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Nicholas Dale, M. Iqbal Bakti Utama, Dongkyu Lee, Nicolas Leconte, Sihan Zhao, Kyunghoon Lee, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, Roland J. Koch, Jeil Jung, Feng Wang, Alessandra Lanzara

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[Layer-Dependent Interaction Effects in the Electronic Structure of Twisted Bilayer Graphene Devices](https://mdr.nims.go.jp/datasets/88ba2c46-324d-4216-b82d-7ca12dcfa598)

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Layer-Dependent Interaction Effects in the Electronic Structure of Twisted Bilayer Graphene DevicesLayer-Dependent Interaction Effects in the Electronic Structure ofTwisted Bilayer Graphene DevicesNicholas Dale, M. Iqbal Bakti Utama, Dongkyu Lee, Nicolas Leconte, Sihan Zhao, Kyunghoon Lee,Takashi Taniguchi, Kenji Watanabe, Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, Roland J. Koch,Jeil Jung, Feng Wang, and Alessandra Lanzara*Cite This: Nano Lett. 2023, 23, 6799−6806 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Near the magic angle, strong correlations drive many intriguingphases in twisted bilayer graphene (tBG) including unconventional super-conductivity and chern insulation. Whether correlations can tune symmetry breakingphases in tBG at intermediate (≳ 2°) twist angles remains an open fundamentalquestion. Here, using ARPES, we study the effects of many-body interactions anddisplacement field on the band structure of tBG devices at an intermediate (3°) twistangle. We observe a layer- and doping-dependent renormalization of bands at the Kpoints that is qualitatively consistent with moire ́ models of the Hartree−Fockinteraction. We provide evidence of correlation-enhanced inversion symmetry-breaking, manifested by gaps at the Dirac points that are tunable with doping. Theseresults suggest that electronic interactions play a significant role in the physics of tBGeven at intermediate twist angles and present a new pathway toward engineeringband structure and symmetry-breaking phases in moire ́ heterostructures.KEYWORDS: twisted bilayer graphene, moire ́ heterostructures, ARPES, symmetry-breaking, electron−electron interaction, band gap.The search for intriguing phases of matter often treadsalong common avenues: generating strong correlationsand breaking symmetries in materials. Correlations developwhen the ratio of interaction strength U to bandwidth W in asystem becomes large (U/W ≫ 1), presenting instabilities tomyriad ground states. Twisted bilayer graphene is an especiallypopular host of correlated phases1−3 due to the ability to tunethe bandwidth with extreme precision using the twist angle,4,5and the ability to tune the interaction strength U in situthrough charge carrier6 and substrate-based7 screening.Most studies of renormalization effects in twisted bilayergraphene to date have focused on how the overall bandwidth ismodified by interactions. Indeed, several theoretical workspredict significant band structure modification from theHartree8−11 and Hartree−Fock interaction,12 which havebeen shown in some cases to drive correlated phases outsidethe twist angle regime predicted by early band structuremodels.6,12,13 However, graphene devices are rarely inversionsymmetric,14 especially in the presence of a displacement field,and at twist angles θ ≳ 2° the K point electronic structure islayer polarized,15 in principle enabling each layer to hostdiffering electronic properties or phases. When inversionsymmetry is broken, so far it is unclear how introducingcorrelations affect electronic structure in each individual layerof twisted graphene and whether these differences couldindependently tune symmetry breaking phases in each layer.Here, we use gated ARPES16−18 to directly measure the layer-dependent electronic structure of an intermediate angle (3°)twisted bilayer graphene device as a function of electrostaticdoping and displacement field. The high momentum andenergy resolution of our experiment allow us to identify directevidence for layer-dependent interaction-driven band narrow-ing as well as a substrate-induced band gap at the K points. Wefind that a combination of displacement field and electron−electron interactions is able to enhance this band gap withinjust a single layer and thus tune the level of symmetry breakingin the system with atomic layer precision.Figure 1a,b presents the sample configuration and geometry,respectively, used for the gated ARPES experiment, and panel cshows the scanning electron micrograph of the sample. Thesample was fabricated using the tear-and-stack flip chip methoddescribed in ref 19 to minimize surface roughness, enablinghigh momentum resolution for photoemission experiments.False color identifies regions of the top monolayer graphene(orange), the bottom monolayer graphene (blue), hBN(white), and graphite back gate (purple). Using a 1 μmReceived: January 20, 2023Revised: May 25, 2023Published: July 24, 2023Letterpubs.acs.org/NanoLett© 2023 The Authors. Published byAmerican Chemical Society6799https://doi.org/10.1021/acs.nanolett.3c00253Nano Lett. 2023, 23, 6799−6806Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on August 12, 2023 at 01:25:40 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Nicholas+Dale"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="M.+Iqbal+Bakti+Utama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Dongkyu+Lee"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Nicolas+Leconte"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sihan+Zhao"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kyunghoon+Lee"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Chris+Jozwiak"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Aaron+Bostwick"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Eli+Rotenberg"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Roland+J.+Koch"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jeil+Jung"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jeil+Jung"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Feng+Wang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Alessandra+Lanzara"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.nanolett.3c00253&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/nalefd/23/15?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/15?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/15?ref=pdfhttps://pubs.acs.org/toc/nalefd/23/15?ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00253?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/NanoLett?ref=pdfhttps://pubs.acs.org/NanoLett?ref=pdfhttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://acsopenscience.org/open-access/licensing-options/beam spot via a capillary focusing optic,20 we produce ascanning photoemission micrograph (SPEM) (panel d) thatmaps the real space configuration of the graphene photo-electrons at EF and confirms the sample geometry. Theintensity of the signal deriving from graphene scales with thelayer number:19 the middle region has a stronger intensity thanthe region on the left, matching the expected location of thetBLG and monolayer graphene regions, respectively asoutlined in panel b.Figure 1e presents the ARPES constant energy map for atBLG region at a back gate voltage of −5 V. Encompassing theK points of the two graphene layers are circular Fermi contoursFigure 1. Gated ARPES on twisted bilayer graphene (a−d) schematic of experimental setup (a) angular geometry (b) of the twisted graphene/hBN sample. (c, d) scanning electron micrograph (c) and scanning photoemission microscopy (SPEM) image integrated over states at EF (d).Regions of graphene upper layer (orange), lower layer (blue), hBN (gray), and graphite (purple) are outlined/filled in with false color. (e) ARPESconstant energy spectrum at EF for sample gate voltage of −5 V. Brillouin zones for the individual graphene upper (lower) layers are outlined in red(blue), while the Brillouin zone for hBN is outlined in cyan. (f) ARPES spectrum along the Kupper − Klower direction (indicated by yellow line in parte) of the twisted graphene/hBN sample.Figure 2. Displacement field characterization of tw-BLG device. (a) schematic of displacement field effect produced in twisted graphene bilayersunder a single back gate potential. (b) Cartoons above indicate relative energy of upper (red) and lower (blue) Dirac cones upon p doping (left) atneutrality (middle) and n doping (right). (c) ARPES spectra along the Kupper − Klower direction at (e) p doping (−5 V, left) equilibrium (0 V,middle), and n doping (5 V, right). Red (blue) dashed lines indicate linear fits to quasiparticle peak positions extracted from Lorentzian fits. (d)Carrier density ne as a function of gate voltage, extracted from Fermi wavevector of each cone. Red (blue) curves are linear fits to the data in theupper (lower) Dirac cone away from the neutrality point. (e) EF − ED as a function of gate voltage, extracted from linear fits to the graphene spectrafor the upper (red) and lower (blue) graphene layers. Band displacement (black) is extracted as the energy difference between the two layers. Errorbars indicate statistical errors to the linear fit. Red, blue, and black curves indicate V fits to the data.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c00253Nano Lett. 2023, 23, 6799−68066800https://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig2&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00253?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aswhose matrix elements smoothly drop to zero along one side,suggesting that the low energy Fermions in the sample are ofDirac nature.21,22 Upper and lower graphene layers can bedistinguished by the difference in spectral weight near therespective K points, as the photoelectrons from the bottomlayer are attenuated as they pass through the top layer.23−25The twist angle can be measured in ARPES from themomentum separation of the K points of the two graphenelayers using the relationship ΔK = 2 |K| sin θ/2. On the samplea twist angle of 3° was measured, corresponding to a moire ́wavelength of 6 nm and a momentum separation ΔK ≈ 0.09Å−1. The angular alignment of the hBN substrate can beextracted in a similar manner: the momentum separation of≈0.54 Å−1 between the ky location of the hBN K point(parabola at EF − 2.2 eV in panel f) and the lower graphene Kpoint indicates a ≈19° relative twist.Figure 1f presents ARPES spectra along the Kupper − Klowerdirection. At large (>2°) twist angles, the K point spectra forthe upper and lower graphene layers can be approximated asDirac cones.23,25,26 This is apparent visually by eye within≈200 meV of the Fermi level in panel f, whose bands from leftto right we label as a, c, f, and h. Around 200 meV below EF(panel f), a van Hove singularity forms from the hybridizationbetween intersecting bands from the lower and uppercones.23−25 Other evidence of graphene−graphene interlayercoupling in our sample is very prominent: Dirac cone replicasof the upper and lower layers are clearly observed at thecorresponding mini Brillouin zone (mBz) corners (panel e),and at energies beyond 500 meV (panel f) a series of additionalbands (b, d, e, and g) are present, similar to previous reportson SiC-supported graphene samples at similar twist angles.26,27Upon applying a negative (positive) back gate voltage to thesample, the two graphene layers become doped by holes(electrons), resulting in an upward (downward) shift of theDirac cone spectrum with respect to EF. Due to the imperfectout-of plane screening in graphene multilayers, application of aback gate voltage Vbg to our sample generates an electric fieldbetween the upper and lower graphene layers, resulting in botha difference in charge carrier density δ n = nu − nl and chemicalpotential difference D = μu − μl23,28,29 (see Figure 2a).Such an effect, illustrated by the cartoon in Figure 2b, isclearly reflected in our data (Figure 2c). The lower layerreceives higher absolute doping and therefore a larger absoluteshift of its Dirac cone spectrum as compared to the upperlayer, resulting in a band displacement D that is tunable inmagnitude and sign with the back gate voltage.23,28,29The carrier density, calculated as n = kF2/π for the upper andlower Dirac cones, is quantified in Figure 2d (seeSupplementary Note 1 for details). Away from the neutralitypoint at Vg = 1 V, the density scales linearly with gate voltage,i.e., n(Vg) ∼ C Vg, implying that the system is effectively aparallel plate capacitor with geometric capacitance C. Near theneutrality point, n(Vg) flattens, suggesting contributions ofquantum capacitance due to a strong drop in the density ofstates, likely from the presence of a gap in the dispersion (seeSupplementary Note 6 for more details). We will return to thispoint later in the text.Linear fits to the band dispersions (dashed lines in panel c)at low energy yield the position of the Dirac point for theupper and lower layers, which are plotted as a function of gatevoltage in panel e. The Dirac point position as a function ofvoltage roughly scale as | |E E a VF D g (red and bluecurves) with a = 0.09 ± 0.01 and a = 0.06 ± 0.01 for lower andupper layers, respectively). The band displacement, taken asthe difference between the two Dirac cone energies, thereforehas the same qualitative scaling D b Vg where b = 0.03 ±0.01.The stronger scalings of both EF − ED and n(Vg) with gatevoltage in the lower layer indicates the larger amount of chargeinduced by the gate in the lower layer, confirming previousreports on large twist angle bilayer graphene.23,28,29As we shall demonstrate in the following, both doping anddisplacement fields can be used to control the band structurebeyond what would be expected by a single particle picture.Figure 3 presents the evolution of the upper and lower Kpoint electronic structures as a function of doping for the 3°twisted graphene sample. Figure 3b displays band dispersionsalong Γ − Klower for dopings of −2.0 × 1012 cm−2, −0.1 × 1012cm−2, and 1.0 × 1012 cm−2 (see Supplementary Note 1 fordetails on the calculation of the carrier density). Thesedispersions have been shifted by the position of the Dirac pointof the upper layer for the ease of comparison. From the rawdata, it is clear by eye that all three spectra are linear within300 meV of the Dirac point. Notably, the hole-dopeddispersion (green) is less steep than the dispersion at neutrality(brown), which is less steep than the dispersion at electrondoping (red). Indeed, a similar effect occurs in the upper layer(Figure 3a) though at much smaller magnitude.Figure 3. Doping-induced band renormalization. (a, b) Band dispersions as a function of doping along Γ − Kupper (a) and Γ − Klower (b), see insetcartoon for details on the cut in momentum space. (c) Band velocities as a function of doping, for both layers, measured along energy regionindicated by inset cartoon. Error bars correspond to 1σ standard deviation in the fits.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c00253Nano Lett. 2023, 23, 6799−68066801https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig3&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00253?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asThese results clearly indicate a narrowing of the valenceband upon hole-doping and are summarized in panel c, wherethe band velocities, measured by the slope of the dispersion,are plotted as a function of doping. These results do not matchthe behavior of monolayer graphene,18,30,31 which has alogarithmic divergence of band velocity at the neutrality point.Instead, we see a near monotonic decrease in band velocitywith hole-doping. Indeed, this may be explained in models oftwisted bilayer graphene that incorporates the interactionsspurring from change in charge distribution in the moire ́ unitcell.6,8−11 At neutrality, charge localizes on the AA sites,creating a Hartree−Fock potential that is stronger in theseregions than the rest of the moire ́ unit cell which has moredelocalized electrons. As the doping changes, chargeredistributes in the moire ́ cell, causing band renormalizationwith the same doping dependence as our results: upon hole-doping, the valence band narrows, and upon electron doping,the valence band steepens.6 The relatively small band velocitychange with doping in the upper graphene layer suggests thatthe electron−electron interaction is more strongly screened,perhaps due to the presence of the doped graphene layerbeneath it. Indeed, reduced vF32−35 and changes withdoping31,35,36 are observed in single layer graphene uponincreasing the dielectric constant of the substrate. The lowergraphene layer, which is supported by a lower dielectricstrength substrate, therefore, receives a stronger band velocityenhancement from the Hartree−Fock interaction. While thechanges of band velocity with doping predicted by Hartree−Fock models are on the ≈1% scale for a doping change of ≈ns/8,6,12 we are able to modify the band velocity by up to 40%in the lower graphene layer. Indeed these theoretical models ofgraphene may underestimate renormalization effects from theFigure 4. Gate-tunable gap at neutrality point. (a1, a2) 3° twisted graphene second derivative spectra along Γ − Kupper for two different displacementfield values: −1 meV (a1) and 61 meV (a2). Gaps in the dispersion are indicated by orange shaded regions. Red dashed lines in the right panel arevalence band dispersions deriving from the upper graphene layer. (b1, b2) Corresponding MDCs for parts a1 and a2, between energy E1 and E11.Black ticks indicate quasiparticle peak positions extracted from fitting to Lorentzian lineshapes. Purple curves are in the gap, where the peaks aredispersionless. (c) Extracted dispersions from raw data associated with parts a1 (left) and a2 (right). Dashed lines indicate linear fits to theconduction and valence dispersions. Gray regions indicate gaps in the band structure, bordered by kinks in the MDCs dispersion. (d1, d2) 3°twisted graphene second derivative spectra along Γ − Klower for two different displacement field values: −1 meV (a1) and 61 meV (a2). Gaps in thedispersion are indicated by orange shaded regions. Red (white) dashed lines in right panel are valence band dispersions deriving from the upper(lower) graphene layer. (e1, e2.) Corresponding MDCs for parts d1 and d2, between energy E1 and E11. Black ticks indicate quasiparticle peakpositions extracted from fitting to Lorentzian lineshapes. Purple curves are in the gap, where the peaks are dispersionless. Red ticks indicatequasiparticle peaks deriving from the upper graphene layer. (f) Extracted dispersions from raw data associated with d1 (left) and d2 (right). Dashedlines indicate linear fits to the conduction and valence dispersions. Gray regions indicate gaps in the band structure, bordered by kinks in the MDCsdispersion. (g) Schematic of band gap renormalization with displacement field and doping. (h) Summary of band gaps in the upper and lowerlayers as a function of doping.Nano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c00253Nano Lett. 2023, 23, 6799−68066802https://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?fig=fig4&ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00253?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aslong-range electron−electron interaction, similar to the case ofsingle layer graphene.36−38 Band structure renormalizationfrom Hartree interaction is in fact enhanced when the initialgraphene band structure incorporates the band velocityenhancements present in graphene on a dielectric substrate(see Supplementary Note 2 for more details). Furtherinvestigation is necessary to determine the exact origin ofthis behavior.The difference in band velocity in the upper and lower layersis clear evidence of C2x inversion symmetry breaking in thegraphene sample. While this often occurs in graphene samplessupported by hBN substrates39−42 or undergoing hetero-strain,43 the level of symmetry breaking here is dopingdependent. This signature is in other parts of the electronicstructure.Figure 4 presents the layer-dependent evolution of the Kpoint electronic structure with doping and a displacement field.Charge neutral ARPES spectra at the upper layer K point(Figure 4a1) exhibit the typical Dirac cone dispersion with acrossing at the Fermi level. Given a sample temperature of 300K, division by the Fermi Dirac distribution provides insightinto the electronic structure within 4kBT ≈ 100 meV of theFermi level (see Materials and Methods in the SupportingInformation), which presents a drop in the density of states atthe neutrality point followed by the bottom of a conductionband which is energetically separated from the valence band by≈130 meV. This can be confirmed by the raw MDCs spectra(panel b1) which are dispersionless in a similar range in energy.Similar electronic structure is observed in the lower layer Kpoint electronic structure (panels d1, e1) These data constitutedirect evidence for a band gap in this twisted graphene/hBNsample near the charge neutrality point. Such property isobserved in samples with broken C2z inversion symmetry,which can occur in the presence of an hBN sub-strate.14,39,40,42,44Upon electron doping the sample, the upper layer electronicstructure (panels a2, b2) appears similar to the spectrum atneutrality but rigidly shifted by about 150 meV, with the bandgap remaining relatively constant. However, the lower layerband structure (panels d2, e2) undergoes significant mod-ification: whereas the spectrum at neutrality has one valenceband, the electron doped spectrum (panel d2) exhibits two.Indeed, the raw MDCs spectra (panel e2) exhibit 2 peaks,represented as shoulders, between 500 and 200 meV below EF.Interestingly, these peaks at higher momenta have dispersionand energy very similar to those of the valence band of theupper Dirac cone (red curves in panel a2 and red peaks inpanel b2). We therefore propose the lower energy band (reddashed lines in panel d2) to be a replica of the upper layerelectronic structure and to be independent of the lower layerelectronic structure. Indeed, such replicas manifest in zone-unfolded band structure calculations in the presence of anelectric field between upper and lower graphene layers (seeSupplementary Note 3 for more details). The lower layervalence band at higher energy (white dashed line in panel d2)is therefore dramatically separated from the conduction band,indicating a significant increase in the band gap size withdoping and displacement.The layer and doping dependent behavior of the band gapsis confirmed by the quasiparticle dispersions in the upper andlower K points (Figure 4, parts c and f) respectively. Gaps inARPES manifest as kinks or regions of abrupt upturn in theMDCs dispersions,42,45,46 and in Dirac materials such asgraphene these regions are bounded by linear dispersions.46 Inboth layers at all dopings, there is a nonzero region of energy atwhich the dispersions have an abrupt upturn bounded bylinearly dispersive features. This behavior is consistent as afunction of momentum surrounding the upper and lower Kpoints, demonstrating the unambiguous signature of a bandgap (see Supplementary Note 4 for more details). Themagnitude of the band gap is determined from the energeticdistance between linearly dispersive regions in the bandstructure which are denoted by dashed black lines. Uponapplication of a 61 meV displacement and doping the upperlayer by 0.3 × 1012 cm−2, the bandgap at Kupper remainsconstant at 140 ± 50 meV. However, upon applying the sameband displacement and doping the lower layer by 1.0 × 1012cm−2 the bandgap at Klower increases from 130 ± 50 meV to200 ± 50 meV. Such layer-dependent doping behavior of bandgaps in our data, summarized in panel h, are qualitativelyconsistent with the amount of inversion symmetry-breakingpresent in the sample.The layer and doping dependent behavior of the band gapsis confirmed by the quasiparticle dispersions in the upper andlower K points, (Figure 4, parts c and f) respectively. Gaps inARPES manifest as kinks or regions of abrupt upturn in theMDCs dispersions,42,45,46 and in Dirac materials such asgraphene these regions are bounded by linear dispersions.46 Inboth layers at all dopings, there is a nonzero region of energy atwhich the dispersions have an abrupt upturn bound by linearlydispersive features. This behavior is consistent as a function ofmomentum surrounding the upper and lower K points,demonstrating the unambiguous signature of a band gap (seeSupplementary Note 4 for more details). The magnitude of theband gap is determined from the energetic distance betweenlinearly dispersive regions in the band structure, which aredenoted by dashed black lines. Upon application of a 61 meVdisplacement and doping the upper layer by 0.3 × 1012 cm−2,the bandgap at Kupper remains constant at 140 ± 50 meV.However, upon applying the same band displacement anddoping the lower layer by 1.0 × 1012 cm−2 the bandgap at Klowerincreases from 130 ± 50 meV to 200 ± 50 meV. Such layer-dependent doping behavior of band gaps in our data,summarized in panel h, are qualitatively consistent with theamount of inversion symmetry-breaking present in the sample.Indeed, the inversion symmetry-breaking produced by amisaligned hBN substrate41,44 can be significantly enhancedby electron−electron interactions.7,41,47 In graphene, themagnitude of interaction-driven gap enhancement scales withthe interaction strength,7,41,47 which in tBG scales linearly withdoping.8−11 Therefore, a charge imbalance between the twographene layers, generated, e.g., via a displacement field, candrive a doping-dependent gap mechanism which enables layer-dependent gap enhancements such as those seen in ourexperiment.The magnitude of gaps observed in our data is much largerthan those observed in the literature at similar twist angle.48−50Whereas other probes such as transport and STS commonlydefine gaps as regions with zero density of states, ARPESdefines the band gap using the band edges, at which thedensity of states rarely has an abrupt drop to zero.42 Impuritiesmay also contribute to in-gap states that decrease the apparentgap size in a transport or STS measurement. Notably, bothsingle layer51 and bilayer graphene52 in particular exhibit in-gap conductive resonances as a response to the presence ofcharged impurities, which significantly alters the accuracy of aNano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c00253Nano Lett. 2023, 23, 6799−68066803https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00253?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asgap measurement using STS dI/dV or transport. ARPES canstill measure the gap in these cases because band edges arebordered by regions of dispersionless spectral weight.45 Finally,as transport is only sensitive to the spatially integratedelectronic states at the Fermi level, it may miss the gapentirely because (1) at the neutrality point, the spatiallyinhomogeneuos doping present in tBG samples6,53,54 canproduce insulating regions adjacent to conductive regions,which upon spatial integration could appear as a minordecrease in conductivity48,50 (see Supplementary Note 5 formore details), and (2) upon electron doping, the gap increaseobserved here occurs when the Dirac point is below the Fermilevel.The data reported here provide evidence for a method oftuning the band velocities and band gaps in twisted bilayergraphene in operando. While we considered several alternativeexplanations (see Supplementary Note 7), we believe thatthese effects can be best explained by a combination of thesubstrate interaction and the spatially inhomogeneousHartree−Fock interaction, which is controlled within differentlayers by using a displacement field. Indeed, these interactionscan qualitatively explain the presence of the gap at chargeneutrality, the linear dependence of band velocity with dopingand the layer-dependent gap enhancement upon electrondoping the sample.In conclusion, we have demonstrated that gated ARPES isan exceptional tool to study the interplay of interactions andsymmetry breaking in 2D homo- and heterostructures. Ourresults indicate that both the spatially inhomogeneous Hartreeinteraction and a displacement field can be used toindependently tune the bandwidth and band gaps in twistedbilayer graphene, opening up the intriguing possibility toengineer bands and enabling access to novel correlated phasesin a larger range of twisted homobilayers6,55,56 and otherheterostructures.57−60■ ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253.Methods for tBG device fabrication, ARPES measure-ments and data analysis; notes on carrier densitymeasurements, Hartree interaction effects in 3° tBG,evidence for presence of replicas of primary bands in 3°tBG, and additional analysis of the gap at the Kupper andKlower points in the band structure; and dditional noteson the effects of spatial inhomogeneity on the carrierdensity measurements, as well as a discussion of theorigin of doping- and layer-dependent band velocityband gap enhancements (PDF)■ AUTHOR INFORMATIONCorresponding AuthorAlessandra Lanzara − Department of Physics, University ofCalifornia, Berkeley, California 94720, United States;Materials Sciences Division, Lawrence Berkeley NationalLaboratory, Berkeley, California 94720, United States; KavliEnergy NanoScience Institute at University of CaliforniaBerkeley and Lawrence Berkeley National Laboratory,Berkeley, California 94720, United States;Email: Alanzara@lbl.govAuthorsNicholas Dale − Department of Physics, University ofCalifornia, Berkeley, California 94720, United States;Materials Sciences Division, Lawrence Berkeley NationalLaboratory, Berkeley, California 94720, United States;orcid.org/0000-0001-8432-2135M. Iqbal Bakti Utama − Materials Sciences Division,Lawrence Berkeley National Laboratory, Berkeley, California94720, United States; Department of Materials Science andEngineering, University of California at Berkeley, Berkeley,California 94720, United States; orcid.org/0000-0002-4454-8348Dongkyu Lee − Department of Physics and Department ofSmart Cities, University of Seoul, Seoul 02504, KoreaNicolas Leconte − Department of Physics, University of Seoul,Seoul 02504, KoreaSihan Zhao − Interdisciplinary Center for QuantumInformation, Zhejiang Province Key Laboratory of QuantumTechnology and Device, State Key Laboratory of SiliconMaterials, and School of Physics, Zhejiang University,Hangzhou 310027, China; orcid.org/0000-0003-2162-734XKyunghoon Lee − Department of Physics, University ofCalifornia, Berkeley, California 94720, United States;Materials Sciences Division, Lawrence Berkeley NationalLaboratory, Berkeley, California 94720, United States;orcid.org/0000-0002-3409-9454Takashi Taniguchi − International Center for MaterialsNanoarchitectonics, National Institute for Materials Science,Tsukuba 305-0044, Japan; orcid.org/0000-0002-1467-3105Kenji Watanabe − Research Center for Functional Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0003-3701-8119Chris Jozwiak − Advanced Light Source, Lawrence BerkeleyNational Laboratory, Berkeley, California 94720, UnitedStates; orcid.org/0000-0002-0980-3753Aaron Bostwick − Advanced Light Source, Lawrence BerkeleyNational Laboratory, Berkeley, California 94720, UnitedStatesEli Rotenberg − Advanced Light Source, Lawrence BerkeleyNational Laboratory, Berkeley, California 94720, UnitedStates; orcid.org/0000-0002-3979-8844Roland J. Koch − Advanced Light Source, Lawrence BerkeleyNational Laboratory, Berkeley, California 94720, UnitedStates; orcid.org/0000-0001-5748-8463Jeil Jung − Department of Physics and Department of SmartCities, University of Seoul, Seoul 02504, KoreaFeng Wang − Department of Physics, University of California,Berkeley, California 94720, United States; Materials SciencesDivision, Lawrence Berkeley National Laboratory, Berkeley,California 94720, United States; Kavli Energy NanoScienceInstitute at University of California Berkeley and LawrenceBerkeley National Laboratory, Berkeley, California 94720,United StatesComplete contact information is available at:https://pubs.acs.org/10.1021/acs.nanolett.3c00253Author ContributionsN.D. and A.L. initiated and directed the research project. T.T.and K.W. synthesized the hBN crystals. N.D., M.I.B.U., S.Z.,and K.L. fabricated the graphene samples. N.D. and A.B.performed the ARPES measurements. N.D. analyzed theNano Letters pubs.acs.org/NanoLett Letterhttps://doi.org/10.1021/acs.nanolett.3c00253Nano Lett. 2023, 23, 6799−68066804https://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acs.nanolett.3c00253/suppl_file/nl3c00253_si_001.pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Alessandra+Lanzara"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfmailto:Alanzara@lbl.govhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Nicholas+Dale"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0001-8432-2135https://orcid.org/0000-0001-8432-2135https://pubs.acs.org/action/doSearch?field1=Contrib&text1="M.+Iqbal+Bakti+Utama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-4454-8348https://orcid.org/0000-0002-4454-8348https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Dongkyu+Lee"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Nicolas+Leconte"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Sihan+Zhao"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-2162-734Xhttps://orcid.org/0000-0003-2162-734Xhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kyunghoon+Lee"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-3409-9454https://orcid.org/0000-0002-3409-9454https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takashi+Taniguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-1467-3105https://orcid.org/0000-0002-1467-3105https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kenji+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-3701-8119https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Chris+Jozwiak"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-0980-3753https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Aaron+Bostwick"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Eli+Rotenberg"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-3979-8844https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Roland+J.+Koch"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0001-5748-8463https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Jeil+Jung"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Feng+Wang"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.nanolett.3c00253?ref=pdfpubs.acs.org/NanoLett?ref=pdfhttps://doi.org/10.1021/acs.nanolett.3c00253?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asARPES data with inputs from A.L. D.L., N.L., and J.J. ran theTB simulations provided in the Supporting Information. N.D.and A.L. wrote the manuscript, with input from all of theauthors.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSWe thank Salman Kahn for technical assistance in the samplefabrication setup. This work was primarily supported by theU.S. Department of Energy, Office of Science, Office of BasicEnergy Sciences, Materials Sciences and Engineering Divisionunder Contract No. DEAC02- 05CH11231 (UltrafastMaterials Science Program KC2203). This research usedresources of the Advanced Light Source, a US DOE Office ofScience User Facility under Contract No. DE-AC02-05CH11231. A.L. and N.D. acknowledge partial support forthis research from the Gordon and Betty Moore Foundation’sEPiQS Initiative through Grant GBMF4859. This work wassupported by the Korean NRF through the Grants No.2020R1A5A1016518 (D.L.), 2020R1A2C3009142 (N.L.), andSamsung Science and Technology Foundation Grant No.SSTF-BA1802-06 (J.J.). We acknowledge computationalsupport from KISTI Grant No. KSC-2022-CRE-0514 and bythe resources of the Urban Big Data and AI Institute (UBAI)at UOS. D.L. also acknowledges support by the KoreanMinistry of Land, Infrastructure and Transport (MOLIT) fromthe Innovative Talent Education Program for Smart Cities.K.W. and T.T. acknowledge support from JSPS KAKENHI(Grant Numbers 19H05790, 20H00354, and 21H05233).■ REFERENCES(1) Cao, Y.; Fatemi, V.; Fang, S.; Watanabe, K.; Taniguchi, T.;Kaxiras, E.; Jarillo-Herrero, P. Unconventional superconductivity inmagic-angle graphene superlattices. Nature 2018, 556, 43−50.(2) Cao, Y.; Fatemi, V.; Demir, A.; Fang, S.; Tomarken, S. L.; Luo, J.Y.; Sanchez-Yamagishi, J. D.; Watanabe, K.; Taniguchi, T.; Kaxiras, E.;Ashoori, R. C.; Jarillo-Herrero, P. 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