the large-q polarizability up to sev-eral times of kF (blue dashed line). In Supplementary Note 6 we showthat the 2s exciton energy changes that accompany FT in RTG (Fig. 1)agree quantitatively with the calculations.The surprising exciton energy oscillations we have discovered inthe small filling factor ν 2 �4, 4ð Þ regime of BBG provide anotherexcellent example of our capability on sensing large-q polarizability ofgraphene. As illustrated in Fig. 3e, we interpret the minima in the 2sexciton energy at odd filling factors as evidence for orbital-polarizedstates with differential occupation between the n =0 and n = 1 orbitals,which lead to strong screening over a wide range of wavevectors frominter-orbital contribution (see SupplementaryNote 6); and themaximaat even filling factors as evidence for states in which both orbitals of agiven flavor are completely occupied or empty. The differencesbetween even and odd fillings only appear at nonzero q (Fig. 3d),therefore the oscillation shows up in optical sensing but not com-pressibility (Fig. 3a). The convenient optical probe of the orbital con-tent of fractional states in the ν 2 �4, 4ð Þ regime of BBG could aidefforts to optimize robust non-Abelian quantum Hall states in thebilayer graphene platform39–41.Wide field imaging of FTBesides FT sensitivity, our technique also offers wide-field imagingcapability to capture spatial patterns of FT with high throughput.Figure 4a, b shows the optical microscope image and reflection con-trast spectra of a magic angle twisted bilayer graphene (MATBG)device D5. FT has been widely reported in MATBG, giving rise to Diracrevivals and Chern insulators at integer fillings1,26,42–47. Indeed, weobserve clear features in 2s exciton resonance at integer moiré fillingsv = ±1 to ±4 (orange arrows)48,49. On the other hand, MATBG isknown for its high sensitivity to twist angle and intrinsic spatialinhomogeneity from lattice relaxation. Figure 4c shows reflectioncontrast on a different spot in the same device, where we only observethe band insulator at v = ±4 but no features in between. In transportmeasurement of this device (Supplementary Fig. 6), we consistentlyobserve strongly insulating states at v = ±4, while the features at±1 to ±3 are generally weak and inconsistent between different source-drain configurations. These observations exemplify a common chal-lenge plaguing the study of twisted graphene systems, wheredevices vary strongly and it can often be difficult to extract intrinsicphysics3,26. For example, different transport phenomena can bedominated by different conducting channels and may not be directlycorrelated.Our technique offers a potential solution. As a demonstration, weperform wide-fielding imaging of the v = 4 band insulator and v = 2cascade feature in Fig. 4d, e, respectively. This allows us to extract aspatialmapof twist angle fromthe chargedensity at v = 4, and amapofthe correlation strength from the prominence of cascade feature atv = 2. Each map is obtained in 15min without spatial scanning (see“methods” and Supplementary Fig. 7). The cascade features onlyappear in a small spatial region close to the left edge of this device,which explains the weak and inconsistent features in transport. Bycomparing the FT map and angle map, we find that the cascade fea-tures emerge in a twist angle range between 1.01 and 1.07 ° and are themost prominent at angles around 1.04°. See Supplementary Note 5 formore discussions on potential strain effects.The high-throughput imaging capability of our technique isfurther augmented by its broad environment compatibility. Itencodes low-energy flavor physics into exciton responses at a muchhigher energy scale and is less susceptible to noise. Figure 4f showsthe 2s exciton energy at different temperatures up to 50K. Excitonresonances remain largely unchanged over this temperature range,allowing us to directly track melting of the cascade features. Inter-estingly, the cascade features remain visible at 50 K, consistent withprevious reports from chemical potential measurements25,26,50,51 andis an order of order of magnitude higher than the temperature atwhich hysteresis of isospin ferromagnetism disappears1,4,42,43. Thismay suggest the existence of vestigial FT or flavor fluctuations over abroad temperature range25,50 (see Supplementary Note 4 for morediscussions).DiscussionMoiré graphene multilayers have been previously reported to remo-tely “imprint” a superlattice potential in an adjacent WSe2 layer andgenerate exciton replicas48,49,52. On the other hand, optical studies offlavor physics in flatband graphene remain largely unexplored, espe-cially in non-moiré systems. The technique reported here applies toboth moiré and crystalline graphene and opens several excitingopportunities in studying flavor orders, transitions, and their interplaywith other correlated phases (see Supplementary Note 3 for morediscussions). It offers an attractive approach to disentangle large-qchanges of graphene polarizability, such as flavor orders and fluctua-tions, from local Fermi surface distortion, such as single particle gaps,nematicity and charge densitywaves53–57, thereby shedding light on theroles of these instabilities. The high-throughput imaging capability,along with the wide temperature and device geometry compatibility,enables investigation of FT spatial patterns near and across criticalpoints. A particularly exciting opportunity lies in in-situ imaging of FTthroughout the superconductivity domes in magic angle multi-layergraphene22,23, which can be correlated to transport measurements todisentangle extrinsic and intrinsic effects and potentially elucidate theinterplay between FT and superconductivity. By establishing anopticalArticle https://doi.org/10.1038/s41467-025-60675-8Nature Communications |         (2025) 16:5555 5www.nature.com/naturecommunicationstechnique to detect FT, our work also paves the way for dynamicmanipulation and investigation of flatband graphene systems usingultrafast light pulses, such as Floquet engineering of FT and studyingits non-equilibrium dynamics.MethodsSample fabricationThe preparation of multilayer graphene, hexagonal boron nitride(hBN), and tungsten diselenide (WSe2) flakes involves mechanicalexfoliation ofbulk crystals onto silicon substrateswith a 285 nmsiliconoxide layer. Rhombohedral domainswithin trilayer grapheneflakes areidentified using a Horiba T64000 Raman spectrometer equipped witha 488-nmmixed-gas Ar/Kr ion laser beam. Subsequent isolation of therhombohedral domains is performed utilizing a Dimension Icon 3100atomic force microscope58,59.All Van der Waals heterostructures are constructed through astandard dry-transfer technique employing a poly (bisphenol A car-bonate) (PC) film on a polydimethylsiloxane (PDMS) stamp. The fab-rication process involves initially creating the lower hBN/graphite part,releasing them onto a 90nm Si/SiO2 substrate. The removal of poly-carbonate residue on the sample is accomplished by dissolving it inchloroform, followed by rinsing with isopropyl alcohol and annealingat 375 °C. The upper part of the heterostructure is separately assem-bled and transferred onto the lower part. This stacking sequence ismeticulously implemented to minimize mechanical stretching of themultilayer graphene. Standard electron-beam lithography, dry-etchingprocesses, and vacuum deposition are employed to fabricate electro-des for electrical contacts (~150 nm gold with ~5 nm chromium and~15 nm palladium adhesion layers).Calibration of carrier density, displacement field, andtwist angleCarrier densities in all devices are calibrated from the hBN thicknessmeasured by a Dimension Icon 3100 atomic force microscope. UsinghBN dielectric constant εhBN = 3.52, we compute the geometricalcapacitance per unit area ct,b = εhBNε0/dt,b between the top/bottomgate and sample, where dt (db) is the top (bottom) hBN thickness. Thecharge density and displacement field are obtained as n0 = (ctVt +cbVb)/2e and D = (ctVt - cbVb)/2ε0, respectively, where Vt (Vb) is the top (bot-tom) gate voltage and e is elementary charge.The twist angle of MATBG and MATTG are extracted from thecascade features at superlattice filling factors ν = ±4 (Fig. 2 and Fig. 4).From the corresponding carrier density nν=4, the twist angle θ wasobtained from nν=4 = (8θ2)/(p3a02), a0 = 0.246 nm is the graphenelattice constant.Reflection contrast (RC) measurementThe devices were mounted in a closed-cycle cryostat (QuantumDesign, OptiCool) for all optical experiments with a base temperatureof 3 K. A broadband tungsten lampwas beam-shaped by a singlemodefiber and subsequently collimatedby a lens. The lightwas focusedontothe sample by an objective (NA =0.45), resulting in a beam diameterof ~ 1μm on sample with a power of ~ 20 nW. The reflected lightwas collected by a liquid-nitrogen-cooled CCD camera coupled witha spectrometer. The reflection contrast was computed as RC = (R’ −R)/R, where R’ and R represent the reflected light intensity from regionswith and without the sample, respectively. Keithley 2400 sourcemeters were employed to apply gate voltages to adjust the chargedensity.aEnergy (eV)1.851.811.73-2 0 2ne (1012 cm-2)ν-4 20 4-21.77∆ R/R-0.060.06d ecbf4μmangle (θ)0.9 1.24μm 4μmcorrelation (arb. units)0.025 0.525Energy (eV)1.851.811.73-2 0 2ne (1012 cm-2)ν-4 20 4-21.77∆ R/R-0.030.03Energy (eV)1.791.771.781.81.810 2ne (1012 cm-2)1 350K30K15K10K5K3KFig. 4 | Wide field imaging of FT. a Optical microscope image for MATBG deviceD5. Scale bar: 4μm. b,c RC of representative magic-angle (b) and non-magic angle(c) spots in device D5 with local twist angle of 1.04° and 1.14°, respectively. Theirlocations are marked by blue and orange dots in (a). d, e Spatial map of twist angle(d) and correlation strength (e) extracted from the ν = 4 and ν = 2 cascade features,respectively. Both maps are obtained by wide-field imaging without scanning.f Temperature dependence of the extracted 2s exciton energy. The cascade fea-tures persist to above 50K.Article https://doi.org/10.1038/s41467-025-60675-8Nature Communications |         (2025) 16:5555 6www.nature.com/naturecommunicationsExtraction of 2s exciton energyWe extracted the 2s exciton energy at each carrier density from thelocal maximum in the slope of RC vs. probe energy (SupplementaryFig. 2a and 2c). The obtained 2s exciton energy shows a smoothlydecreasing background with increasing charge density due tostronger screening. This background dominates the exciton energyshift in MATTG owing to the large range of carrier density. Tohighlight the cascade features associated with the FT, we fitted thesmooth background for the hole (electron) side using a 3rd (7th)-order polynomial (Supplementary Fig. 2d, Orange curve). Thebackground-subtracted 2s exciton energy shows clear cascade fea-tures at integer fillings (Supplementary Fig. 2d). The same back-ground was used for all displacement fields to ensure that noartifacts were introduced (Fig. 2e).Capacitance and transport measurementPenetration field capacitance measurements were performed onWSe2/RTG device D1 and WSe2/BBG graphene devices D3. The devicecapacitance cp was isolated from the environment using a low-temperature capacitance bridge60. The inverse compressibility κ wasobtained from cp through cp = ctcb/(ct+cb + κ-1) ≈ κctcb61. Themagnitudeof κ increases when the sample is incompressible (gapped) anddecreaseswhen it is compressible (conducting). Themeasurement of κinvolved applying a fixed AC excitation (17–88 kHz) to the top gate.The phase and amplitude of a second AC excitation of the same fre-quency were adjusted and applied to a standard reference capacitor(cref) on the low-temperature amplifier to balance the capacitancebridge. A commercial high-electron-mobility transistor (FHX35X)transformed the small sample impedance to a 1 kΩ output impedance,yielding a gain of about 1000. The DC components of Vt and Vb weresupplied by Keithley 2400 source meters and were connected to thecorresponding gate though bias tee. Additional electrodes were pat-terned in WSe2/MATTG device D2 and WSe2/MATBG device D5 forelectrical transport. Four-point longitudinal resistance was obtainedby supplying an AC current of 10 nA amplitude at frequency of17.777Hz.Widefield imaging of cascade featuresA broadband supercontinuum laser (YSL photonics SC-OEM) was fil-tered by a home-built double monochromator to generate probe lightof tunable center wavelength and <0.2 nm full width at half maximum(FWHM). The probe light was expanded before focusing on the sam-ple, giving rise to a field of view of ~ 900μm2 that covers the entiredevice. The wide-field image of sample was collected by an EMCCDcamera (ProEM-HS 512BX3) without spatial scanning. To obtain a mapof the cascade features, we tuned the probe light energy to be slightlyabove the WSe2 2s exciton resonance and took a sample reflectionimage at each carrier density. Ordinarily, the 2s exciton energy red-shifts with increasing carrier density, leading to decrease of samplereflection at the probe energy. On the other hand, the cascade featuresat integer fillings lead to abnormal blueshifts of 2s exciton energy withincreasing carrier density (Fig. 4b) and thereby increase of samplereflection. This allowed us to extract both carrier density and strengthof the cascade features by comparing sample images at neighboringcarrier density.We further employed a lock-in algorithm to improve the signal tonoise ratio. The carrier density in the devicewasmodulated at66Hzbya small AC gate voltage ΔVg = 0.01 V on top of the DC gate voltage Vg.The EMCCD camera was externally triggered and synchronized withthe AC gate modulation, thereby directly obtaining the differentialreflection image of the sample between slightly different carrier den-sities. Supplementary Movies 1 and 2 show the obtained differentialreflection images for a range of carrier densities near v = 2 and v = 4 ofMATBG, respectively. Supplementary Fig. 7 shows the carrier density-dependent differential reflection near v = 4 for a representative spatialspot (blue boxed pixel). The non-monotonic dip from the cascadefeatures was fitted by a 2nd-order polynomial, from which we extrac-ted the carrier density and the amplitude of the v = 4 cascade feature.Similar fitting was performed on each pixel for carrier densities nearv = 4 and v = 2, from which we obtained a map of the twist angle andcorrelation strength (Fig. 4d, e).Data availabilityData in themain text and Supplementary fig. 1−8 are available onOpenScience Framework62. All other data that supports the findings of thisstudy are available from the corresponding authors upon request.References1. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiréheterostructure. Science 367, 900–903 (2020).2. Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayergraphene. Nature 626, 759–764 (2024).3. Tschirhart, C. L. et al. Imaging orbital ferromagnetism in a moiréChern insulator. Science 372, 1323–1327 (2021).4. Tseng, C.-C. et al. 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One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).62. Xie, T. Optical imaging of flavor order in flat band graphene. OSFhttps://osf.io/nupys/ (2025).AcknowledgmentsWe acknowledge the use of the research facilities within the CaliforniaNanoSystems Institute, supported by the University of California, SantaBarbara and the University of California, Office of the President. C.J.acknowledges support from Air Force Office of Scientific Researchunder award FA9550-23-1-0117. The sample fabrication is supported bythe National Science Foundation through a CAREER award DMR-2337606. T.X. acknowledges the support from the National ScienceFoundation Graduate Research Fellowship under Grant No.2139319.A.F.Y. acknowledges primary support by the Department of Energyunder award DE-SC0020043. A.F.Y. acknowledges the support of theGordon and Betty Moore Foundation under award GBMF9471 and thePackard Foundation under award 2016-65145 for general group activ-ities. Thisworkmade use of facilities funded by EnablingQuantumLeap:Convergent Accelerated Discovery Foundries for Quantum MaterialsScience, Engineering and Information (Q-AMASE-i) award number DMR-1906325 from the National Science Foundation. A.H.M. and T.M.W.acknowledge financial support from the NSF (Award No. DMR–2308817and DMR–2308817). S.T. acknowledges primary support from DOE-SC0020653 (materials synthesis), DMR 2111812, DMR 2206987 andCMMI 2129412 (manufacturing). S.T. acknowledges support from Lawr-ence Semiconductor Labs. K.W. and T.T. acknowledge support from theJSPS KAKENHI (Grant Numbers 20H00354 and 23H02052) and WorldPremier International Research Center Initiative (WPI), MEXT, Japan.Author contributionsC.J. conceived and supervised the project. S.X., Z.C. and T.X. fabricatedthe device. T.X. and R.X. performed the optical measurements. L.F.H.,Y.G., O.I.S., C.P. and T.A. performed the electrical measurements. T.X.analyzed the data. T.M.W. and A.H.M. contributed to the theoreticalinterpretation and performed numerical simulations. Y.O., P.H. andS.A.T. grew the WSe2 crystals. K.W. and T.T. grew hBN crystals. C.J.,A.H.M. and A.F.Y. wrote the paper with input from all the authors.Competing interestsThe authors declare no competing interests.Article https://doi.org/10.1038/s41467-025-60675-8Nature Communications |         (2025) 16:5555 8https://www.science.orghttps://www.science.orghttps://doi.org/10.1017/CBO9780511619915https://osf.io/nupys/www.nature.com/naturecommunicationsAdditional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-025-60675-8.Correspondence and requests for materials should be addressed toAllan H. MacDonald or Chenhao Jin.Peer review information Nature Communications thanks the anon-ymous reviewer(s) for their contribution to thepeer reviewof thiswork. Apeer review file is available.Reprints and permissions information is available athttp://www.nature.com/reprintsPublisher’s note Springer Nature remains neutral with regard to jur-isdictional claims in published maps and institutional affiliations.Open Access This article is licensed under a Creative CommonsAttribution 4.0 International License, which permits use, sharing,adaptation, distribution and reproduction in any medium or format, aslong as you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons licence, and indicate ifchanges were made. The images or other third party material in thisarticle are included in the article’s Creative Commons licence, unlessindicated otherwise in a credit line to the material. If material is notincluded in the article’s Creative Commons licence and your intendeduse is not permitted by statutory regulation or exceeds the permitteduse, you will need to obtain permission directly from the copyrightholder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2025Article https://doi.org/10.1038/s41467-025-60675-8Nature Communications |         (2025) 16:5555 9https://doi.org/10.1038/s41467-025-60675-8http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/www.nature.com/naturecommunications Optical imaging of flavor order in flat band graphene Results Optical sensing of FT Selective detection of FT Wide field imaging of FT Discussion Methods Sample fabrication Calibration of carrier density, displacement field, and twist angle Reflection contrast (RC) measurement Extraction of 2s exciton energy Capacitance and transport measurement Widefield imaging of cascade features Data availability References Acknowledgments Author contributions Competing interests Additional information