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Junxiong Hu, Junyou Tan, Mohammed M. Al Ezzi, Udvas Chattopadhyay, Jian Gou, Yuntian Zheng, Zihao Wang, Jiayu Chen, Reshmi Thottathil, Jiangbo Luo, [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), Andrew Thye Shen Wee, Shaffique Adam, A. Ariando

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[Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures](https://mdr.nims.go.jp/datasets/39bf3ddc-06dc-44a0-9457-22185a3dc3b0)

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Controlled alignment of supermoireÌ• lattice in double-aligned graphene heterostructuresArticle https://doi.org/10.1038/s41467-023-39893-5Controlled alignment of supermoiré latticein double-aligned graphene heterostructuresJunxiong Hu 1,2,7, Junyou Tan2,7, Mohammed M. Al Ezzi1,2,7,Udvas Chattopadhyay1,2, Jian Gou 1, Yuntian Zheng1, Zihao Wang 3,4,Jiayu Chen1, Reshmi Thottathil 1, Jiangbo Luo1, Kenji Watanabe 5,Takashi Taniguchi 6, Andrew Thye Shen Wee 1, Shaffique Adam 1,2,3 &A. Ariando 1The supermoiré lattice, built by stacking two moiré patterns, provides a plat-form for creating flat mini-bands and studying electron correlations. An ulti-mate challenge in assembling a graphene supermoiré lattice is in thedeterministic control of its rotational alignment, which ismade highly aleatorydue to the random nature of the edge chirality and crystal symmetry.Employing the so-called “golden rule of three”, here we present an experi-mental strategy to overcome this challenge and realize the controlled align-ment of double-aligned hBN/graphene/hBN supermoire ́ lattice, where thetwist angles between graphene and top/bottom hBN are both close to zero.Remarkably, we find that the crystallographic edge of neighboring graphitecan be used to better guide the stacking alignment, as demonstrated by thecontrolled production of 20moiré sampleswith an accuracy better than ~ 0.2°.Finally, we extend our technique to low-angle twisted bilayer graphene andABC-stacked trilayer graphene, providing a strategy for flat-band engineeringin these moiré materials.The moiré superlattice, created by stacking van der Waals (vdW) het-erostructures with a controlled twist angle1–6, enables the engineeringof electronic band structures and provides a platform for investigatingexotic quantum states, both in the weakly interacting electronsystems7–10, as well as recently in the strongly correlated electronsystems11–17. Particularly, when two moiré superlattices contact andinterface together, the overlay of double moiré will create a newstructure called supermoiré lattice, strongly modifying the latticesymmetry and electronic band structure18–22. Comparedwith the singlemoiré potential, the double moiré potential will further break the lat-tice symmetry and create isolated flat moiré minibands, providing astrategy for the band flattening effect23. Recently, evidence of possiblecorrelated states was observed in the double-aligned graphenesupermoiré lattice24, which triggered further effort to search for othercorrelated phenomena, such as superconductivity and ferromagneticstates, as observed in twisted graphene systems25. However, due to thesophisticated stacking and the lack of control of rotational alignment,searching for these correlated phenomena in double-aligned super-moiré lattice remains elusive.In previous studies of double-aligned hexagonal boron nitride/graphene/hexagonal boron nitride (hBN/G/hBN) supermoiré lattice,several techniques have been developed to control the rotationalignment, such as in situ rotation mediated by atomic force micro-scope (AFM) tips and polydimethylsiloxane (PDMS) hemisphere20,21.Received: 2 February 2023Accepted: 30 June 2023Check for updates1Department of Physics, National University of Singapore, Singapore 117542, Singapore. 2Centre for Advanced 2D Materials and Graphene Research Centre,National University of Singapore, Singapore 117551, Singapore. 3Department of Materials Science and Engineering, National University of Singapore, Sin-gapore 117575, Singapore. 4Institute for Functional Intelligent Materials, National University of Singapore, Singapore 117544, Singapore. 5Research Center forFunctional Materials, National Institute for Materials Science, Tsukuba 305-0044, Japan. 6International Center for Materials Nanoarchitectonics, NationalInstitute for Materials Science, Tsukuba 305-0044, Japan. 7These authors contributed equally: Junxiong Hu, Junyou Tan, Mohammed M. Al Ezzi.e-mail: ariando@nus.edu.sgNature Communications |         (2023) 14:4142 11234567890():,;1234567890():,;http://orcid.org/0000-0002-1586-3293http://orcid.org/0000-0002-1586-3293http://orcid.org/0000-0002-1586-3293http://orcid.org/0000-0002-1586-3293http://orcid.org/0000-0002-1586-3293http://orcid.org/0000-0001-8779-6491http://orcid.org/0000-0001-8779-6491http://orcid.org/0000-0001-8779-6491http://orcid.org/0000-0001-8779-6491http://orcid.org/0000-0001-8779-6491http://orcid.org/0000-0003-2169-1456http://orcid.org/0000-0003-2169-1456http://orcid.org/0000-0003-2169-1456http://orcid.org/0000-0003-2169-1456http://orcid.org/0000-0003-2169-1456http://orcid.org/0009-0008-1013-691Xhttp://orcid.org/0009-0008-1013-691Xhttp://orcid.org/0009-0008-1013-691Xhttp://orcid.org/0009-0008-1013-691Xhttp://orcid.org/0009-0008-1013-691Xhttp://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/0000-0002-5828-4312http://orcid.org/0000-0002-5828-4312http://orcid.org/0000-0002-5828-4312http://orcid.org/0000-0002-5828-4312http://orcid.org/0000-0002-5828-4312http://orcid.org/0000-0002-3095-9920http://orcid.org/0000-0002-3095-9920http://orcid.org/0000-0002-3095-9920http://orcid.org/0000-0002-3095-9920http://orcid.org/0000-0002-3095-9920http://orcid.org/0000-0002-0598-426Xhttp://orcid.org/0000-0002-0598-426Xhttp://orcid.org/0000-0002-0598-426Xhttp://orcid.org/0000-0002-0598-426Xhttp://orcid.org/0000-0002-0598-426Xhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39893-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39893-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39893-5&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-023-39893-5&domain=pdfmailto:ariando@nus.edu.sgHowever, these techniques are restricted by either specialized equip-ment or complicated sample preparation steps. Consequently, theoptical alignment of straight edges is still themost popular and reliabletechnique for moiré device fabrication8–10,14–19,22–30. Nevertheless,the conventional optical alignment has two limitations. First, the lackof prior understanding of the crystallographic orientation of grapheneor hBN, leading to only a 50% and 25% success rate for alignment of asingle and double moiré structure, respectively, because the zigzag(armchair) edge of graphene can be unintentionally aligned to eitherthe zigzag or armchair edge of hBN.Moreover, the lattice symmetry ofhBN layer also obscures the inversion symmetry of the moiréheterostructure20,21, further decreasing the success rate to 12.5% indoublyaligned hBN/graphene/hBN heterostructures. Second, theoptical alignment highly depends on the crystal edge of the grapheneitself, and usually, it has a short and non-perfect straight edge. This canlead to an error in the representation of the actual principle crystal-lographic axes (PCA) during alignment.In this work, we overcome the above two limitations and realizethe control alignment of double-aligned graphene supermoiré lattice.First, we use a 30° rotation technique to control the alignment of tophBN and graphene, while we use a flip-over technique to control thealignmentof tophBNandbottomhBN. Basedon these two techniques,we can control the lattice symmetry and tune the graphene bandstructure. In a high-quality perfect double-aligned devicewithmobilityof ~700,000 cm2/Vs at 2 K, we observe sharp resistive peaks at bandfillings of 0, −4, −8 electrons per moiré unit cell, consistent with ourcalculated band structure. Second, we show that the neighboringgraphite edge can be used to better guide the alignment, as demon-strated by the controlled production of 20 moiré samples with accu-racy better than ~0.2°. Moreover, we have developed a so-called“Golden Rule of Three” that further guarantees the success rate andprecisionof our technique. Finally, we extendour alignment techniqueto other strongly correlated electron systems, such as low-angle twistbilayer graphene and ABC-stacked trilayer graphene, enabling us toexamine moiré potential effects in these strongly correlated electronsystems.Results30° rotation techniqueFirst, we study the controlled alignment between top hBN (T-hBN) andgraphene. In the optical alignment technique, the G/hBN moirésuperlattice is achieved by aligning the PCA between graphene andhBN. Based on the crystallographic structures, they can form twobasicmoiré patterns: 0° G/hBN and 30° G/hBN (Fig. 1a, also SupplementaryFig. 1). When in the assembly of hBN/graphene/hBN sandwich struc-ture, there are eight possible configurations: C1 (0°/0°) & C1* (0°/60°),C2 (0°/30°) & C2* (0°/90°), C3 (30°/30°) & C3* (30°/90°) and C4 (30°/0°) & C4* (30°/60°) (Fig. 1a). All possible configurations lead to 1/2(50%) success rate for single alignment (C2, C2*, C4, C4*), and 1/8(12.5%) success rate for double alignment (C1). Our theoretical calcu-lations investigate the adhesive energies of two basic moiré patternsand find that there are two energy minima at 0° and 30° twist angles,indicating these two moiré patterns are energetically stable states(Fig. 1b, c). These calculations also suggest thatgraphene andhBN tendto self-rotate to 0° or 30° when stacked together, depending on theinitial states31,32.Based on these calculations, we develop the so-called “30°-rota-tion technique” to simultaneously obtain these two energy-stablestates. The central concept of this technique is illustrated in Fig. 1d–f.Instead of directly picking up the whole graphene as in theconventional optical alignment, the hBN is aligned partially with agraphene layer (Fig. 1d). Thanks to a stronger vdW interactionbetweengraphene and hBN, the graphene layer canbe torn into twopieces. Thegraphene area in contact with hBN can be selectively detached (G1),leaving behind a section of the graphene layer (G2) on the siliconwafer. The critical step in our technique is that the left graphene (G2) isFig. 1 | Control alignment of tophBNandgraphene by rotating 30°. aAlignmentof top hBN (T-hBN), graphene and bottom hBN (B-hBN). The Zigzag (ZG) edge ofT-hBN is aligned with the ZG edge or Armchair (AR) edge of graphene and is thenalignedwith theZGorAR edgeof B-hBN, leading toeight possible combinations: C1(0°/0°) & C1* (0°/60°), C2 (0°/30°) &C2* (0°/90°), C3 (30°/30°) &C3* (30°/90°) andC4 (30°/0°) & C4* (30°/60°), whereC (or C*) represents the configuration when theT-hBN and B-hBN have the same (or opposite) lattice symmetry. The middle car-toons are two basic moiré patterns of 0° G/hBN and 30° G/hBN. b, c Calculatedinteraction energies for G/hBN heterostructure around 0° and 30°. Total energy(red circles) contributions from intralayer (elastic energy/blue triangles) andinterlayer interactions (adhesive energy/black squares). d–f Side view and bottomview of 30° rotational alignment. PCA refers to the principle crystallographic axesof crystals. G1 and G2 refer to graphene 1 and graphene 2 which come from thesame flake.gOptical image ofG/hBNstackon Polydimethylsiloxane (PDMS) stamp.The red dash line profiles the outline of 0° G1/hBN and the green dash line profilesthe outline of 30° G2/hBN. Scale bar, 20μm. h Spatial map of the full width at halfmaximum (FWHM) of 2D-band for the dashed area in (g). The red color map refersto 0°G1/hBN,while the green colormap refers to 30°G2/hBN. Scale bar, 5μm. iTheSTM topography image of 0° G1/hBN shows ~14 nm moiré patterns (left,500mV,15pA), and the topography image of 30° G2/hBN shows the characteristicof quasicrystal (right, 100mV, 100pA). Scale bar, 10 nm.Article https://doi.org/10.1038/s41467-023-39893-5Nature Communications |         (2023) 14:4142 2rotated manually by a twist-angle of 30° (Fig. 1e), and G2 is thenstacked at another location on the same hBN (Fig. 1f). This processresults in two G/hBN structures based on the same hBN layer: G1/hBNand G2/hBN. Since G1 and G2 are 30° rotated to each other, one ofthemmust be 0° alignedwith hBN, and the other onemust be 30°withhBN (Supplementary Fig. 1). To examine our concept, we investigatethe resulting G/hBN structures using optical microscopy, Ramanspectroscopy and scanning tunneling microscopy (STM). Figure 1gshows the optical image of G/hBN stacks, showing two sections ofgraphene rotated 30° to each other as indicated by the dashed lines.Figure 1h shows the respective full width at half maximum (FWHM)mapping of Raman 2D peaks. The FWHM mapping of the red area isclose to 40 cm−1, indicating the 0° rotation between graphene andhBN33 (Supplementary Fig. 2). While the FWHM mapping of the greenarea is close to 20 cm−1, indicating the 30° G/hBN. Moreover, thehomogeneous distribution mapping indicates the spatially uniformtwist angles. To further confirm the twist angles, we also use STM todirectly characterize themoiré patternsofG1/hBNandG2/hBN (Fig. 1i).The 0° G1/hBN has a clear moiré wavelength of ~14 nm34,35, while the30° G2/hBN shows the character of quasicrystal line, which has 12-foldrotational order but lacks translational symmetry36,37 (SupplementaryFig. 3). Moreover, the twist angles are also confirmed by our transportmeasurements, as discussed later. Therefore, using this 30°-rotationtechnique, we can always obtain the 0° G/hBN without the need toconsider the exact chirality edge of each layer.Using neighboring graphite edgeEven though we can overcome the uncertainty in the edge chirality,there are still two other challenges for optical alignment. First, it isincredibly challenging to find a single-layer graphene flake with astraight edge, which usually happens in <1% from all exfoliated flakes(Supplementary Fig. 4). Second, the edge of single-layer grapheneusually is not long and straight enough, decreasing the accuracy in thealignment (Supplementary Figure 5). To improve productivity andaccuracy, we show that the neighboring graphite edge can be betterfor alignment. The concept is illustrated in Supplementary Fig. 6.Figure 2 illustrates three typical cases of neighboring graphite edgesthat can be used for perfect alignment. The first case is that the single-layer graphene has a direct connection with its neighboring graphiteedge (Fig. 2a). In this case, the single-layer graphene must share thesame PCA with neighboring graphite edges, which means the PCA ofgraphite can be used for alignment. Our Raman 2D-band mappingconfirms one part belongs to 0° G/hBN and the other to 30° G/hBN, asthe FWHMof the 2Dpeaks is 40 and 20 cm−1, respectively (Fig. 2c). Thesecond case is that the single-layer graphene has no direct connectionwith the graphite edge, but one edge of graphene is multiples of 30°with the graphite edge. In this case, the graphene and the neighboringgraphite also share the same PCA (Supplementary Fig. 7). Therefore,the PCA of graphite can be used for alignment. Raman 2D-band con-firms the alignment since they have 0° G/hBN and the second part has30 °G/hBN (Fig. 2f). The third case is that the single-layer grapheneneither hasany connectionnor ismultiples of 30°with theneighboringgraphite edge (Fig. 2g), we show that the PCA of neighboring graphitecan still be used for alignment, since our Raman spectra show that onepart is 0° G/hBN and the second part is 30° G/hBN (Fig. 2i). Regardingthe distance between graphene and graphite, we have studied threedifferent cases with a distance of 40, 130 as well as 250μm (Supple-mentary Fig. 8). We found that in all three cases, the neighboringgraphite edge can be used for alignment if we use the so-called “non-overlap exfoliation” method (Supplementary Fig. 9).The best advantage of our technique is that the alignment is notlimited by the geometry of graphene itself, and any random shape ofsingle-layer graphene flake can be used for fabricating moiré samples,as long as its neighboring graphite can provide the straight edgeswhich are nominally sharing the same termination as reference points(Supplementary Fig. 10). In order to demonstrate the high productivityFig. 2 | Perfect alignment of top hBN and graphene using the neighboringgraphite edge. a Optical image of single-layer graphene connecting with a neigh-boring graphite edge. bG/hBN stack after alignment using the graphite edge of (a).The red line profiles the outline of 0° G/hBN and the green line profiles the outlineof 30° G/hBN. c Spatial map of the FWHM of Raman 2D-band for the black dashedarea in (b).d Single-layer graphenewith one edge (white dashed line) has 60°with aneighboring graphite edge. e G/hBN stack after alignment using the graphite edgeof (d). f Spatial map of the FWHM of Raman 2D-band for the black dashed area in(e).g Single-layer graphenewithout any connectionwith anadjacent graphite edge.h G/hBN stack after alignment using the graphite edge of (g). i Spatial map of theFWHM of Raman 2D-band for the black dashed area in (h). Scale bars, 20 µm(a,d,g); 5 µm(b, e,h); 2 µm(c, f, i). jHistogramof the FWHMofRaman2D-band andtwist angle for 20moiré samples. The FWHMof ~20 cm−1 (green color) correspondsto 30° G/hBN, and the FWHMof ~40 cm−1 (red color) corresponds to 0° G/hBN. TheFWHM of 20 moiré samples is larger than 40cm−1, as indicated by the horizontaldashed line, indicating that the accuracy of our technique is better than ~0.2°.Article https://doi.org/10.1038/s41467-023-39893-5Nature Communications |         (2023) 14:4142 3and accuracy of our strategy, we further fabricated 20 moiré samples,where all the single-layer graphene flakes have a random edge. Thehistogram shows that the FWHM of all the samples is larger than40 cm−1, indicating that the accuracy of our alignment is better than~0.2°. (Fig. 2j, see also Supplementary Fig. 11). In comparison, thealignment accuracy when using a conventional technique is merely0.5- 1° (See the summary in Supplementary Table 1). Compared withsingle-layer graphene alignment, we find that using the neighboringgraphite edges can be better for alignment because the thick graphiteedge can have a longer and more straight edge. Moreover, followingthe “Golden Rule of Three” (see discussion section for details) whenusing the neighboring graphite edges further guarantees the successrate and precision of our technique. Our results show that a straightgraphite edge can always ensure the alignmentbetter than0.2°,while anon-perfect straight edgeor short straight edge (5–10 μm)will lead to asignificant deviation from an ideal alignment (>0.5°) (SupplementaryFig. 5). Therefore, using the neighboring graphite edge for alignment,we can not only significantly improve the device yields, but alsoguarantee the high accuracy of alignment.Flip-over techniqueNext, we study the control alignment of T-hBN and B-hBN. Because ofthe uncertain edge chirality of B-hBN, there are again two possiblecases when we stack the 0° and 30° T-hBN/G on the B-hBN: C1/C3, ifT-hBN andB-hBNhave the sameedges (Supplementary Fig. 12) andC2/C4, if T-hBN and B-hBN have the different edges (SupplementaryFig. 13). To secure the crystallographicorientationof T-hBNandB-hBN,we can use the same edge of the same hBN for alignment. However,apart from the edge chirality, we also need to consider the latticesymmetry of each hBN layer. As shown in Fig. 3a, for the conventionalpick-up process, we pick up BN1 and stack it on BN2, so the bottomsurface of BN1 is in contact with the top surface of BN2. Depending onthe surface symmetry determinedby the layer number of hBN, thefinalstack can be C1 (0°/0°) or C1* (0°/60°) (Fig. 3b, c). The C1 (0°/0°)heterostructure has three-fold rotationally symmetric, and the overallstructure breaks inversion symmetry, while the C1* (0°/60°) hetero-structure has a six-fold rotationally symmetric and the structure hostinversion symmetry. Even though these two structures have the samemoiré wavelength, the change of local stack induces a change in theatomic relaxation, consequently leading to totally differentbandgaps20,23.In order to control the alignment of T-hBN and B-hBN, we thendevelop a “flip-over technique” based on the same crystal edge as wellas the same atomic surface of hBN. As illustrated in Fig. 3a, the key stepis that BN2 is flipped over before placing BN1 on BN2. In this case, thesame lattice symmetry of T-hBN and B-hBN can be guaranteed. Weprefer to choose the bottom surface of the hBN instead of the topsurface because the two disjoint sections of the hBN may have a dif-ferent number of layers, and their top surfacesmight not be atomicallyflat and clean.On theother hand, however, it is highly likely thebottomsurfaces of the hBN flakes have the same termination and are muchcleaner, as the bottom surfaces of the two hBN flakes are cleaved fromthe same crystallographic facets of hBN crystal and are not in directcontact with the tape used for the cleaving. Further, the difference inthickness should not affect the termination of the bottom surface.Therefore, the main aim during the flip-over step is to attach thebottom surface of one of the flakes onto the bottom surface of theother flake (both bottom surfaces should have the same termination)instead of combining both top surfaces.Based on this concept, we can consider three different routes forobtaining BN1 and BN2 to be used in the flip-over technique (Supple-mentary Fig. 14). First, one hBN can be cut into two (BN1 and BN2). Inthis case, we can make sure that BN1 and BN2 share not only the samePCA, but also the same surface. However, this cutting process istedious, requiring complicated lithography steps. Second, BN1 andBN2 can come from naturally fractured hBN flakes, which can alwaysbe found during mechanical exfoliation. Figure 3d shows the opticalimages of two pieces of fractured hBN that can be regarded as T-hBNand B-hBN, respectively. Combining the 30° rotation and flip-overtechnique,wecanfirst realize the single alignment and then thedoublealignment, as demonstrated by the increase in FWHM of Raman 2D-band from ~40 cm−1 (single alignment) to ~70 cm−1 (double alignment)at the same area19 (Fig. 3e, see also Supplementary Fig. 15). Third, wecan also obtain BN1 and BN2 from two neighboring hBN flakes whoseFig. 3 | Control alignment of top hBN and bottom hBN using the neighboringhBN surface. a Schematics of conventional pick-up and flip-over technique fordouble alignment. b, c Schematics of hBN/graphene/hBN heterostructures withodd (b) and even (c) hBN layers. Lattice models at the high symmetry points of themoiré pattern show the atomic arrangement for each. Purple shading in (c) denotesthe overlap of boron (red) and nitrogen (blue) in the T-hBN and B-hBN. d Opticalimages of fractured hBN and alignment of T-hBN and B-hBN using the flip-overtechnique. The black lines profile the T-hBN, and the red lines profile the B-hBN.e Maps of the FWHM of Raman 2D-band of graphene for the single and doublealignment using the hBN in (d). fOptical images of two neighboring hBNand one ofhBNhave 60°with PCA can also be aligned using the flip-over technique. gMaps ofthe FWHM of Raman 2D-band of graphene for the single and double alignmentusing the hBN in (f). Scale bars, 10 µm (d, f); 1 µm (e, g).Article https://doi.org/10.1038/s41467-023-39893-5Nature Communications |         (2023) 14:4142 4straight edges have integer multiples of 30 degrees to each other, asshown in Fig. 3f, then the two adjacent hBNflakes have ahigh chanceofcoming from the same crystal (Supplementary Fig. 14). In this case, wecan also realize a perfect double alignment based on the same surfaceof hBN, as confirmed by the Raman 2D-band shown in the same area(Fig. 3g, see also Supplementary Fig. 15).Therefore, combining the 30° rotation andflip-over technique,wecan overcome the uncertainty in the edge chirality and lattice sym-metry during rotation alignment, and realize the 100% success rate forthe alignment of the doublemoiré structure. This is in stark contrast tothe conventional technique that can only lead to a 12.5% success rate24.Electronic transport measurementsFinally, to reveal the role of moiré potential in the reconstruction oflattice symmetry and band structure, we study the electronic proper-ties of C1–C3 configurations by top-gate devices38,39 (Fig. 4a, b).Wefirstuse Raman to verify the sample twist angle, and typical Ramandata of aperfectly double-aligned device is shown in Fig. 3e, g. Subsequently, astandard lithographic technique is used topattern aHall bar geometry.For double-aligned C1 (0°/0°) device, apart from the charge neutralitypoint (CNP), there are also two successive satellite peaks that appear athole-side, locating at −ns and −2ns, where ns = 2.3 × 1012 cm−2 (Fig. 4c).Since ns is the carrier density required to reach the edge of its firstBrillouin zone of amoiré pattern λ by ns =8ffiffi3pλ28–10, we can calculate themoiré wavelength of C1 of ~14 nm, in good agreement with our Ramanand STM measurements. Moreover, our band structure calculation(Inset of Fig. 4c) shows that the doublemoiré superlattice significantlysplits the hole-sided bands at higher energy into minibands with fullydeveloped gaps at electron fillings of −ns, −2 ns and −3 ns, which isconsistent with our observation since these satellite peaks in hole-sidebands are more developed than in the electron-side. Moreover, apartfrom thesebandfilling peaks, wedonot observe any extra peakswhichmay come from themisalignment18–24. Therefore, we can conclude thatthe C1 sample is a perfect double-aligned sample, where the twistangles between graphene and top/bottom hBN are both close to zero.A similar feature is also observed in the second perfect double-alignedsample (Supplementary Fig. 16). While for single-aligned C2 (0°/30°)device, we only observe one satellite peak at hole-side, locating at−ns = −2.2 × 1012 cm−2, corresponding to the moiré wavelength of~14.5 nm (Fig. 4d). The slightly larger moiré periodicity in C2 can beattributed to the strain effect in the heterostructure19,24. The lack of−2ns peak in C2 suggests that the overlap between the second andthird band, as our band structure calculation shows a rather smallbandgap (Inset of Fig. 4d). When the moiré potential disappears in C3(30°/30°) device, there is only one main Dirac point, consistent withour band structure calculation (Inset of Fig. 4e).When the electrons simultaneously subjected to both a magneticfield and a spatially periodic electrostatic fields, the energy spectrumdevelops into a Landau fan with a fractal structure known as the Hof-stadter butterfly8–10, which can be renormalized into a diagramdefinedby the Diophantine equation: nn0= v ϕϕ0+ s, where v is the Hall con-ductivity in units of a conductance quantum e2/h, as indicated by blacksolid lines in Fig. 4f, g, h, with topological index ν of ±2, ±6, ±10, ±14,…,and s the index of band filling. ϕ=B � A is flux per moiré unit area atmagnetic field B, and ϕ0 =h=e is a flux quantum with h being thePlanck’s constant. Figure 4f shows the fracture spectrum of C1 (0°/0°)device. The straight minigaps arises at ϕϕ0qðq= 1, 2,3, . . .Þ, resultingin Brown-Zak (BZ) oscillations with the fundamental period fieldof Bf = 24.49 T (ϕ0=A). Thus, we can calculate the moiré periodicity ofD1 of 13.97 nm, which is consistent with the first band filling densityat −ns = −2.35 × 1012 cm−2. Similarly, the BZ oscillations for C2device has the Bf = 23 T (Fig. 4g). We can then calculate the moiréperiodicity of C2 to be 14.417 nm, also consistent with the first bandfilling −ns = −2.2 × 1012 cm−2. Apart from the integer filling factions ofFig. 4 | Lattice symmetry and band structure tuned by moiré potential in tophBN/graphene/bottomhBNheterostructure. aArt viewof the supermoiré latticewith twist angles (θt and θb) between graphene and T-hBNand B-hBN.b Schematicsof the top-gate device with double moiré. Longitudinal resistance (Left axis) andHall resistance (right axis) with B =0.5 T versus carrier density for (c), C1 (0°/0°),(d), C2 (0°/30°), and (e), C3 (30°/30°). The insets show the corresponding bandstructures at the K-point. CNP refers to the charge neutrality point of Dirac band.Landau fan diagram of (f), C1, (g), C2 and (h), C3 plotted inmagnetic field (left) andcorrespondingϕ=ϕ0 versus n=n0.ϕ=ϕ0 and n=n0 are the normalizedmagnetic fluxand carrier density, respectively. The top number are the topological index ν to be±2, ±6, ±10, etc. T = 2K.Article https://doi.org/10.1038/s41467-023-39893-5Nature Communications |         (2023) 14:4142 50,� 4, � 8 in the Landau fan diagram, there are also some anomalousfeatures between them, which can be ascribed to the low energy VanHove singularities. Similar phenomena were previously observed insingle-aligned devices by transport study40 as well as the opticalstudy41. Finally, when themoiré periods disappear in C3 device, the BZoscillations also disappear, as there is only the Landau levels spectrum(Fig. 4h). These results suggest that the control alignment of moirépatterns, acting as a periodic moiré potential, can tune the latticesymmetry and engineer the band structure.DiscussionIn this work, we overcome the uncertainty of the edge chirality andcrystal symmetry by using 30° rotation technique and flip-over tech-nique, and finally realize the control alignment of double-alignedgraphene supermoiré lattice. Moreover, we show that neighboringgraphite edges can be used to better guide the stacking alignment. Asuccessful alignment of graphene and hBN relies on two things: (1)Precise representation of the PCA before alignment, and (2) Correctalignment techniques as reported in ourmain text. Since graphene andhBN come from two different flakes, there is a challenge to preciselyrepresent the PCA of each flake. We have overcome this challenge andset several rules, the so-called “Golden Rule of Three”, that have to bestrictly followed to guarantee the alignment precision and successrate. The rules are as follows:Golden Rule 1: Do not use the edge of graphene itself. Instead, usethe straight edge of the neighboring graphite. Moreover, the length ofthe straight edge should be no less than 100 μm (SupplementaryFig. 17a–c).Golden Rule 2: Do not use a graphite flake with a single straightedge. Instead, use a graphite flake withmultiple straight edges that areoffset by integermultiples of 30degrees to eachother (SupplementaryFig. 17d–f).Golden Rule 3: Do not accept random fluctuation of angle mea-surements larger than 0.2 degree. Instead, aim tominimize fluctuationby measuring angle multiple times when representing the PCA on theoptical microscopy system (Supplementary Fig. 17g–i).Below we explain why we must strictly follow the “Golden Ruleof Three”.First, we do not suggest using the edge of graphene, because thegraphene has a poor contrast under optical microscopy, making itdifficult to represent the PCA. On the contrary, the edge of thick gra-phite ismore obvious.Moreover, in order to keep the high precision of0.2 degrees for alignment, the error of the PCA should be controlledwithin 0.2 degrees. Therefore, we must choose a graphite flake with along straight edge. The longer the edge, the smaller the error is. Sup-plementary Fig. 18 demonstrates how the length of the graphite edgeaffects the angle measurement. When the length of the edge is smallerthan 50 μm (Supplementary Fig. 18a–c), the random error of PCA islarger than 0.5 degrees even with three measurement repeats. In thiscase, it is impossible to realize precise alignment below 0.2 degrees.Thus, we can also explain why, in earlier reports, the misalignment isusually as large as 0.5–1 degree, as summarized in SupplementaryTable 1. On the other hand, if the length of the edge is more than 100μm (Supplementary Fig. 18d–f), the random error can be controlledwell below 0.2 degrees. In this case, it is possible to achieve the precisealignment of below0.2 degrees, as shown in Fig. 2j. TheGoldenRule#1thus dictates that we must use graphite flakes with a straight edge ofmore than 100 μm. Second, it is very common to get disordered edgesthat are an admixture of zigzag and armchair terminations. Therefore,we cannot represent PCAwith 100% certainty if only depending on onesingle edge. Our Golden Rule #2 thus dictates that we must use gra-phite flakes withmultiple straight edges aligned at integermultiples of30 degrees. Third, when utilizing an optical microscope (in our caseNikon-LV100NDA) to identify and measure the angle of the graphiteedge, the measured angles are not exact and prone to error (that canbe easily larger than 0.2 degrees) due to human error and the limitedoptical microscope resolution. When the fluctuation of the measuredangles is more than 0.2 degrees, keeping the alignment precisionbetween graphene and hBN as good as 0.2 degrees will be impossible.Our Golden Rule #3 thus dictates that we must measure the angle ofthe edges at least three times and ensure the angle fluctuation is below0.2 degrees. Strictly following the above three golden rules and threemain alignment techniques, we can remove the 1/8 (12.5%) limitation,allowing a high yield of close to 100% to be realized for the double-aligned hBN/graphene/hBN heterostructure. Moreover, the twistangle between each layer can be controlled well below 0.2 degrees.Furthermore, our technique can greatly improve the efficiency offabricating samples. There is a clear improvement in the sample yield,precision and fabrication time using our technique, as we summarizedin Supplementary Table 3.In conclusion, we develop a generic strategy to overcome theedge chirality and lattice symmetry uncertainty in rotation alignment.Moreover, we show that the neighboring graphite edge can be usedfor better alignment of the stacking structures, significantly improvingthe device yield and alignment accuracy. Compared with previousconventional techniques, the current technique is easier and reliableto operate with robust and definite control of alignment. Consideringthe emerging area of “twistronics”, our technique can be beneficialfor much effort in this area in many laboratories. For example, ourstrategy can also be applied to the family of transition metal dichal-cogenide (TMD) semiconductors3,4 such as WSe2/WS2 moiré super-lattice, where a prior measurement of edge chirality in each crystal isnecessary before alignment42–45. To show the universality of our tech-nique, we also extend our technique to other correlated systems,like low-angle twisted bilayer graphene (Supplementary Fig. 19) andABC-stacked trilayer graphene (Supplementary Fig. 20). We believeour technique can help effort in exploring the physics of strong elec-tronic correlations and non-trivial band topology in these moirématerials.MethodsFabrication of devices and characterizationsFor sample preparation, the general process is as follows. We usepolycarbonate (PC), or poly-propylene carbonate (PPC) film mountedon a thick PDMS stamp to move and orientate the flakes. The stamp isused to pick up the first top hBN layer. The hBN is then positioned andaligned to a graphene edge or neighboring graphite edge before thetwo are brought into contact.We quickly lift the stamp once the hBN isfully passed across the graphene. After this, we invert the stamp andperform various characterizations. We then pick up a bottom hBNlayer and repeat our characterizations. Last, the stack of crystals ispositioned and brought into contact with a silicon wafer at the PCmelting point of 180 °C. Themembrane is then removed slowly so thatall the stacks are left on the silicon wafer. The standard Hall bar geo-metry of the devices is shaped by electron-beam lithography andetched by CHF3/O2 plasma. The edge contact electrodes and topelectrodes (3 nm Cr/65 nm Au) are deposited by standard electron-beam evaporation. The carrier mobility of our device is calculatedfrom the slopes of conductivity σ(Vg) at a small concentration of n∼1011 cm−2.Details of flip-over techniqueThe flip-over technique includes three steps. First, we used a thin filmof polycarbonate (PC, Sigma-Aldrich, 6% dissolved in chloroformpurchased at HQ Graphene) and polydimethyl-siloxane (PDMS) stackon a glass slide to pick up the first piece of hexagonal boron nitrideflake (BN1) at60 °C. Thenweused the vanderWaals forcebetweenBN1andmonolayer graphene to tear andpickuphalf of the graphene flake.The remaining graphene flake on the silicon was rotated by 30° andpicked up at 40 °C. Second, the polypropylene carbonate (PPC) layerArticle https://doi.org/10.1038/s41467-023-39893-5Nature Communications |         (2023) 14:4142 6was spun on top of a bare silicon wafer, released with a hollow-shapedScotch tape, and then transferred on top of the second PDMS stack ona glass slide. The PPC (Sigma-Aldrich, CAS 25511-85-7) is made of pro-pylene carbonate and anisole with a mass fraction of 5%. To enhancethe interaction between PPC and PDMS, the PDMS is treated withoxygen plasma for 10mins before being covered with PPC film. Thenthe PPC/PDMS stamp is used to pick up the second piece of hexagonalboronnitrideflake (BN2) at60 °C. Third, in order to expose thebottomsurface of BN2, we flip over the PDMS/PPC/BN2 and make the bottomsurface of BN2 to be exposed to the bottom surface of BN1. Finally, weuse PC/BN1/G to pick up BN2 from PPC at 80–100 °C. The success ofthis procedure relies on the stronger adhesion between PC and BN1compared to BN2 and PPC.The twist angle identified by transportFor transport measurement, the twist angles are estimated from twoindependentmethods. First, wemeasure the gate voltages of full-fillinggaps and convert these voltages to full-filling density ns using both thegate capacitance and Hall measurements. We then calculate the twistangle from which the full filling corresponds to four electrons permoiré unit cell so the moiré unit cell area A = 4/ns. Second, we studyHofstadter’s butterfly features under magnetic fields. Here we usecarrier-density-independent oscillations, also called BZ oscillations, ofthe longitudinal resistance Rxx fields, with the minimum of Rxx undermagnetic moiré unit cell of a fraction of the flux quantum, BA =φ0/N,where B is magnetic field, φ0 is the magnetic flux. The Hofstadterspectrum will exhibit fractal signature (i.e, B-8 T, B-6 T, and B-4.85 T)corresponding to φ =φ0/3, φ =φ0/4, φ =φ0/5.The twist angle identified by Raman spectroscopyRaman spectroscopy offers a simple and fast way to determine thetwist angle. The laser wavelength is 633 nm with a power of 1mWthrough a ×100 objective. High-resolution Raman maps are used tocharacterize the spatiallyunfirm twist angles,whichare acquiredwith ascan parameter of eight points per micrometer over a 10–20μm area.We use the full width at half maximum (FWHM) of the Raman 2D-bandto estimate the twist angle, where the FWHM is analyzed by Gaussianfitting. According to the previous study [33], there is a linear depen-dence between FWHM2D and the moiré wavelength for twist anglesbelow 2°, FWHMð2DÞ ffi 5 + 2:6λM and λM = 1:018aCCffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2:036½1�cosðθÞ� +0:0182p .Therefore, the FWHM of the Raman 2D peak is 41.5 cm−1 when themoiré wavelength is 14 nm at a perfect alignment of 0°.The twist angle identified by scanning tunnelling microscopyFor STMmeasurement, the graphene surface should be on the top sothat it canbe reached by STM tip. Therefore, we use amodifiedpick-upmethod for STM. First, we use a PC and PDMS stack on a glass slide topick up a 20–30nm-thick hBN flake. We then use the van der Waalsforce between hBN and graphene to pick up graphene. In order toexpose the graphene surface at the top, the resulting stack with PC istransferred and released onto a second PDMS stamp. After dissolvingthe PC film in DCM solution, the inverted stack with PDMS is releasedon a SiO2 wafer at 80 °C. After this, the Au/Cr electrode is evaporatedfor the electrical contact using a standard lithographic technique.Before inserting into the STM chamber, the G/hBN device is annealedat 300 °C for 3–5 h in ultrahigh vacuum to remove the surfacecontaminations.Experiments are conducted with an Omicron LT-STM at lowtemperature (T = 77 K) with a base pressure better than 1 × 10−11 mbar.Before the measurement, we check the tip by performing differentialconductance (dI/dV) measurements on a clean Au (111) surface bothbefore and after graphene measurement. dI/dV spectra are measuredusing a lock-in technique with a 20mV (r.m.s.) and 963Hzmodulationapplied to the sample voltage.Data availabilityRelevant data supporting the key findings of this study are availablewithin the paper and the Supplementary Information file. 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Mott and generalized Wigner crystal states inWSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).45. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 hetero-structure superlattices. Nature 567, 76–80 (2019).AcknowledgementsThis work is supported by the Ministry of Education (MOE) Singaporeunder the Academic Research Fund Tier 2 (Grant No. MOE-T2EP50120-0015), by the Agency for Science, Technology and Research (A*STAR)under its Advanced Manufacturing and Engineering (AME) IndividualResearch Grant (IRG) (Grant No. A2083c0054), and by the NationalResearch Foundation (NRF) of Singaporeunder itsNRF-ISF joint program(Grant No. NRF2020-NRF-ISF004-3518). S.A. and M.M.A.E acknowledgethe support of the Singapore National Science Foundation InvestigatorAward (Grant No. NRF-NRFI06-2020-0003). K.W. and T.T. acknowledgesupport from the JSPS KAKENHI (Grant Numbers 19H05790, 20H00354and 21H05233).Author contributionsA.A. conceived and supervised the project. J.X.H. designed and per-formed the experiments. J.Y.T. developed 30°-rotation alignment tech-niques and provided support and training on device fabrication process.M.M.A.E and U.C. carried out theoretical calculations under the super-vision of S.A. Y.T.Z., J.Y.C., R.T. and J.B.L. helped to prepare sample andmake the device. Z.H.W. helped the data analysis and interpretation. T.T.and K.W. provided the bulk hBN crystals. J.G. helped STMmeasurementunder the supervision of A.T.S.W. J.X.H. and A.A. analyzed the experi-mental data and wrote the paper. All authors discussed the results andcommented on the paper.Competing interestsThe authors declare no competing interests.Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-023-39893-5.Correspondence and requests for materials should be addressed to A.Ariando.Peer review information Nature Communications thanks Aaron Sharpeand the other, anonymous, reviewer(s) for their contribution to the peerreview 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/s41467-023-39893-5Nature Communications |         (2023) 14:4142 8https://doi.org/10.48550/arXiv.2205.11042https://doi.org/10.48550/arXiv.2205.11042https://doi.org/10.1038/s41467-023-39893-5http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Controlled alignment of supermoiré lattice in double-aligned graphene heterostructures Results 30° rotation technique Using neighboring graphite edge Flip-over technique Electronic transport measurements Discussion Methods Fabrication of devices and characterizations Details of flip-over technique The twist angle identified by transport The twist angle identified by Raman spectroscopy The twist angle identified by scanning tunnelling microscopy Data availability References Acknowledgements Author contributions Competing interests Additional information