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Canxun Zhang, Tiancong Zhu, Tomohiro Soejima, Salman Kahn, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Alex Zettl, Feng Wang, Michael P. Zaletel, Michael F. Crommie

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[Local spectroscopy of a gate-switchable moiré quantum anomalous Hall insulator](https://mdr.nims.go.jp/datasets/81c0451f-c5bd-4ecd-91e1-febc4c6c9dcc)

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Local spectroscopy of a gate-switchable moiré quantum anomalous Hall insulatorArticle https://doi.org/10.1038/s41467-023-39110-3Local spectroscopy of a gate-switchablemoiré quantum anomalous Hall insulatorCanxun Zhang 1,2,3,6, Tiancong Zhu1,2,6 , Tomohiro Soejima1,6,Salman Kahn 1,2,6, Kenji Watanabe 4, Takashi Taniguchi 5, Alex Zettl1,2,3,Feng Wang 1,2,3, Michael P. Zaletel1,2 & Michael F. Crommie 1,2,3In recent years, correlated insulating states, unconventional super-conductivity, and topologically non-trivial phases have all been observed inseveral moiré heterostructures. However, understanding of the physicalmechanisms behind these phenomena is hampered by the lack of local elec-tronic structure data. Here, we use scanning tunnelling microscopy andspectroscopy to demonstrate how the interplay between correlation, topol-ogy, and local atomic structure determines the behaviour of electron-dopedtwisted monolayer–bilayer graphene. Through gate- and magnetic field-dependent measurements, we observe local spectroscopic signatures indi-cating a quantumanomalousHall insulating statewith a total Chern number of±2 at a doping level of three electrons per moiré unit cell. We show that thesign of the Chern number and associated magnetism can be electrostaticallyswitched only over a limited range of twist angle and sample hetero-strainvalues. This results from a competition between the orbital magnetization offilled bulk bands and chiral edge states, which is sensitive to strain-induceddistortions in the moiré superlattice.Van der Waals stacking of twisted two-dimensional (2D) atomic sheetsprovides a versatile platform for engineering exotic electronic statesthrough rotationalmisalignment that folds dispersive electronic bandsinto flat mini-bands within a moiré Brillouin zone1,2. The resultingsuppression of kinetic energy relative to electron–electron interac-tions can lead to correlated insulating states as well as unconventionalsuperconductivity3,4. Moiré flat bands also inherit the large Berry cur-vature of the individual atomic layers which can result in topologicallynon-trivial phases5–7. Electron-doped twisted monolayer–bilayer gra-phene (tMBLG)—a graphene monolayer rotationally misaligned with aBernal-stacked bilayer—stands out among these since it exhibits thequantum anomalous Hall (QAH) effect (i.e., quantized Hall con-ductance in the absence of external magnetic field) accompanied bydoping-controlled switching of its Chern number, an effect notobserved in other moiré QAH systems8. Such behaviour is expected tobe sensitive to local structural parameters such as twist angle andhetero-strain (i.e., the relative strain between adjacent layers). Forexample, twist angle directly affects the moiré mini-band structurewhile even small hetero-strains (<0.5%) can bemagnified by the moirésuperlattice to induce large moiré distortions, thus altering the ener-getics of mini-bands and the behaviour of emergent correlated andtopological phases9,10. Understanding the rich physics of moiré sys-tems requires understanding the relationship between exotic elec-tronic phases and local structure, something difficult to achieve usingmacroscopic probes that only explore spatially-averaged behaviour.Here we show how scanning tunnelling microscopy and spectro-scopy (STM/STS) enables determination of how changes in localstructure alter correlated and topological electronic behaviour inReceived: 2 December 2022Accepted: 25 May 2023Check for updates1Department of Physics, University of California, Berkeley, CA 94720, USA. 2Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA94720, USA. 3Kavli EnergyNanoScience Institute at the University of California, Berkeley and the Lawrence Berkeley National Laboratory, Berkeley, CA94720,USA. 4Research Center for Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 5Research Centerfor Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan. 6These authors contributed equally: CanxunZhang, Tiancong Zhu, Tomohiro Soejima, Salman Kahn. e-mail: tiancongzhu@berkeley.edu; mikezaletel@berkeley.edu; crommie@berkeley.eduNature Communications |         (2023) 14:3595 11234567890():,;1234567890():,;http://orcid.org/0000-0001-6608-4743http://orcid.org/0000-0001-6608-4743http://orcid.org/0000-0001-6608-4743http://orcid.org/0000-0001-6608-4743http://orcid.org/0000-0001-6608-4743http://orcid.org/0000-0002-0012-3305http://orcid.org/0000-0002-0012-3305http://orcid.org/0000-0002-0012-3305http://orcid.org/0000-0002-0012-3305http://orcid.org/0000-0002-0012-3305http://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/0000-0001-8369-6194http://orcid.org/0000-0001-8369-6194http://orcid.org/0000-0001-8369-6194http://orcid.org/0000-0001-8369-6194http://orcid.org/0000-0001-8369-6194http://orcid.org/0000-0001-8246-3444http://orcid.org/0000-0001-8246-3444http://orcid.org/0000-0001-8246-3444http://orcid.org/0000-0001-8246-3444http://orcid.org/0000-0001-8246-3444http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39110-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39110-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39110-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39110-3&domain=pdfmailto:tiancongzhu@berkeley.edumailto:mikezaletel@berkeley.edumailto:crommie@berkeley.edutMBLG field-effect transistor devices. We find that tuning the electrondoping concentration of tMBLG results in the emergence of chargegaps observable to STS at filling levels ν = 2 and ν = 3 (i.e., twoand threeelectrons per moiré unit cell), indicating the formation of correlatedinsulating states. STS performed in an out-of-plane magnetic fieldallows us to detect non-trivial topology in the ν = 3 QAH insulatingstate which has total Chern number Ctot = ±2, and to demonstrate itsdependence on local twist angle and hetero-strain. In addition toobserving strong variation of correlation and topological properties atdifferent twist angles, we find that regions having nearly identical twistangle but different hetero-strain values exhibit very different beha-viour. In the small-strain regime, the correlation gap evolves into twoseparate gaps at different gate voltages that correspond to Ctot = +2and Ctot = –2, indicating doping-controlled switching of valley polar-ization consistent with previous electrical transport results8. Suchbehaviour is absent, however, when large hetero-strain is present, inwhich case only a single correlation gap with Ctot = +2 is observed. Thisbehaviour canbeunderstoodusing a continuummodel for tMBLG thatreveals how Chern number switching results from a competitionbetween the bulk and edge contributions to orbitalmagnetization thatis highly sensitive to local hetero-strain. These results demonstrate thecrucial role that local structural parameters play in shaping correlationand topological effects in twisted moiré systems.ResultsCorrelated insulating behaviour at integer fillingsFigure 1a shows a schematic of our experiment, which incorporatesa gate-tunable graphene device into an STM measurement geometry.A Bernal-stacked bilayer graphene is placed on top of a monolayergraphene with a twist angle θ between them, and the stack issupported by a hexagonal boron nitride (hBN) substrate placed on aSi/SiO2 wafer (Methods, Supplementary Fig. 1). The carrier density n ofthe graphene stack canbe tuned continuously via voltageVG applied tothe Si back-gate. Our devices were annealed in ultra-high vacuumbefore being loaded into the STM system at T = 4.7 K formeasurement(Methods). Figure 1b shows a representative topographic image of themonolayer–bilayer moiré pattern which exhibits an average wave-length of lM= 11.2 nm, from which we extracted a local twist angle ofθ = 1.25° (Methods). Within each moiré unit cell (dashed box) weobserve three representative regions with different apparent heightsthat correspond to the three local tMBLG stacking orders: BAB, ABC,and AAB (Supplementary Note 1).We access correlated electronic states of tMBLG by tuning thecarrier concentration via VG and performing dI/dV spectroscopy. Fig-ure 1c shows a density plot of gate-dependent dI/dV spectra obtainedin the BAB region. Estimation of the device capacitance allows us toconvert VG to the filling factor ν, defined as the average number ofelectrons/holes per moiré unit cell referenced to charge neutrality(Methods). At ν =0 (VG = 0V) we observe two narrow peaks in the dI/dV spectrum that are centred atVBias = 6mVandVBias = –14mV (Fig. 1d)that we identify as originating from van Hove singularities of thefourfold degenerate conduction flat band (CFB) and valence flat band(VFB). Increasing VG leads to partial occupation of the CFB and shiftsboth peaks toward lower energy. As the filling level approaches ν = 2the CFB peak gradually splits into two branches, CFB– and CFB+, thatare located below and above the Fermi energy EF (VBias = 0mV). At ν = 2Apparent height: 0            25 pm012012012012-60 -40 -20 0 20 40 60012dI/dV)tin u.bra (Bias voltage (mV)CFBVFBCFB+CFB CFB+CFBVFBCFB+CFBgapgapCFB-60-40-200204060-60 -40 -20 0 20 40 60)V(egatlovetaGBias voltage (mV)-4-3-2-101234Filling factor VFB CFBCFB CFB+baVBiaschgfeddI/dV (arb. unit)0 maxBAB (B = 0 T)X5 nmABCBABXAAB= 1.25 ; strain = 0.10%BLGDoped SiSiO2hBNMLGSTM tipCr/AuVGFig. 1 | Correlated insulating states in gate-tunable tMBLG. a Schematic of thegate-tunable tMBLG device used in our STM/STS measurements. MLG monolayergraphene, BLGBernal-stacked bilayer graphene.VBias is the sample bias voltage andVG is the gate voltage referenced to the sample. b Representative STM topographicimage of tMBLG (VBias = –1 V, tunnelling current I0 = 0.02 nA). The dashed boxoutlines themoiré unit cell. The local stacking orders BAB,ABC, andAAB are shownin the side view. c Gate-dependent dI/dV density plot for the BAB stacking regionover the gate range –70V ≤VG ≤ 70V. The vertical dashed line denotes the Fermienergy. d–h dI/dV spectra measured at d VG = 0V (ν =0), e VG = 31.5 V (ν = 2),f VG = 39V (ν = 2.5), g VG = 47V (ν = 3), and h VG = 62.5 V (ν = 4). Spectroscopyparameters: modulation voltage VRMS = 1mV; setpoint VBias = 100mV, I0 = 1.15 nAfor –70V ≤VG ≤ –2 V in (c); setpoint VBias = –100mV, I0 = 0.8 nA for 0 V ≤VG ≤ 70Vin (c) and (d); setpoint VBias = –60mV, I0 = 0.5 nA for (e–h). VFB valence flat band,CFB conduction flat band, CFB– lower branch of CFB, CFB + upper branch of CFB.Article https://doi.org/10.1038/s41467-023-39110-3Nature Communications |         (2023) 14:3595 2(VG = 31.5 V) these two branches have roughly the same spectralweightand a clear charge gap can be observed across EF (Fig. 1e). As thedoping level is further increased from ν = 2 to ν = 2.5 (VG = 39 V) theenergy splitting between CFB– and CFB+ becomes smaller and the gapfeature evolves into a shallow dip (Fig. 1f). At ν = 3 (VG = 47 V) an insu-lating gap reappears atEF withCFB–having significantly greaterweightcompared to CFB+ (Fig. 1g). Finally, at ν = 4 (VG = 62.5 V, full filling oftheCFB) theCFB– andCFB+branchesmerge into a single peak that liescompletely below EF (Fig. 1h). The presence of charge gaps at ν = 2 andν = 3 demonstrates the formation of correlated insulating states atthese filling factors, corroborating results from previous electricaltransport studies8,11–13 (Supplementary Note 2, SupplementaryFigs. 2, 3).Gate-switchable QAH insulating stateTo discern the nature of the ν = 2, 3 correlated insulating states intMBLG, we applied an out-of-plane magnetic field B = (0, 0, B) to oursample and performed gate-dependent dI/dV spectroscopy.Figure 2a–c shows density plots of gate-dependent dI/dV spectrameasured near ν = 2 for B = 0, 1, and 2 T, respectively. The insulatinggap feature, marked by vanishing dI/dV at EF and maximum CFB peaksplitting, always appears at the same filling level (white arrows)regardless of the B value. dI/dV spectrameasured near ν = 3 (Fig. 2d–i),however, exhibit very different field-dependent behaviour. The chargegap (white arrows) is seen to remain constant in energy splitting(Supplementary Note 3) but to evolve into two separate gaps forB >0T. These two gaps bracket ν = 3 and split away from it as Bincreases.We can better visualize the magnetic field evolution of the ν = 3correlated insulating state by plotting normalized dI/dV atVBias = 0mV(EF) as a function of both ν (VG) and B (Fig. 2j). The dark region in theplot indicates vanishing dI/dV due to the emergence of a charge gap,which forms a V-shape (white dashed lines) that is roughly symmetricabout the ν = 3 horizontal line. This linear scaling of the correlation gapposition with magnetic field is reminiscent of correlated Chern insu-lating states reported previously in magic-angle twisted bilayer gra-phene (MA-tBLG)14–16 where the change in carrier concentration n of aChern insulating state is related to the out-of-plane field B through theStředa formula ΔnΔB = CtotΦ0(Ctot is the total Chern number and Φ0 = h/e isthe magnetic flux quantum)17. Our observations thus imply that theν = 3 insulating state in tMBLG has Chern number Ctot = ±2 as derivedfrom the slope of the lines in Fig. 2j. Two significant differences,however, distinguishour results from those reported inMA-tBLG. First,Δn/ΔB linear scaling is observed in MA-tBLG only under high externalfields (B > 3T) that break time-reversal symmetry and stabilize theChern insulating states, whereas such behaviour in tMBLG can beresolved in fields as low as B = 0.2T (Supplementary Fig. 4) and can betraced back to B =0T. Combined with the robust charge gap at ν = 3,this indicates that the zero-field ground state of tMBLG is a topologi-cally non-trivial QAH insulator with spontaneous time-reversal0 1 2444546474849B (T))V( egatlov etaG2.93.03.1Filling factor Ctot = +2Ctot = 22930313233-40 -20 0 20 40Bias voltage (mV))V( egatlov etaGB = 0.0 T-40 -20 0 20 40Bias voltage (mV)1.92.02.1Filling factor B = 2.0 T-40 -20 0 20 40Bias voltage (mV)2.93.03.1Filling factor B = 2.0 T-40 -20 0 20 40Bias voltage (mV)B = 1.6 T-40 -20 0 20 40Bias voltage (mV)B = 1.2 T-40 -20 0 20 40Bias voltage (mV)B = 0.8 T-40 -20 0 20 40Bias voltage (mV)B = 0.4 T f444546474849-40 -20 0 20 40Bias voltage (mV))V( egatlov etaGB = 0.0 T-40 -20 0 20 40Bias voltage (mV)B = 1.0 T cbad e g h ijdI/dV (arb. unit)0 maxZero-bias dI/dV (arb. unit)0 maxdI/dV (arb. unit)0 maxBAB ( )BAB ( )Fig. 2 | Topological behaviour of correlated insulating states in an out-of-planemagnetic field. a–c Gate-dependent dI/dV density plot for the BAB region nearν = 2 at a B =0.0 T, b B = 1.0 T, and c B = 2.0 T (modulation voltage VRMS = 1mV;setpoint VBias = –60mV, I0 = 0.5 nA). Arrows indicate correlation gaps. d–i Gate-dependent dI/dVdensity plot for the BAB regionnear ν = 3 atdB =0.0 T, eB =0.4 T,f B =0.8 T, g B = 1.2 T, h B = 1.6 T, and i B = 2.0 T (modulation voltage VRMS = 1mV;setpoint VBias = –60mV, I0 = 0.1 nA). Arrows indicate correlation gaps. jNormalizeddI/dV at VBias = 0mV (EF) as a function of gate voltage and magnetic field. Dashedlines are guides to the eye following the Středa formula with total Chern num-ber Ctot = ±2.Article https://doi.org/10.1038/s41467-023-39110-3Nature Communications |         (2023) 14:3595 3symmetry breaking (Supplementary Note 4). Second, each non-zerointeger filling of MA-tBLG features only a single correlation gap thatshifts monotonically with increasing B, while in tMBLGwe observe twoseparate gaps corresponding to Ctot = +2 and Ctot = –2. This indicatesthat the total Chern number for the tMBLG QAH state is switchablebetween +2 and –2 by simply tuning the carrier concentrationacross ν = 38.Tuning Chern number switching with twist angle and strainSimultaneous structural measurement via STM and local electroniccharacterization via STS provide a unique opportunity to investigatehow correlation and topological effects in tMBLG are affected by localstructural variations at the moiré scale. Figure 3a summarizes ourexperimental results as a function of local twist angle and local hetero-strain obtained through analysis of moiré anisotropy in our STMtopographs (Methods). While the emergence of an insulating gap atν = 2 is robust in all of our data, the behaviour at ν = 3 depends stronglyon both local twist angle and local hetero-strain. Gate tunability of theChern number is only observed when the twist angle is between 1.25°and 1.28°, as indicated by the green data points in Fig. 3a. When thetwist angle increases slightly above this range (orange data points) thecharge gap at ν = 3 persists but Chern number switching is suppressed.Figure 3b–d shows representative data from this regime in which thegap feature (white arrows) evolvesmonotonically toward higher fillingfactors as the magnetic field is increased instead of developing intotwo separate gaps. When the twist angle deviates even further thecorrelation gap at ν = 3 disappears (red data points in Fig. 3a; seeSupplementary Fig. 5).To reveal the effect of hetero-strain, we directly compare tworegions with almost identical twist angle (~1.26°) but different hetero-strain values (0.10% versus 0.24%) for the same device, thus allowingother variables such as carrier concentration, electric field, and cor-relation strength to be kept mostly constant. In the region with asmaller hetero-strain (Fig. 3e), the ν = 3 insulating gap develops intotwo branches under application of an out-of-plane magnetic field(Fig. 3f), indicating gate-induced switching between Ctot = +2 andCtot = –2 QAH insulating states. In contrast, the region with a largerhetero-strain (Fig. 3g) exhibits only one branch of the ν = 3 insulatinggap (Fig. 3h; see Supplementary Fig. 6), corresponding toCtot = +2withno gate-controlled switching.DiscussionThe emergence of correlated QAH insulating states in electron-doped tMBLG can be understood as resulting from spontaneoussymmetry breaking driven by electron–electron Coulomb interac-tions. The CFB of tMBLG is fourfold degenerate due to spin andvalley degrees of freedom. Each CFB sub-band in the unfolded gra-phene K+ (K–) valley hosts a non-zero Chern number of C = +2 (–2)Apparent height (pm)0 27Apparent height (pm)0 320.0 0.5 1.045464748B (T)gap position )V(egatlovetaGCtot = +2Ctot = 20.0 0.5 1.045464748 gap position B (T))V(egatlovetaGCtot = +2X7 nm7 nmX= 1.25 0.01strain = 0.10% 0.03%= 1.26 0.01strain = 0.24% 0.02%gfeh1.20 1.25 1.30 1.35 1.400.00.10.20.3 Ctot = +2 and Ctot = 2 only Ctot = +2 no correlation gap)%(niarts-oreteHTwist angle (°)-40 -20 0 20 40Bias voltage (mV)2.93.03.1Filling factor B = 1.6 T-40 -20 0 20 40Bias voltage (mV)B = 0.8 T4546474849-40 -20 0 20 40Bias voltage (mV))V(egatlovetaGB = 0.0 TdI/dV (arb. unit)0 max= 1.33 ; strain = 0.12%b c daFig. 3 | Local structural effects on correlation and topology. a Electronic phasediagram of tMBLG at ν = 3 in the parameter space of local twist angle and localhetero-strain. Ctot is the total Chern number. b–d Gate-dependent dI/dV densityplot for the BAB region at b B =0.0 T, c B =0.8 T, and d B = 1.6 T where only theCtot = +2 gap is observed (modulation voltage VRMS = 1mV; setpoint VBias = –75 mV,I0 = 0.2 nA). Arrows indicate correlation gaps. e STM topographic image of a regionwith θ = 1.25° and small hetero-strain of 0.10% (VBias = –1 V, I0 = 0.02 nA). Standarddeviations for angle and strain are calculated from uncertainties in the moiréwavelength. f Evolution of the correlation gap position near ν = 3 in an out-of-planemagnetic field shows two branches for small strain. The data points were extractedfrom dI/dV spectra taken in the BAB region marked in (e) with the error barsdetermined via linear fitting (SupplementaryNote 5). Dashed lines are guides to theeye following the Středa formula with Ctot = ±2. g STM topographic image of aregion with θ = 1.26° and large hetero-strain of 0.24% (VBias = –1 V, I0 = 0.02nA).h Evolution of the correlation gap position near ν = 3 in an out-of-plane magneticfield showsonlyonebranch for large strain. Thedatapointswere extracted fromdI/dV spectra taken in the BAB region marked in (g). The dashed line is a guide to theeye following the Středa formula with Ctot = +2.Article https://doi.org/10.1038/s41467-023-39110-3Nature Communications |         (2023) 14:3595 4due to the large Berry curvature inherited from constituent gra-phene layers18,19. At integer fillings (e.g., ν = 2 and ν = 3) strong cor-relation can drive spontaneous polarization along a certain axis inthe spin–valley space, splitting the CFB into occupied lower sub-bands (CFB–) and unoccupied upper sub-bands (CFB+) separatedby a charge gap as observed in the experimental dI/dV (Fig. 1e, g). Atν = 3 the spin and valley polarization leads to breaking of time-reversal symmetry and topologically non-trivial states with Ctot ≠ 0.Figure 4a shows one possible filling configuration with doubleoccupancy of CFB sub-bands in the K+ valley, resulting in a QAHinsulating state with Ctot = +2. Similarly, double occupancy of K–valley sub-bands can result in a Ctot = –2 state that is energeticallyequivalent to the Ctot = +2 state in the absence of an external mag-netic field.The large Berry curvature in the tMBLGmoiré flat bands producesout-of-plane orbital magnetic moments that respond to an externalmagnetic field. The competition between bulk orbital magnetization(Mbulk) due to self-rotation of electron wave packets and edge orbitalmagnetization (Medge) due to circulation of electrons in thetopologically-protected in-gap chiral edge states is responsible for thegate-controlled switching behaviour at ν = 3 (spin magnetism plays noexplicit role in the switching due to negligible spin–orbit coupling intMBLG)8. When the chemical potential resides in the bulk correlationgap the sign ofMedge is the same as the sign of Ctot and itsmagnitude isdetermined by how much the edge state band is filled20. The sign andmagnitude of Mbulk, on the other hand, are sensitive to the detailedband structure and are not simply related to Ctot other than the factthat a reversal in Ctot is accompanied by a reversal in Mbulk (Supple-mentary Note 6). The total orbital magnetization is the sum of MbulkandMedge and can be altered electrostatically by changing the filling ofthe edge states.Our data is consistent with the special case illustrated in Fig. 4b, cwhich shows magnetic states for both Ctot = +2 and Ctot = –2 near ν = 3under the condition thatMbulk andMedge are antiparallel and |Medge| >|Mbulk|. When EF is placed at the top of the correlation gap (ν ≳ 3,Fig. 4b), the chiral edge states are fully filled, and the total orbitalmagnetization is in the same direction as Medge. When EF is moved tothe bottom of the correlation gap (ν ≲ 3, Fig. 4c), however, the edgestates are empty and the total magnetization is in the direction ofMbulk. In an external magnetic field the system will be driven into amagnetic ground state that aligns the total orbital magnetic momentwith the applied field to minimize the orbital Zeeman energy. For thecase shown here the energetically favourable states are Ctot = +2 forν ≳ 3 and Ctot = –2 for ν ≲ 3, thus illustrating how electrostatic gatingcan cause Chern number switching in tMBLG consistent with ourexperimental observations.We have performed theoretical simulations that support theassumptions made in the switching picture described above (i.e., thatMbulk andMedge are antiparallel and that |Medge| > |Mbulk|) and that alsoexplain why some tMBLG regions do not exhibit switching. For theexperimental regimes shown in Fig. 3e–h (where the tMBLG twist anglelies close to 1.26°)wefind that the key physical parameter that controlsmagnetic switching functionality is hetero-strain. To see this we cal-culated the strain-induced behaviour of Mbulk and Medge for a con-tinuummodel of 1.26° tMBLG in the ν = 3 QAH insulating state with EFset to the top of the correlation gap (a single phenomenologicalparameter characterizing the electron–electron interaction strength isincluded similar to ref. 8; see Supplementary Note 6 for details). Fig-ure 4d shows a plot of the resulting Medge andMbulk for Ctot = +2 (top)and Ctot = –2 (bottom) as a function of hetero-strain with all otherparameters kept constant. For small strain (<0.15%) |Medge| is sig-nificantly greater than |Mbulk| whileMedge andMbulk are anti-aligned. For0ygrenenameeZMB) tinu .bra(0Filling factorSmall strainLarge strainCtot = +2Ctot = 2Ctot = +2Ctot = 2 Edge Bulk Edge Bulk0.000.020.04M (B nm-2)0.00 0.05 0.10 0.15 0.20-0.04-0.020.00M (B nm-2)Hetero-strain (%)Ctot = +2Ctot = 2Ground stateGround stated eCFBCFB+EFCFBCFB+EFaCFB+C = +2 C = 2C = 2CFBK+ KbCFB+C = +2 C = 2C = +2CFBK+ KcMbulkMedgeMbulkBCtot = +2 Ctot = 2K+ valley-polarizedCtot = +2K valley-polarizedCtot = 2MbulkMedgeMbulkFig. 4 | Bulk–edge magnetization competition and gate-controlled Chernnumber switching. a Energy configuration of the K+ valley-polarized state and theK– valley-polarized state at ν = 3 in tMBLG. Arrows represent electron spin.Eg is thesize of the correlation gap. The total Chern numberCtot is the sumofChernnumberC for all occupied sub-bands. b Schematic of orbital magnetization for both valley-polarized stateswhen EF is at the topof the correlation gapand the chiral edge stateband is occupied (ν ≳ 3). Grey arrows represent the direction of current flow in edgestates. Mbulk and Medge are bulk and edge orbital magnetic moments. Under anapplied out-of-planemagneticfieldB (green arrowon right) theCtot = +2 state is theenergetically favourable ground state. c Same as b, but EF is at the bottom of thecorrelation gap and the edge state band is depleted (ν ≲ 3). Dashed grey linesrepresent empty edge states. Here the Ctot = –2 state is the ground state.dBulk andedge orbital magnetization for both valley-polarized states (Ctot = ±2) calculatedbased on a continuum model of 1.26° tMBLG. The vertical dashed line divides theparameter space into a small-strain regime whereMbulk and Medge have oppositesign and a large-strain regime where they have the same sign. e Top sketch showsthe depletion/occupation of the edge states (represented by dashed/solid greylines) for different filling levels. Orbital Zeeman energy is plotted for both valley-polarized states (Ctot = ±2) as a function of filling factor when EF is inside the cor-relation gap. Solid (dashed) lines represent the energetically favourable (unfa-vourable) states. CFB– lower branchof conduction flat band, CFB+ upper branchofconduction flat band.Article https://doi.org/10.1038/s41467-023-39110-3Nature Communications |         (2023) 14:3595 5large hetero-strain (>0.15%), however, the situation changes sig-nificantly. The sign ofMedge remains the same as Ctot, butMbulk flips itssign due to a strain-induced redistribution of Berry curvature andbanddispersion throughout the mini-Brillouin zone. This divides the strainparameter space into tworegimes separatedby the vertical dashed linein Fig. 4d: the small-strain regimewhereMbulk andMedge have oppositesign (and switching can occur), and the large-strain regime where theyhave the same sign (and switching does not occur). To better illustratethis behaviour, Fig. 4e shows a schematic of the resulting orbitalZeeman energy for B >0 as a function of filling factor near ν = 3. Herethe solid lines show the energetically favourable ground state and thedashed lines show the unfavourable state having opposite Ctot. Forsmall hetero-strain Mbulk dominates for ν ≲ 3 (when the edge stateband is empty) and results in Ctot = –2 whereas Medge dominates forν ≳ 3 (as the edge states are filled), resulting in a switching to Ctot = +2.For large hetero-strain, Mbulk and Medge both line up parallel to theapplied field at all fillings and the system stays at Ctot = +2 withoutswitching, consistent with our experimental observations.In conclusion, we have observed local spectroscopic signatures ofstrong correlation and non-trivial topology at the moiré scale intMBLG, and have demonstrated local control of the QAH Chernnumber via electrostatic gating. Combining STM and STS allows us tocharacterize the topological andmagnetic switching phase diagramoftMBLG in the parameter space of local twist angle and hetero-strain.We observe magnetic switching only at low strain, revealing the sen-sitive interplay between correlation, topology, and local structuralparameters that determines electronic and magnetic ground states intwisted moiré systems. This provides insight into the many phasediagrams observed in related moiré systems via measurements thataverage over regions having different structural parameters, and cre-ates new opportunities for future manipulation of QAH insulatingdomains and the chiral edge states that lie between them.MethodsSample preparationSamples were prepared using the “flip-chip” method21 followed by aforming-gas anneal22,23. Electrical contacts were made by evaporatingCr/Au (5 nm/70 nm) through a silicon nitride shadow-mask onto theheterostructure. The sample surface cleanliness was confirmed usingcontact-AFM prior to STM measurements. Samples were annealed at300 °C overnight in ultra-high vacuum before insertion into the low-temperature STM stage.STM/STS measurementsSTM/STSmeasurements were performed in a commercial CreaTec LT-STM held at T = 4.7 K using tungsten (W) tips. STM tips were preparedon aCu(111) surfaceand calibrated against theCu(111) Shockley surfacestate before measurements to avoid tip artifacts. A voltage VG wasapplied to the Si back-gate to change the carrier densityn in the tMBLGstack (n= εDε0VGedDwhere εD ≈ 3.6 is the average out-of-plane dielectricconstant of hBN and SiO2, ε0 is the vacuum permittivity, e is the ele-mentary charge, and dD = 335 nm is the thickness of the dielectriclayers). dI/dV spectra were recorded using standard lock-in techniqueswith a small bias modulation VRMS = 1mV at 613Hz. All STM imageswere edited using WSxM software24.Determination of local twist angle and hetero-strainThe local twist angle and hetero-strain were determined byanalysing the monolayer–bilayer moiré pattern. The moiréwavelength was obtained for three directions bymeasuring the spatialseparation between peaks in STM topographs and averaging overseveral moiré unit cells. The reciprocal primitive vectors Ki (i =0, 1, 2)were derived through Fourier transform analysis. In thepresence of hetero-strain, Ki can be approximately written asKi = k θ+ 1 + νP� �ϵcos α + i 2π3� �sin α + i 2π3� �� �where k = 4.694 nm–1 is thelengthof the graphene reciprocal primitive vectors, θ is the twist angle,ϵ is the hetero-strain amplitude, νP = 0.16 is Poisson’s ratio for gra-phene, and α is the angle between the principal axis of the strain tensorand one of the graphene reciprocal primitive vectors25. This allows usto solve both θ and ϵ from the extracted Ki.Data availabilityThe data that support the plots within this paper and the findings ofthis study are provided in the Source Data file. Source data are pro-vided with this paper.Code availabilityThe computer codes that support the plots within this paper and thefindings of this study are available from the corresponding authorsupon request.References1. Trambly de Laissardière, G., Mayou, D. & Magaud, L. Localization ofDirac electrons in rotated graphene bilayers. Nano Lett. 10,804–808 (2010).2. Bistritzer, R.&MacDonald, A.H.Moirébands in twisteddouble-layergraphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).3. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).4. Cao, Y. et al. Unconventional superconductivity in magic-anglegraphene superlattices. Nature 556, 43–50 (2018).5. Serlin, M. et al. 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Nature 572, 95–100 (2019).AcknowledgementsThe authors thank Birui Yang for technical support. This research wassupported by the Center for Novel Pathways to Quantum Coherence inMaterials, an Energy Frontier Research Center funded by the USDepartment of Energy, Office of Science, Basic Energy Sciences (STM/STS measurements and analysis). Support was also provided by theDirector, Office of Science, Office of Basic Energy Sciences, MaterialsSciences and Engineering Division of the US Department of Energyunder contract number DE-AC02-05CH11231 within the van der WaalsHeterostructures program KCWF16 (device architecture development);by the Molecular Foundry at LBNL, which is funded by the Director,Office of Science, Office of Basic Energy Sciences, Scientific UserFacilities Division, of the US Department of Energy under Contract No.DE-AC02-05CH11231 (graphene layer characterization); by the NationalScience Foundation AwardDMR-2221750 (device AFMcharacterization);and by the US Department of Energy, Office of Science, Office of BasicEnergy Sciences, Materials Sciences and Engineering Division underContract No. DE-AC02-05-CH11231 within the Theory of Materials pro-gram KC2301 (tMBLG simulations). K.W. and T.T. acknowledge supportfrom JSPS KAKENHI (Grant Numbers 20H00354, 21H05233, and23H02052) and World Premier International Research Center Initiative(WPI), MEXT, Japan (hBN crystal synthesis and characterization). C.Z.acknowledges support from a Kavli ENSI Philomathia Graduate StudentFellowship. T.S. acknowledges fellowship support from the MasasonFoundation.Author contributionsC.Z., T.Z., S.K., andM.F.C. initiated and conceived the research. C.Z. andT.Z. carried out STM/STS measurements and analyses. M.F.C.supervised STM/STS measurements and analyses. S.K. prepared gate-tunable devices. A.Z., F.W., and M.F.C. supervised device preparations.T.T. and K.W. provided the hBN crystals. T.S. performed theoreticalcalculations and analyses. M.P.Z. supervised theoretical calculationsand analyses. C.Z., T.Z., andM.F.C. wrote themanuscript with help fromall authors. All authors contributed to the scientific discussion.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-39110-3.Correspondence and requests for materials should be addressed toTiancong Zhu, Michael P. Zaletel or Michael F. Crommie.Peer review information Nature Communications thanks TigranSedrakyan, and the other, anonymous, reviewer(s) for their contributionto the peer review of this work. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2023Article https://doi.org/10.1038/s41467-023-39110-3Nature Communications |         (2023) 14:3595 7https://doi.org/10.3791/52711https://doi.org/10.1038/s41467-023-39110-3http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Local spectroscopy of a gate-switchable moiré quantum anomalous Hall insulator Results Correlated insulating behaviour at integer fillings Gate-switchable QAH insulating state Tuning Chern number switching with twist angle and strain Discussion Methods Sample preparation STM/STS measurements Determination of local twist angle and hetero-strain Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information