# Fileset

[s41467-024-55432-2.pdf](https://mdr.nims.go.jp/filesets/8b564741-71b4-41bd-97b5-4e45b04127f7/download)

## Creator

[Xirui Wang](https://orcid.org/0000-0003-4414-1270), Cheng Xu, Samuel Aronson, [Daniel Bennett](https://orcid.org/0000-0003-0892-2125), Nisarga Paul, [Philip J. D. Crowley](https://orcid.org/0000-0002-9836-7569), Clément Collignon, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Raymond Ashoori](https://orcid.org/0000-0001-5031-1673), Efthimios Kaxiras, [Yang Zhang](https://orcid.org/0000-0003-4630-5056), [Pablo Jarillo-Herrero](https://orcid.org/0000-0001-8217-8213), [Kenji Yasuda](https://orcid.org/0000-0003-4894-0205)

## Rights

[Creative Commons BY-NC-ND Attribution-NonCommercial-NoDerivs 4.0 International](https://creativecommons.org/licenses/by-nc-nd/4.0/)

## Other metadata

[Moiré band structure engineering using a twisted boron nitride substrate](https://mdr.nims.go.jp/datasets/b4311822-0d4d-4386-ac7d-dcd1dae7ed61)

## Fulltext

Moiré band structure engineering using a twisted boron nitride substrateArticle https://doi.org/10.1038/s41467-024-55432-2Moiré band structure engineering using atwisted boron nitride substrateXirui Wang 1, Cheng Xu2, Samuel Aronson1, Daniel Bennett 3, Nisarga Paul1,4,Philip J. D. Crowley 5, Clément Collignon1, Kenji Watanabe 6,Takashi Taniguchi 7, Raymond Ashoori 1, Efthimios Kaxiras3,5,Yang Zhang 2,8, Pablo Jarillo-Herrero 1 & Kenji Yasuda 1,9Applying long wavelength periodic potentials on quantum materials hasrecently been demonstrated to be a promising pathway for engineering novelquantum phases of matter. Here, we utilize twisted bilayer boron nitride (BN)as a moiré substrate for band structure engineering. Small-angle-twistedbilayer BN is endowedwith periodically arranged up and down polar domains,which imprints a periodic electrostatic potential on a target two-dimensional(2D) material placed on top. As a proof of concept, we use Bernal bilayergraphene as the target material. The resulting modulation of the band struc-ture appears as superlattice resistance peaks, tunable by varying the twistangle, and Hofstadter butterfly physics under a magnetic field. Additionally,we demonstrate the tunability of the moiré potential by altering the dielectricthickness underneath the twisted BN. Finally, we find that near-60°-twistedbilayer BN also leads to moiré band features in bilayer graphene, which maycome from the in-plane piezoelectric effect or out-of-plane corrugation effect.Tunable twisted BN substrate may serve as versatile platforms to engineer theelectronic, optical, and mechanical properties of 2D materials and van derWaals heterostructures.The emerging concept of quantum metamaterials enables us to engi-neer electronic structures and physical properties that do not exist innatural crystals1. This ismost strikingly exemplifiedbymoirématerials,where two-dimensional (2D)materials are stacked at controlled angles.For instance, twisted bilayer graphene and transition metal dichalco-genide moiré bilayers exhibit topological and strongly-correlatedphases of matter, absent in their constituent layers2–11. Despite theprosperous findings in these moiré systems, the method of creating amoiré potential by twisting the target material itself poses limitationsin the choice of materials, moiré periodicity, and potential strength.This is mainly due to the requirement of the proximity of two atomiclayers with similar or identical lattice constants.A remote tunable superlattice potential isolated from a targetlayer can overcome these constraints. Past research has etched peri-odic holes in gate dielectrics or gate electrodes via electron beamlithography or focused ion beam milling, and introduced an electro-static periodic potential in the target layers via gating12–18. The effect ofa periodic potential on graphene was observed as superlatticeReceived: 12 November 2024Accepted: 11 December 2024Check for updates1Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA. 2Department of Physics and Astronomy, University of Tennessee,Knoxville, TN, USA. 3John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA. 4Kavli Institute of TheoreticalPhysics, University of California, Santa Barbara, Santa Barbara, CA, USA. 5Department of Physics, Harvard University, Cambridge, MA, USA. 6Research Centerfor Electronic and Optical Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba, Japan. 7Research Center for Materials Nanoarchitectonics,National Institute for Materials Scim- ence, 1-1 Namiki, Tsukuba, Japan. 8MinH. Kao Department of Electrical Engineering and Computer Science, University ofTennessee, Knoxville, TN, USA. 9School of Applied and Engineering Physics, Cornell University, Ithaca, NY, USA. e-mail: pjarillo@mit.edu;kenji.yasuda@cornell.eduNature Communications |          (2025) 16:178 11234567890():,;1234567890():,;http://orcid.org/0000-0003-4414-1270http://orcid.org/0000-0003-4414-1270http://orcid.org/0000-0003-4414-1270http://orcid.org/0000-0003-4414-1270http://orcid.org/0000-0003-4414-1270http://orcid.org/0000-0003-0892-2125http://orcid.org/0000-0003-0892-2125http://orcid.org/0000-0003-0892-2125http://orcid.org/0000-0003-0892-2125http://orcid.org/0000-0003-0892-2125http://orcid.org/0000-0002-9836-7569http://orcid.org/0000-0002-9836-7569http://orcid.org/0000-0002-9836-7569http://orcid.org/0000-0002-9836-7569http://orcid.org/0000-0002-9836-7569http://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/0000-0001-5031-1673http://orcid.org/0000-0001-5031-1673http://orcid.org/0000-0001-5031-1673http://orcid.org/0000-0001-5031-1673http://orcid.org/0000-0001-5031-1673http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0003-4630-5056http://orcid.org/0000-0001-8217-8213http://orcid.org/0000-0001-8217-8213http://orcid.org/0000-0001-8217-8213http://orcid.org/0000-0001-8217-8213http://orcid.org/0000-0001-8217-8213http://orcid.org/0000-0003-4894-0205http://orcid.org/0000-0003-4894-0205http://orcid.org/0000-0003-4894-0205http://orcid.org/0000-0003-4894-0205http://orcid.org/0000-0003-4894-0205http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55432-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55432-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55432-2&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-024-55432-2&domain=pdfmailto:pjarillo@mit.edumailto:kenji.yasuda@cornell.eduwww.nature.com/naturecommunicationsresistance peaks due to band folding and Hofstadter physics14–18.Despite the versatility in shape and the tunability in the potentialstrength, this method suffers from two limitations. First, the pitchresolution is technically restricted when the pattern is defined byelectron beam lithography or focused ion milling, being difficult toachieve below 16 nm17, because of the secondary electrons or limita-tion in beam size. Second, as each pitch is written independentlythrough lithography or focused ion beam, the unavoidable non-identicality among moiré sites works as disorder in the moiré poten-tial, leading to broadened superlattice peaks and potentially smearingout detailed features. A natural way to overcome this issue is to createmoiré potentials via twisted van der Waals (vdW) materials, which canachieve arbitrary moiré periodicity by controlling the twist angle, andhighly periodic moiré superlattices formed from identical unit cellsdue to their crystalline nature19–21.We engineer such amoiré substrate using a twisted 2D insulator—twisted bilayer boron nitride (BN). Hexagonal BN is one of the mostimportant constituents of vdW heterostructures, which is primarilyused as an atomically-flat substrate and gate dielectric. Recently, it hasbeen demonstrated that out-of-plane ferroelectricity can be obtainedby stacking twomonolayers of BN in parallel22–24. Furthermore, amoirépolar pattern is generated by introducing a small angle between themonolayers (Fig. 1b), which is characterized by upward and downwardpolarizations periodically arranged in the lateral direction22–25. Usingtwisted bilayer BN as a substrate, we can apply a moiré electrostaticpotential to arbitrary 2D materials26. Here, we use bilayer graphene asthe target material, illustrating the resultant band structure modifica-tion and the tunability of the twisted BN moiré substrates.A monolayer BN consists of boron (B) and nitrogen (N) atomsalternately arranged at honeycomb lattice sites. When two BN mono-layers are twisted at a small angle away from parallel stacking, a moirépattern consisting of AA, AB, and BA stacking regions is formed asillustrated in Fig. 1b. In AA stacking, the top and bottom layers directlyoverlap, having no net polarization. In AB (BA) stacking, meanwhile, B(N) sits on top of the N (B) atom, forming an electric dipole and givingrise to downward (upward) polarization (Fig. 1a)23,24. We consider suchtwisted bilayer BN as forming a moiré polar substrate, referring to thefact that the moiré potential comes from the electrostatic potential inthese staggered up and down polar domains. Figure 1c illustrates theschematic of our device, where we placed a target layer on top of thetwisted BN moiré substrate, controlled with a top metal gate and abottom graphite gate. In this device geometry, we expect the mod-ulation of the potentialUon the target layer yielding a peakmagnitudeof around 29mVwhen themoiré wavelength is 18.5 nm, and the targetlayer is bilayer graphene (Fig. 1d, see simulation details in Methods).Figure 1e displays the theoretical calculation of the band structure. Thesuperlattice moiré potential leads to the band folding into a mini-Brillouin zone, with density of state (DOS) minima at the band edges(see calculation details in Supplementary Note 1).ResultsBand structure modulation in bilayer grapheneWe fabricated a series of bilayer graphene/twisted bilayer BNdevices (A1-A5), aiming at different twist angles between 0.4° and 1.3°. We first madethe topstackby sequentiallypickingup the topBN,bilayergraphene, andtwisted bilayer BN using the tear-and-stack technique. We intentionallymisaligned the bilayer graphene with top and bottom BN layers to avoidthe formation of long-periodicity moiré patterns by the BN to graphenealignment. Subsequently, we performed piezoresponse force micro-scopy (PFM) to identify regions with uniformmoiré patterns. Finally, weplaced the top stack onto the bottomgraphite, etched and contacted thedevice. The detailed parameters of the devices are summarized in Sup-plementary Table 1, and the optical microscope images are shown inSupplementary Fig. 2. For transport measurements of devices A1-A5, weFig. 1 | Twisted bilayer BN as a moiré polar substrate. a Three high-symmetrystacking orders that exist in near-0°-twisted bilayer BN65. N and B atoms are shownin silver and green, respectively. In AA stacking (left), top and bottom atoms alignright on top of each other, and there is no out-of-plane polarization. In AB (middle)and BA (right) stacking, the vertical alignment of N and B atoms creates an out-of-plane electric dipole, leading to downward (upward) polarization in AB (BA)stacking. b Schematic of twisted bilayer BN, where moiré patterns form with AB(downward polarization), BA (upward polarization), and AA local stackingarrangements65. cDevice schematic for using twisted BNas amoiré polar substrate.Target layer sits on top of twisted bilayer BN, feeling its periodicmoiré potentialU.The target layer is encapsulated by a thick BN on top, and electrically gated with ametal top gate and a graphite bottom gate. d Electrostatic simulation of potentialstrengthU imposed on bilayer graphene in the device structure shown in c, and themoiré wavelength a is taken to be 18.5 nm. e Band structure calculation of bilayergraphene under the electrostatic moiré potential in (d). Arrows mark the locationsof density of state (DOS) minima in the conduction band and valence band due toband folding induced by the superlattice potential.Article https://doi.org/10.1038/s41467-024-55432-2Nature Communications |          (2025) 16:178 2www.nature.com/naturecommunicationsgrounded both the bilayer graphene and bottom graphite to preventtunneling or capacitive coupling between them. Figure 2a plots thelongitudinal sheet resistivity ρxx as a function of carrier density n, cali-brated from Landau fan diagram measurements. We observe satelliteresistance peaks symmetrically located around the charge neutralitypoint (CNP) at different carrier densities for A1-A5. According to the bandstructure calculation in Fig. 1e, we expect DOS minima, i.e., resistancepeaks, at the filling of one moiré band on both the electron and holesides, corresponding ton0=4/A, whereA=ffiffiffi3p=2a2 is themoiré unit cellarea, and the prefactor 4 corresponds to the spin and valley degeneracy.The moiré wavelength of device A2 calculated from the satellite resis-tance peak positions is around 13.4nm, which is consistent with the oneobtained from the PFM image, 11.9 nm (Fig. 2c). This agreement confirmsthat the satellite resistance peaks originate from the band structuremodulation induced by the twisted BN moiré substrate. Additional PFMimages are included in Supplementary Fig. 3.Our method can produce arbitrary moiré periodicity by tuningthe twist angle, which is in contrast to themoiré periodicity formed byBN to graphene alignment. The latter cannot be longer than 14 nmbecause of the finite lattice mismatch. We also note that when themoiré potential was induced by aligning a piece of BN to graphene, thehole side typically featured amore prominent resistance peak than theelectron side27–29, while in our devices, the heights of resistance peakson both sides are comparable, in line with the symmetric DOS minimaon the electron and hole sides in Fig. 1e and Supplementary Fig. 1. Wespeculate that the variations in the satellite resistance peak widthscome from the twist angle disorder in our devices (see discussions inSupplementary Note 3).The Hall resistivity ρyx under a small magnetic field (B =0.2 T) as afunction of n shows sign reversals at the satellite resistance peakpositions as well as between CNP and satellite resistance peak posi-tions (Fig. 2b). The former can be attributed to the moiré band edges,and the latter to the Van Hove singularities (VHSs). We note that boththe satellite resistance peaks in ρxx and sign reversals in ρyx becomestronger when the moiré wavelength increases. We can qualitativelyunderstand this trend as the following: since the wavevector is inver-sely proportional to the moiré wavelength, as the moiré wavelengthincreases, the kinetic energy at the mini-Brillouin zone boundaryFig. 2 | Band structure modulation of bilayer graphene on twisted bilayer BNmoiré polar substrate. a Longitudinal resistivity ρxx as a function of carrier densityn in devices A1-A5, measured at 4.2 K. Satellite resistance peaks symmetricallylocated around CNP are observed at different carrier densities that correspond todifferent moiré wavelengths. Arrows indicate the positions of the satellite resis-tance peaks. b Hall resistivity ρyx as a function of n in devices A1-A5 at B =0.2 T,T = 4.2 K. c Piezoresponse force microscopy (PFM) image of twisted BN beforemaking into device A2. Scale bar: 50nm. Inset: Fourier transform image. Scale bar:0.3 nm-1. d Longitudinal conductance σxx as a function of filling factor n/n0 andmagnetic field B (right y axis: normalizedmagnetic fluxϕ/ϕ0), measured at 0.3 K indevice A3.ϕ = BA, the magnetic flux per moiré unit cell, and flux quantum ϕ0 = h/e.e Transverse conductance σxy as a function of n/n0 and B (right y axis: ϕ/ϕ0),measured at 0.3 K in device A3.Article https://doi.org/10.1038/s41467-024-55432-2Nature Communications |          (2025) 16:178 3www.nature.com/naturecommunicationsdecreases. Therefore, the relative effect of the electrostatic potential isenhanced, leading to a stronger band reconstruction (see discussionsin Supplementary Note 4).We further investigate the magnetic field response by increasingthe magnetic field and plotting the longitudinal conductance σxx ver-sus filling factor n/n0 and the normalizedmagnetic fluxϕ/ϕ0 in Fig. 2d.We observe Landau fan features emanating from n/n0 = +4 and −4,respectively, indicating the formation ofmoirémini bands27–29.We alsoobserve Brown-Zak oscillations, corresponding to enhanced con-ductivity when the cyclotron orbits are commensurate with the moiréwavelengths atϕ/ϕ0 =½, 1/3,¼, and so on30. In the Landau fandiagramof transverse conductance σxy, the sign reversals diminish at a criticalfield of around0.7 T on the hole side and0.3 T on the electron side dueto the magnetic breakdown (Fig. 2e, see data of other devices in Sup-plementary Fig. 6), where the electronmotion deviates from the orbitsdetermined by moiré band structure in our previous calculation inFig. 1e. The difference in the critical magnetic fields points to theelectron-hole asymmetry in the system. We can estimate the strengthof themoiré potential based on the VHS location, which is expected tohappen at a smaller filling factor as themoiré potential becomes larger(see calculation details in Supplementary Note 1). From the VHS loca-tion of n/n0 ≈ −1.9 on the hole side, we quantify the peak potentialmagnitude to be 105mV, which is of the same order of magnitude as(albeit bigger than) our simulated moiré potential strength. As shownin the temperature dependence in Supplementary Fig. 7, the satelliteresistancepeaks persist up to 100K,which is consistentwith themoirépotential energy scale. Our transport measurements, together withPFM characterization and theoretical calculations, demonstrate thattwisted bilayer BN can work as a substrate to engineer moiré super-lattices with different wavelengths and induce band structure mod-ifications to 2D materials. The satellite resistance peaks, and the signreversals of the Hall resistance are also observable in monolayer gra-phene on twisted BN (Supplementary Fig. 8), demonstrating the ver-satility of our moiré band engineering method.Besides the moiré electrostatic effect, the structural latticedeformation effect has also been considered important in moiré het-erostructures and band structure modulation20,31–39. To verify thedominating role of electrostatic effect in band structuremodulationofthe target layer, we fabricated devices with inserted few-layer BNbetween bilayer graphene and twisted BN, in order to suppress thestructural effect while maintaining the electrostatic effect (Fig. 3a). Asshown in Fig. 3b, c, we observed clear satellite resistance peaks andHall sign reversals in devices B1-B7. The strength of these moiré bandfeatures is comparable to devices A1-A5, showing that electrostaticeffect plays a leading role here in band structure engineering.Tuning moiré potential by inserting extra dielectric BNNext, we demonstrate the tunability of the strength of the moirépotential by inserting extra dielectric BN underneath the twistedbilayer BN.When a thick BN is inserted between the bottomgate and aferroelectric bilayer BN (in this paper, “thick BN” stands for 5 to80nm), the doping induced in the target layer is suppresseddue to thelarger distance between the target layer and the gate electrode23. InFig. 4a, we simulated the superlattice potential induced by the twistedbilayer BN at different total bottom BN thicknesses, denoted as d. Thepeak potential Upeak is plotted as a function of d, decreasing from29mV in the case without bottom thick BN to 11mV at d ≥ 10 nm (seesimulation details in Supplementary Note 7). Figure 4b presents acomparison between two devices with a similar moiré wavelength:deviceA3without bottom thickBNanddeviceC1withbottomthickBN(d = 15.1 nm). The heights of satellite resistance peaks in device C1 areless than one third of those in device A3, consistent with the smallermagnitude of the moiré potential.As themagnetic field is turned on, we observe a similar yet weakerHofstadter spectrum in device C1, with Landau levels emerging frommoiré band edges, as well as Brown-Zak oscillations (Fig. 4c). The signreversals in σxy diminish at around 0.3 T on the hole side, and no signreversal is observed on the electron side except for a weakly reducedHall conductance (Fig. 4d). The VHS is located at n/n0 ≈ −3.0 on thehole side, from which we extracted the peak potential to be 41mV,around 40% of the value we extracted in device A3. The shifts in VHSlocations, the lower satellite peak heights, weaker Hofstadter spec-trum, and smaller critical field of Hall sign reversals, are all consistentwith theweakermoiré potential in deviceC1 as compared to deviceA3.Additional data of more devices with inserted thick bottom BN areshown in Supplementary Figs. 10 and 11.Moiré effect from near-60°-twisted BNSo far, we have only considered the electrostatic effect from the polardomains in the twisted bilayer BN. However, multifaceted moiré phy-sics exist in our system besides the ferroelectric charge transfer, suchas corrugation, lattice relaxation, interlayer hybridization and piezo-electric effect40. Using near-60°-twisted BN, we demonstrate thateffects other than the polar domain effect can also give rise to bandfolding and moiré physics in the target layer.Different from the near-0°-twisted case, near-60°-twisted bilayerBN consists of AA’, AB’, and BA’ stacking arrangements (Fig. 5b). Here,’means one layer is rotated by 60° with respect to the other. The AA’stacking has each B atom stacked on top of an N atom or vice versa,and the AB’ (BA’) stacking has N (B) stacked on top of N (B) atoms(Fig. 5a). Importantly, all of these stacking orders have an inversioncenter, i.e., the top and bottom layers are connected by the inversionoperation. This also holds true for low-symmetry stacking orders otherFig. 3 | Devices with inserted BN above near-0°-twisted bilayer BN. a Schematicof devices with inserted BN between twisted bilayer BN and bilayer graphene. b ρxxas a function of n in devices B1-B7 measured at 4.2 K. c ρyx as a function of n indevices B1-B7 at 4.2 K, B =0.2 T.Article https://doi.org/10.1038/s41467-024-55432-2Nature Communications |          (2025) 16:178 4www.nature.com/naturecommunicationsthan AA’, AB’, and BA’. Hence, the polar domains and associated elec-trostatic potential are absent in near-60°-twisted BN (Fig. 5a). Weprepared a device consisting of a bilayer graphene on top of a 60.90°-twisted bilayer BN, encapsulated by top and bottom thickBNs (Fig. 5c).Weobserved small satellite resistance peaks in ρxxplotted as a functionof n, corresponding to the full filling of the moiré unit cell (Fig. 5d, e).Additional data from devices with near-60°-twisted BN are included inSupplementary Figs. 11 and 12.We propose two possible mechanisms of the moiré band mod-ulation by the near-60°-twisted BN – in-plane piezoelectric effect andout-of-plane corrugation effect. Themoiré lattice relaxation in twistedBN causes in-plane strain, leading to in-plane charge redistributionthrough the piezoelectric effect40. This can modulate the charge dis-tribution periodically in the adjacent bilayer graphene. Meanwhile, theinterlayer distance (d0) between the two monolayers of BN variesdepending on the stacking order, with spatial modulation as large as7% according to the density functional theory (DFT) calculations(Fig. 5f, see calculation details in Supplementary Note 9). This out-of-plane corrugation may imprint partially into the interlayer distance ofbilayer graphene, modulating the interlayer tunneling strength by themoiré periodicity and giving rise to band folding. The strength of thepiezoelectric effect and corrugation effect depend on the twist angle,and their quantitative contributions are still under explore, which callsfor future experimental and theoretical studies to uncover the richmoiré physics from twisted BN system31,40.DiscussionIn conclusion, we demonstrated that twisted bilayer BN can serve as aversatile moiré substrate for band structure engineering with tunablemoiréwavelength andpotential strength.With awell-definedpotentiallandscape from polar domains, twisted BN hosts advantage for engi-neering the band structure of a wide range of 2D materials41,42 com-pared with moiré potential formed by doped electrons in moirésuperlattices19–21,43.Ourmoiré polar substrate design principle is applicable not only toBN, but also to other bipartite 2D insulators or semiconductors, such astransition metal dichalcogenides, which have different magnitudes ofelectrostatic potential and spin-orbit interaction44,45. The application ofthemoiré substratesonvarious2Dmaterialsmay lead to theobservationof exotic physics related to correlations and topology in the future26,46–59.Moreover, this lithographically free method for introducing highly per-iodic electrostatic potentials at the nanoscale may find applications inother fields of nanotechnology beyond 2D materials60–62.MethodsDevice fabricationBN and graphite crystals were exfoliated onto SiO2 (285 nm-295 nm)/Sisubstrates. For monolayer BN, we used SiO2 (90nm)/Si substrates. Thethickness of thick BN flakes ( > 5 nm) was acquired by atomic forcemicroscopy (AFM). Monolayer BN, graphene and bilayer graphene wereidentified by optical contrast. We first prepared the bottom stacks. Fordevices A1-A6, B1-B7 we exfoliated graphite for bottom gates on SiO2(285nm)/Si substrates with pre-patterned markers, followed by heatcleaning in an atmosphere of Ar (40 sccm) and H2 (20 sccm) gases at350 °C for more than 12hours to remove the tape residues. For devicesC1-C5, D1, and D2, a thick BN (5 ~ 20nm) and graphite were sequentiallypicked up by poly(bisphenol A carbonate) (PC)-film-covered Poly-dimethylsiloxane (PDMS) stamp on a glass slide, and then released to a0 5 10 15 20d (nm)051015202530Upeak (mV)agraphitetop gatethick BNthick BN dtarget layertwisted BNb NB kciht mottob htiwNB kciht mottob tuohtiw15.1 nmA3 C10n (1012 cm-2)1.50.0ρxx (kΩ)0n (1012 cm-2)-2 20.60.40.20.0ρxx (kΩ)-2 -1 1 21.50.0ρxx (kΩ)-2 0 2n (1012 cm-2)0.60.40.20.0ρxx (kΩ)-2 -1 0 1 2n (1012 cm-2)0.11 k0.36 k-6 -4 -2 0 2 4 60123456781/71/61/51/41/31/2n/n0B (T)dC1, T = 0.3 K-1.5 0 1.5xy (mS)-6 -4 -2 0 2 4 60123456781/71/61/51/41/31/2n/n0B (T)cC1, T = 0.3 K10-1 100xx (mS)Fig. 4 | Tuning moiré polar potential by changing dielectric thickness.a Electrostatic simulation of themoiré potential peakmagnitudeUpeak as a functionof total bottomBN thickness d. Inset: Device schematic. A thick BN layer is insertedbetween the twisted bilayer BN and the bottom graphite. b ρxx as a function of n indevices A3 (without bottom thick BN) and C1 (with bottom thick BN), measured at4.2 K. Insets: Device schematics (left) and large-scale plots (right). c σxx as a functionof n/n0 and B (right y axis:ϕ/ϕ0), measured at 0.3 K in device C1. d σxy as a functionof n/n0 and B (right y axis: ϕ/ϕ0), measured at 0.3 K in device C1.Article https://doi.org/10.1038/s41467-024-55432-2Nature Communications |          (2025) 16:178 5www.nature.com/naturecommunicationsSiO2/Si substrate at 170 °C.We removed the trapped bubbles bymovingthe PC stamp and the stack up and down slowly a few times at 170 °C.After the PC was dissolved, the bottom stacks were heat cleaned in anatmosphere of Ar (40 sccm) and H2 (20 sccm) gases at 350 °C for3 ~ 12 hours. After that, contactmodeAFMwas performed at a deflectionvoltage of 0.1 ~ 0.2 V for cleaning the PC residues.Each top stack was made by the sequential pickup of top BN,bilayer/monolayer graphene, (few-layer BN) and twisted bilayer BN.Twisted bilayer BN was obtained by the sequential pickup of mono-layer BN flake at room temperature with the tear-and-stack methoddescribed in refs. 63,64. Then the stack on PC was scanned by PFM tosearch for regions with periodic moiré patterns. The whole stack wasthen released to the bottom graphite or bottom BN/graphite stack at170 °C. The stack was identified with an optical microscope and AFMfor bubble-free regions. Then the stack was etched into a Hall barshape by reactive ion etching, leaving the bubble-free regions withperiodic moiré patterns remained. All the contacts and top gates weredeposited with Cr/Au with a thermal evaporator.Piezoresponse force microscopy measurementsWe performed lateral PFM measurements on the top stack containingtwistedbilayer BN. ThePFMmeasurementswereperformedwithAsylumResearch Cypher S atomic force microscope at room temperature. Weused AC240TM-R3 tip with a force constant of around 1.5Nm−1 and acontact resonance frequencyof around600kHzwith theappliedACbiasvoltage of 2 V. The contact strength was set to be lower than 30 nN toavoid unintentional damage to the flake and twist angle relaxation.Transport measurementsThe devices were bonded by aluminum wire. The four-probe mea-surementswere doneusing lock-in amplifiers (SRS: SR830 and SR860),a current preamplifier (DL:Model 1211) and voltage preamplifiers (SRS:SR560) at the frequency of 17 ~ 35Hz. The gate voltages were appliedby source meters (Keithley: Model 2400 and 2450). Devices weremeasured in a He-3 cryostat (Janis research) or in a variable tempera-ture insert (Cryogenics).Electrostatic simulationWeusedCOMSOLMultiphysics® to simulate the electrostatic potentialin bilayer graphene.Initial condition and boundary condition: First, we built the geo-metries composed of the bilayer graphene, twisted bilayer BN, (bottomthick BN,) and bottom graphite in shapes of rectangular cuboids (Sup-plementary Fig. 9). The device lateral size was set to be 80nm×80nm,and the thicknesses were assigned according to the device structuresthat we study. We set the moiré wavelength of twisted bilayer BN to be18.5 nm. For the initial condition, we assume sinusoidal 2D charge den-sity distribution on either side of the twisted bilayer BN, taking the formρ=2ρ0ðsinðkx +ffiffiffi3pkyÞ � sin 2kx + sinðkx �ffiffiffi3pkyÞÞ=3ffiffiffi3p, where k= 1/a.The peak value of charge density is taken to be ρ0 = ϵ0ϵBNVp=dB, whereϵ0 is the vacuumpermittivity,Vp=0.109V is the interlayer potential, anddB is the interlayer distance between bilayer BN23,44. For the boundarycondition, we set the bilayer graphene and bottom graphite to begrounded, i.e., chemical potential V0=0.Quantum capacitance treatment: Since bilayer graphene is not aperfect metal and has finite DOS, we need to consider the effect fromits quantum capacitance. After the first round of simulation asdescribed above,we acquired the electricfield distribution close to thebilayer graphene, and calculated the doping induced by the electricfield using Gauss’s law: n= ϵ0ϵBNE, where ϵBN is taken to be 3. Then wecalculated the chemical potential shift V1 in bilayer graphene due tothis doping effect. We then set the new boundary condition at bilayergraphene to be V2 = 1/2(V0 +V1), and performed the simulation again.We performed the above steps in an iterative way until the electric10-1xx (k )6×10-1cbaAA' BA' AB' AB' BA' AA' Inversion centerNitrogen Borontarget layer60.90° twistedbilayer BNgraphitetop gatethick BNthick BN1x⅔½d 0 (Å)d fAB' BA'  'AA 'AA0.300.250.200.150.100.050.00ρ xx (kΩ)-4 -2 0 2 4n (1012 cm-2)D13.603.403.203.001.00.50.0ρ xx (kΩ)-4 0 4n (1012 cm-2)⅓0-2 0 20246800.10.20.30.4n (1012 cm-2)B (T)eFig. 5 | Moiré potential in near-60°-twisted bilayer BN. a Three stacking ordersthat exist in near-60°-twisted bilayer BN65. In AA’ stacking (left), B andN atoms alignon top of each other alternatively. Here,’ means one layer is rotated by 60° withrespect to the other. In AB’ stacking (middle), N sits on top of N. In BA’ stacking(right), B sits on top of B. All of these stacking arrangements have an inversioncenter, and therefore no net polarization is allowed. b Schematic of near-60°-twisted bilayer BN, where moiré patterns formwith AA’, AB’, and BA’ local stackingarrangements. c Device schematic of D1. The target layer sits on top of a near-60°-twisted bilayer BN. The stack is encapsulated between the top and bottom BN andcontrolled by a topmetal gate and a bottomgraphite gate.d ρxx as a functionofn indevice D1 with near-60°-twisted bilayer BN, measured at 4.2 K. Arrows indicate thepositions of the satellite resistance peaks. Inset: Large-scale plot. e ρxx as a functionof n and B (right y axis: ϕ/ϕ0), measured at 0.3 K in device D1. f Density functionaltheory (DFT) calculation of the interlayer distance d0 between the two near-60°-twisted monolayer BNs at different moiré sites. x: fractions of the moiré unit cell.Article https://doi.org/10.1038/s41467-024-55432-2Nature Communications |          (2025) 16:178 6www.nature.com/naturecommunicationspotential in bilayer graphene converges, where the system reaches theelectrochemical equilibrium. This means that the electrostatic poten-tial shift due to geometric capacitance and the chemical potential shiftdue to quantum capacitance are both considered, and the potentialprofile is self-consistent. To calculate V1, we first acquired Fermiwavevector from kF =ffiffiffiffiffiffiffiπnp, considering the valley and spindegeneracyin bilayer graphene, and then derived V1 from kF using the dispersionrelation calculated from Supplementary Equation 1.Data availabilityThe experimental data in the study are available at Harvard Dataverse:https://doi.org/10.7910/DVN/YJV5AK. The DFT calculation were gen-erated using free and open-source first-principles packages as descri-bed in Supplementary Note 9. The datasets generated during the DFTcalculation are available from the corresponding author upon request.Code availabilityThe COMSOL Multiphysics® file and Matlab code for electrostaticsimulation are available at https://github.com/xirui-wang/TwistedBN-Simulation. Further simulation details are available from the corre-sponding author upon request. The code for band structure calcula-tion is available at https://github.com/chengxu20/hBN_gra_moire. Thecode for the DFT calculation is available from the correspondingauthor upon request.References1. Song, J. C.W.&Gabor, N.M. Electronquantummetamaterials in vander Waals heterostructures. Nat. Nanotechnol. 13, 986–993 (2018).2. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).3. Cao, Y. et al. Unconventional superconductivity in magic-anglegraphene superlattices. Nature 556, 43–50 (2018).4. Sharpe, A. L. et al. Emergent ferromagnetism near three-quartersfilling in twisted bilayer graphene. Science 365, 605–608 (2019).5. Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiréheterostructure. Science 367, 900–903 (2020).6. Wang, L. et al. Correlated electronic phases in twisted bilayertransition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).7. Li, T. et al. Quantum anomalous Hall effect from intertwined moirébands. Nature 600, 641–646 (2021).8. Cai, J. et al. Signatures of fractional quantum anomalous Hall statesin twisted MoTe2. Nature 622, 63–68 (2023).9. Park, H. et al. Observation of fractionally quantized anomalous Halleffect. Nature 622, 74–79 (2023).10. Xu, F. et al. Observation of Integer and Fractional QuantumAnomalous Hall Effects in Twisted Bilayer MoTe 2. Phys. Rev. X 13,031037 (2023).11. Zeng, Y. et al. Thermodynamic evidence of fractional Chern insu-lator in moiré MoTe2. Nature 622, 69–73 (2023).12. Dubey, S. et al. Tunable Superlattice in Graphene To Control theNumber of Dirac Points. Nano Lett. 13, 3990–3995 (2013).13. Drienovsky, M. et al. Towards superlattices: Lateral bipolar multi-barriers in graphene. Phys. Rev. B 89, 115421 (2014).14. Forsythe, C. et al. Band structure engineering of 2Dmaterials usingpatterned dielectric superlattices. Nat. Nanotechnol. 13, 566–571(2018).15. Huber, R. et al. Gate-Tunable Two-Dimensional Superlattices inGraphene. Nano Lett. 20, 8046–8052 (2020).16. Li, Y. et al. Anisotropic band flattening in graphene with one-dimensional superlattices. Nat. Nanotechnol. 16, 525–530 (2021).17. Barcons Ruiz, D. et al. Engineering high quality graphene super-lattices via ion milled ultra-thin etching masks. Nat. Commun. 13,6926 (2022).18. Sun, J. et al. Signature of Correlated Insulator in Electric FieldControlled Superlattice. Nano Lett. 24, 13600–13606 (2024).19. Zhang, Z. et al. Engineering correlated insulators in bilayer gra-phene with a remote Coulomb superlattice. Nat. Mater. 23,189–195 (2024).20. Gu, J. et al. Remote imprinting of moiré lattices. Nat. Mater. 23,219–223 (2024).21. He, M. et al. Dynamically tunable moiré exciton Rydberg states in amonolayer semiconductor on twisted bilayer graphene.Nat. Mater.23, 224–229 (2024).22. Woods, C. R. et al. Charge-polarized interfacial superlattices in mar-ginally twistedhexagonal boronnitride.Nat. Commun. 12, 347 (2021).23. Yasuda, K., Wang, X., Watanabe, K., Taniguchi, T. & Jarillo-Herrero,P. Stacking-engineered ferroelectricity in bilayer boron nitride.Science 372, 1458–1462 (2021).24. Vizner Stern, M. et al. Interfacial ferroelectricity by van der Waalssliding. Science 372, 1462–1466 (2021).25. Kim,D. S. et al. Electrostaticmoirépotential from twistedhexagonalboron nitride layers. Nat. Mater. 23, 65–70 (2024).26. Zhao, P., Xiao, C. & Yao, W. Universal superlattice potential for 2Dmaterials from twisted interface insideh-BNsubstrate.npj 2DMater.Appl. 5, 38 (2021).27. Hunt, B. et al. Massive Dirac Fermions and Hofstadter Butterfly in avan der Waals Heterostructure. Science 340, 1427–1430 (2013).28. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantumHalleffect in moiré superlattices. Nature 497, 598–602 (2013).29. Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphenesuperlattices. Nature 497, 594–597 (2013).30. Krishna Kumar, R. et al. High-order fractal states in graphenesuperlattices. Proc. Natl Acad. Sci. 115, 5135–5139 (2018).31. Yankowitz, M. et al. Dynamic band-structure tuning of graphenemoiré superlattices with pressure. Nature 557, 404–408 (2018).32. Mao, J. et al. Evidence offlat bands and correlated states in buckledgraphene superlattices. Nature 584, 215–220 (2020).33. McGilly, L. J. et al. Visualization of moiré superlattices. Nat. Nano-technol. 15, 580–584 (2020).34. Kazmierczak, N. P. et al. Strain fields in twisted bilayer graphene.Nat. Mater. 20, 956–963 (2021).35. Ni, G. X. et al. Soliton superlattices in twisted hexagonal boronnitride. Nat. Commun. 10, 4360 (2019).36. Moore, S. L. et al. Nanoscale lattice dynamics in hexagonal boronnitride moiré superlattices. Nat. Commun. 12, 5741 (2021).37. Luo,Y. et al. In situnanoscale imagingofmoiré superlattices in twistedvan der Waals heterostructures. Nat. Commun. 11, 4209 (2020).38. de Jong, T. A. et al. Imaging moiré deformation and dynamics intwisted bilayer graphene. Nat. Commun. 13, 70 (2022).39. Li, H. et al. Imaging moiré flat bands in three-dimensional recon-structed WSe2/WS2 superlattices. Nat. Mater. 20, 945–950 (2021).40. Magorrian, S. J. et al. Multifaceted moiré superlattice physics intwisted WSe 2 bilayers. Phys. Rev. B 104, 125440 (2021).41. Zeng, Y. et al. Gate-tunable topological phases in superlatticemodulated bilayer graphene. Phys. Rev. B 109, 195406 (2024).42. Tan, T., Reddy, A. P., Fu, L. & Devakul, T. Designing Topology andFractionalization in Narrow Gap Semiconductor Films via Electro-static Engineering. Phys. Rev. Lett. 133, 206601 (2024).43. Angeli, M. & MacDonald, A. H. Γ valley transition metal dichalco-genide moiré bands. Proc. Natl Acad. Sci. 118, e2021826118 (2021).44. Wang, X. et al. Interfacial ferroelectricity in rhombohedral-stackedbilayer transition metal dichalcogenides. Nat. Nanotechnol. 17,367–371 (2022).45. Weston, A. et al. Interfacial ferroelectricity in marginally twisted 2Dsemiconductors. Nat. Nanotechnol. 17, 390–395 (2022).46. Ghorashi, S. A. A. & Cano, J. Multilayer graphenewith a superlatticepotential. Phys. Rev. B 107, 195423 (2023).47. Ghorashi, S. A. A. et al. Topological and stackedflat bands in bilayergraphene with a superlattice potential. Phys. Rev. Lett. 130,196201 (2023).Article https://doi.org/10.1038/s41467-024-55432-2Nature Communications |          (2025) 16:178 7https://doi.org/10.7910/DVN/YJV5AKhttps://github.com/xirui-wang/TwistedBN-Simulationhttps://github.com/xirui-wang/TwistedBN-Simulationhttps://github.com/chengxu20/hBN_gra_moirewww.nature.com/naturecommunications48. Suri, N., Wang, C., Hunt, B. M. & Xiao, D. Superlattice engineering oftopology inmassive Dirac fermions. Phys. Rev. B 108, 155409 (2023).49. Hougland, N., Ramachandran, R., Levy, J. & Pekker, D. Theory ofengineering flat bands in graphene using doubly-periodic electro-static gating. Preprint at https://arxiv.org/abs/2110.15477 (2021).50. Skurativska, A., Tsirkin, S. S., Natterer, F. D., Neupert, T. & Fischer,M.H. Flat bands with fragile topology through superlattice engineer-ing on single-layer graphene. Phys. Rev. Res. 3, L032003 (2021).51. Shi, L.,Ma, J. &Song, J.C.W.Gate-tunableflatbands in vanderWaalspatterned dielectric superlattices. 2D Mater. 7, 015028 (2020).52. Zhou, H. et al. Half- and quarter-metals in rhombohedral trilayergraphene. Nature 598, 429–433 (2021).53. Liu, K. et al. Spontaneous broken-symmetry insulator and metals intetralayer rhombohedral graphene. Nat. Nanotechnol 19,188–195 (2024).54. Han, T. et al. Correlated insulator andChern insulators in pentalayerrhombohedral-stacked graphene. Nat. Nanotechnol. https://doi.org/10.1038/s41565-023-01520-1 (2023).55. Dong, Z., Patri, A. S. & Senthil, T. Theory of Quantum AnomalousHall Phases in Pentalayer Rhombohedral Graphene Moiré Struc-tures. Phys. Rev. Lett. 133, 206502 (2024).56. Dong, J. et al. Anomalous Hall Crystals in Rhombohedral MultilayerGraphene. I. Interaction-Driven Chern Bands and Fractional Quan-tum Hall States at Zero Magnetic Field. Phys. Rev. Lett. 133,206503 (2024).57. Zhou, B., Yang, H. & Zhang, Y.-H. Fractional Quantum AnomalousHall Effect in Rhombohedral Multilayer Graphene in the MoirélessLimit. Phys. Rev. Lett. 133, 206504 (2024).58. Tan, T. & Devakul, T. Parent Berry Curvature and the Ideal Anom-alous Hall Crystal. Phys. Rev. X 14, 041040 (2024).59. Tan, T., May-Mann, J. & Devakul, T. Wavefunction approach to thefractional anomalous Hall crystal. Preprint at https://doi.org/10.48550/arXiv.2409.06775 (2024).60. Barthelemy, P. & Vandersypen, L. M. K. Quantum Dot Systems: aversatile platform for quantum simulations. Ann. Phys. 525,808–826 (2013).61. Hensgens, T. et al. Quantum simulation of a Fermi–Hubbard modelusing a semiconductor quantumdot array.Nature 548, 70–73 (2017).62. Freeney, S. E., Slot, M. R., Gardenier, T. S., Swart, I. & Vanmae-kelbergh, D. Electronic QuantumMaterials Simulated with ArtificialModel Lattices. ACS Nanosci. Au 2, 198–224 (2022).63. Kim, K. et al. van der Waals heterostructures with high accuracyrotational alignment. Nano Lett. 16, 1989–1995 (2016).64. Cao, Y. et al. Superlattice-Induced Insulating States and Valley-Protected Orbits in Twisted Bilayer Graphene. Phys. Rev. Lett. 117,116804 (2016).65. Izumi, F. et al. VESTA3 for three-dimensional visualization of crystal,volumetric and morphology data. J. Appl. Crystallogr. 44,1272–1276 (2011).AcknowledgementsWe thank A. Reddy for help in fabrication, and J. Cano, S.A.A. Ghorashi,M. Koshino, and V.I. Fal’ko for fruitful discussions. This research wassupported by the Center for the Advancement of Topological Semi-metals, an Energy Frontier Research Center funded by the U.S. Depart-ment of Energy Office of Science, through the Ames Laboratory undercontract DE-AC02-07CH11358 (measurements and data analysis), theMIT/Microsystems Technology Laboratories Samsung SemiconductorResearch Fund, the Gordon and Betty Moore Foundation’s EPiQS Initia-tive through grant GBMF9463, and the Ramon Areces Foundation. Thiswork was performed in part at the Harvard University Center forNanoscale Systems (CNS), a member of the National NanotechnologyCoordinated Infrastructure Network (NNCI), which is supported by theNational Science Foundation under NSF ECCS award No. 1541959. Thiswork was carried out in part through the use of MIT.nano’s facilities. C.X.and Y.Z. are supported by the start-up fund at University of TennesseeKnoxville, and the Max Planck Partner lab on quantum materials fromMax Planck Institute Chemical Physics of Solids. S.A. is partially sup-ported by the NSF Graduate Research Fellowship Program via grant no.1122374. D.B. and E.K. acknowledge the US Army Research Office (ARO)MURI project under grant No. W911NF-21-0147 and from the SimonsFoundation award No. 896626. N.P. acknowledges the Kavli Institute forTheoretical Physics (KITP) graduate fellowship. K.W. and T.T. acknowl-edge support from the JSPS KAKENHI (Grant Numbers 21H05233 and23H02052) and World Premier International Research Center Initiative(WPI), MEXT, Japan.Author contributionsK.Y., X.W., and P.J-H. conceived the project and experiments. K.Y., X.W.,and S.A. fabricated the devices and performed measurements with thehelp of C.C.; X.W. performed electrostatic simulations with ComsolMultiphysics®. Y.Z., C.X., D.B., N.P., and P.J.D.C. performed the theore-tical calculations. K.W. and T.T. grew the BN crystals. K.Y., P.J-H., Y.Z.,E.K., andR.A. supervised theproject. X.W. andK.Y. analyzed thedataandwrote the manuscript with input from all the other authors.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-024-55432-2.Correspondence and requests for materials should be addressed toPablo Jarillo-Herrero or Kenji Yasuda.Peer review information Nature Communications thanks Jianming Lu,and the other, anonymous, reviewer(s) for their contribution to the peerreview of this work. A peer 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-NonCommercial-NoDerivatives 4.0 International License,which permits any non-commercial use, sharing, distribution andreproduction in any medium or format, as long as you give appropriatecredit to the original author(s) and the source, provide a link to theCreative Commons licence, and indicate if you modified the licensedmaterial. Youdonot havepermissionunder this licence toshare adaptedmaterial derived from this article or parts of it. The images or other thirdparty material in this article are included in the article’s CreativeCommons licence, unless indicated otherwise in a credit line to thematerial. If material is not included in the article’s Creative Commonslicence and your intended use is not permitted by statutory regulation orexceeds the permitted use, you will need to obtain permission directlyfrom the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.© The Author(s) 2024Article https://doi.org/10.1038/s41467-024-55432-2Nature Communications |          (2025) 16:178 8https://arxiv.org/abs/2110.15477https://doi.org/10.1038/s41565-023-01520-1https://doi.org/10.1038/s41565-023-01520-1https://doi.org/10.48550/arXiv.2409.06775https://doi.org/10.48550/arXiv.2409.06775https://doi.org/10.1038/s41467-024-55432-2http://www.nature.com/reprintshttp://creativecommons.org/licenses/by-nc-nd/4.0/http://creativecommons.org/licenses/by-nc-nd/4.0/www.nature.com/naturecommunications Moiré band structure engineering using a twisted boron nitride substrate Results Band structure modulation in bilayer graphene Tuning moiré potential by inserting extra dielectric BN Moiré effect from near-60°-twisted BN Discussion Methods Device fabrication Piezoresponse force microscopy measurements Transport measurements Electrostatic simulation Data availability Code availability References Acknowledgements Author contributions Competing interests Additional information