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David Barcons Ruiz, Hanan Herzig Sheinfux, Rebecca Hoffmann, Iacopo Torre, Hitesh Agarwal, Roshan Krishna Kumar, Lorenzo Vistoli, [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Kenji Watanabe](https://orcid.org/0000-0003-3701-8119), Adrian Bachtold, Frank H. L. Koppens

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[Engineering high quality graphene superlattices via ion milled ultra-thin etching masks](https://mdr.nims.go.jp/datasets/891c03fc-4ab8-4edd-88bd-8c9a41681ac5)

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Engineering high quality graphene superlattices via ion milled ultra-thin etching masksArticle https://doi.org/10.1038/s41467-022-34734-3Engineering high quality graphenesuperlattices via ion milled ultra-thinetching masksDavid Barcons Ruiz 1, Hanan Herzig Sheinfux1, Rebecca Hoffmann1,Iacopo Torre 1, Hitesh Agarwal 1, Roshan Krishna Kumar 1, Lorenzo Vistoli1,Takashi Taniguchi 2,3, Kenji Watanabe 2,3, Adrian Bachtold1,4 &Frank H. L. Koppens 1,4Nanofabrication research pursues the miniaturization of patterned featuresize. In the current state of the art, micron scale areas can be patterned withfeatures down to ~30 nm pitch using electron beam lithography. Here, wedemonstrate a nanofabrication technique which allows patterning periodicstructures with a pitch down to 16 nm. It is based on focused ion beammillingof suspended membranes, with minimal proximity effects typical to standardelectron beam lithography. The membranes are then transferred and used ashard etching masks. We benchmark our technique by electrostatically indu-cing a superlattice potential in graphene and observe bandstructure mod-ification in electronic transport. Our technique opens the path towards therealization of very short period superlattices in 2D materials, but with theability to control lattice symmetries and strength. This can pave the way for aversatile solid-state quantum simulator platform and the study of correlatedelectron phases.Nanoscale fabrication is at the heart of the technological revolution ofsemiconductor technology and scientific breakthroughs in nano-technology, progressing rapidly for more than five decades1. Accord-ingly, the push to further improve nanofabrication techniques is anongoing effort to fit more electronic components per unit area or todevelop quantum devices and quantum bits, relying on quantumcoherent control in the nanoscale regime2,3. Another important appli-cation is in quantum materials, where materials’ properties can betuned in situ. Arrays of quantum dots with sufficiently large Coulombinteractions could lead to the observation of metal-Mott insulatorquantum phase transitions and potentially even the d-wave super-conducting phase4. Recent discoveries of correlated phases in twistedbilayer graphene due to the superlattice (SL) potential5,6 motivatefurther exploration of graphene SLs with more versatility in the latticedesign and in situ control.Nanofabrication techniques always involve a trade-off betweenpatterning resolution, throughput and flexibility. For example, scan-ning tunneling microscopy, can be utilized to rearrange materials onthe atomic scale7,8, but is impractically slow for micron-scale litho-graphy. Other techniques, such using self-assembled polymers, canachieve high resolution and yield9, at the expense of limiting designflexibility in what patterns can be implemented. A higher throughputalternative is ultraviolet optical lithography, the main lithographytechnique in the semiconductor industry, which is faster but is notsuited for academic research and development.In academic research, the most common nanopatterning techni-que is basedonelectronbeam lithography (EBL), which canbe thoughtof as a compromise offering reasonable throughput and nanoscaleresolution. Forward scattered electrons limit the minimal patternablefeature size, while secondary electrons due to (inelastic scattering)Received: 9 August 2022Accepted: 4 November 2022Check for updates1ICFO—Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain. 2Research Center forFunctional Materials, National Institute for Materials Science, Tsukuba, Japan. 3International Center for Materials Nanoarchitectonics, National Institute forMaterials Science, Tsukuba, Japan. 4ICREA—Institució Catalana de Recerca i Estudis Avançats, 08010 Barcelona, Spain. e-mail: frank.koppens@icfo.euNature Communications |         (2022) 13:6926 11234567890():,;1234567890():,;http://orcid.org/0000-0002-6271-2244http://orcid.org/0000-0002-6271-2244http://orcid.org/0000-0002-6271-2244http://orcid.org/0000-0002-6271-2244http://orcid.org/0000-0002-6271-2244http://orcid.org/0000-0001-6515-181Xhttp://orcid.org/0000-0001-6515-181Xhttp://orcid.org/0000-0001-6515-181Xhttp://orcid.org/0000-0001-6515-181Xhttp://orcid.org/0000-0001-6515-181Xhttp://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0002-9418-7966http://orcid.org/0000-0003-0857-4466http://orcid.org/0000-0003-0857-4466http://orcid.org/0000-0003-0857-4466http://orcid.org/0000-0003-0857-4466http://orcid.org/0000-0003-0857-4466http://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/0000-0003-3701-8119http://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/0000-0001-9764-6120http://orcid.org/0000-0001-9764-6120http://orcid.org/0000-0001-9764-6120http://orcid.org/0000-0001-9764-6120http://orcid.org/0000-0001-9764-6120http://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-34734-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-34734-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-34734-3&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1038/s41467-022-34734-3&domain=pdfmailto:frank.koppens@icfo.euinteractions with the resist limit the pitch resolution. As such, usinghigh acceleration voltages and thin organic resists, patternswith 35 nmpitch can be obtained, but significant reduction of the feature size hasnot been demonstrated10–12.Another common nanofabrication approach uses focused-ionbeam (FIB) milling to pattern the target material directly. In particular,helium (He) FIB routinely achieves single digit single feature resolutionand pitch on the order of 10 nm13–18. However, two major limiting fac-tors affect He-FIB-based nanofabrication: (1) Milling of materialsdirectly on a substrate is accompanied by deposition of He bubblesinside the substrate, contaminating it and affecting surfacetopography18,19. (2) Secondary collisions damage the quality andintegrity of the patterned material19,20. It is possible to reduce thedamage by milling suspended materials (where substrate scattering isabsent) or using resist lithography17,21. However, suspending thematerial is complex and the amount of FIB induced unintentionaldamage is still expected to modify the material properties in the formof ion implantation and/or amorphization20,22–24. Here, we propose anddemonstrate a nanofabrication technique that combines the highresolution of He-FIB milling with minimal damage to the patternedmaterial.Our technique uses ultrathin suspended hard masks that areplaced in contact with the target substrate material. This alleviatesproximity effects and feature broadening induced by scattering fromthe substrate. The suspended ultrathinmask canbe subjected to harshFIB patterning with minimal proximity effects and later transferredonto the target material to project the pattern by reactive ion etching(RIE). The resolutionofourmethod is demonstrateddirectly byatomicforce microscopy (AFM), whereas the quality is demonstrated byapplying our technique to engineer SL potentials in graphene viapatterned graphite electrodes. Graphene could be very sensitive to thepresence of charge traps, impurities and patterning errors in the pat-terned gate electrode. However, transport data from our samplesindicates minor unintentional damage to the patterned electrodes,even for highly dense patterns with an 18 nm pitch. Similar to moirésystems (e.g. twisted graphene25 or graphene/hexagonal boron nitride(hBN) heterostructures26,27), it is possible to engineer SLs by applying aperiodic electrostatic potential28. When applied to low-dimensionalmaterials, such as graphene, thismodifies its electronic band structurewhen the SL period is much smaller than the electronic coherencelength29. Several approaches have been explored to introduce suchpotentials: from patterning the graphene directly12, to inducing aperiodic potential modulation by patterning the dielectric material30,31or the gate electrode32–34. In all cases, it is essential to reducedamage tothe patterned material, keeping it flat and free of external con-tamination. However, to realize the full potential of artificial SLs, a newlithographic technique is required, one which can create high qualityperiodic patterning on the sub-20-nm scale, approaching the moirélength in graphene aligned on hexagonal boron nitride or magic angletwisted bilayer grapheme (Fig. 1).Results and discussionIon-milled hard mask lithographyAs the hardmask, we use a poly-crystalline silicon suspended ultrathinmembrane (5–10 nm), which is commercially available on a large scaleand high quality. Importantly, the suspended membrane can beremoved from its supporting frame and transferred with a polymericstamp (Fig. 2b). The membrane is placed on top of a mechanicallyexfoliated target graphite flake, coated by a thin 22 nm layer ofpoly(methyl methacrylate) (PMMA) (Fig. 2c), which serves as a sacri-ficial layer for later removal of the membrane (we note it is possible toremove the membrane in other ways, namely etching, but we foundthe use of PMMA layer to be more robust, see Supplementary Note 3).Due to the nanometric thickness of the hard mask, the aspect ratio isnot a limitation and the feature size is only limited by the ion beammilling process. After the Ar/O2 RIE process, we remove the hardmask(Fig. 2d) with a standard acetone lift-off followed by vacuum annealingto remove polymer surface contamination. As a demonstration of thecapabilities of our technique, we achieve a triangular lattice with aperiod as small as 16 nm and a hole diameter down to ∼8 nm (Fig. 2e).To quantify the disorder of our lattices, we perform Fourier ana-lysis of the AFM images (Fig. 2f), finding less than 3% period variationsin our smallest lattices (16 nm period). By inspecting the transmissionelectronmicroscopy (TEM) images of our He-FIB milled silicon masks,we find a diameter of the holes of 13.2 ± 0.4 nm for a 22nm periodlattice, and thus the variation in diameter is only 2% and less than 6% inarea. To showcase the high quality achieved with our technique, weincorporate a patterned graphite gate into two different SL graphenedevices. Both are based on encapsulated single layer graphene with asquare periodic lattice pattern in the bottom gate electrode (Fig. 3a),but with different period—aSL =47 nm (Dev 1) and aSL = 18 nm (Dev 2),and different hBN spacer thickness—tBN =6:2 nm (Dev 1) and tBN = 3:2nm (Dev 2).Electronic transport measurementsFigure 3c shows a zoom-in of the AFM characterization of the pat-ternedgate electrodeofDev 1. The squareSL in single layer graphene isexpected to lead to the emergence of cloned Dirac cones equallyspaced in energy due to band folding in the mini-Brillouin zone32. Bytuning the silicon backgate voltage (Si BG) and the patterned gatevoltage (PBG), one canmodulate the strength of the SL and the carriertype in the graphene layer to observe the cloned Dirac cones, seeFig. 3e. When the Si BG is kept at 70V, two satellite peaks (indicatingcloned Dirac cones) for electrons and another two for holes are clearlyvisible, being roughly of the main size as the main Dirac peak. Thiscontrasts the situation where the Si BG is kept at 0 V, where we doexpect a very small density modulation and indeed no satellite peaksare observed. The carrier density is normalized by the number ofelectrons per SL unit cell, n=n0, and therefore, the spacing of thesatellite indicates the four-fold (spin and valley) degeneracy in gra-phene. The clear observation of multiple satellite peaks, and theirsimilar width and prominence compared to the main Dirac peak,Smallest pitch (nm)Electron beam lithographySample damage 20 40FIB on substrateFIB suspended mask (indirect patterning)(direct patterning)FIB suspended 2D 10Fig. 1 | Comparison chart of focused-ion beam (FIB) alternatives to standardelectron beam lithography (EBL) for 2D materials patterning. While FIBimproves the resolution limit of EBL, substrate damage has to be considered.Suspending the 2Dmaterial for the patterning process alleviates substrate swellingcompared to standard silicon wafer substrates but introduces disorder in thecrystalline lattice. As an alternative, indirect FIB patterning of a suspended mem-brane, later used as an etching mask for the 2D material, results in no substratedamage and still preserves the high resolution of suspended FIB patterning.Article https://doi.org/10.1038/s41467-022-34734-3Nature Communications |         (2022) 13:6926 2demonstrate the high quality of the device and the high uniformity ofthe patterned gate.The seconddevice studied in thiswork,Dev 2, has an 18 nmperiodsquare SL. To the best of our knowledge, there is no experimentalworkabout electrostatically inducedSLswith sucha shortperiodicity. In thiscase, there is a top gate electrode (TG) apart from the PBG. Thiscombination of gates allows us to control the SL strength and the totalcarrier density of the system independently. Therefore, we keep PBGfixed at certain voltages and sweep TG to change the carrier density. Inlongitudinal resistivity, we observe clear signatures of the emergenceof satellite peaks at n=n0 = ± 4, as PBG is increased (Fig. 3f).Furthermore,when the PBG is set at0 V (graydashed line in Fig. 3f), i.e.,no carrier density modulation, we do not observe any superlatticefeature. The observed dependence of the SL features on the PBGconfirms its electrostatic origin. We cannot completely discard thepossibility there is unintentional double alignment to the hBN flakes.This would be an additional effect on top of the electrostaticallyinduced SL. We discuss this possibility and show additional data inSupplementary Note 3 and 7.The prominence of the SL signature is different in the twodevices.To understand this, we must examine the specific characteristics ofboth devices. As a rough approximation for the electrostatic potentiala cbFLGPatterned FLG flakeMilled Si membraned12 nm8 nm20 nmfeFig. 2 | Fabrication process of a patterned few layer graphene (FLG) gateelectrode. a Transmission electron microscope (TEM) image of a thin suspendedsilicon membrane which has previously been milled with a He focused-ion beam(FIB).b Themembrane is transferred with a polypropylene carbonate (PPC) coatedpolydimethylsiloxane (PDMS) stamp onto a FLG flake coated with a thin layer ofpoly(methyl methacrylate) (PMMA). c The sample is etched following a standardO2/Ar reactive ion-etching (RIE) process, followed by a lift-off process to removethe membrane and clean the PMMA layer underneath (d). e Atomic force micro-scopy (AFM) topography image of a 16 nm period triangular lattice on a FLG flake.The scale bar is 50nm. f Fast Fourier transform (FFT) of a larger region of the sameAFM image in panel e, including 2555 lattice sites.101Rxy(k)8 4 0 4 8n/n00246xx(k) BG = 70VBG = 0Va c ebDev 1 - Square aSL = 47 nmSLGPBGSi BGTGDev 2 - Square aSL = 18 nmd f8 4 0 4 8n/n00100200300400xx()0.0 1.8PBG (V)5.0 2.5 0.0 2.5 5.0aSL (eVnm)0246810DoSa SL(eV1 nm1 )0123Ua SL(eVnm)Fig. 3 | Electronic transport characterization of devices Dev 1 and Dev 2.a Heterostructure schematic. The main difference between Dev 1 and Dev 2 is theuse of a graphite top gate in the latter. b Predicted normalized density of states persuperlattice (SL) length aSL, which demonstrates the invariance of the Diracequation with the product aSL and the potential modulation U � aSL. c, d Atomicforce microscopy (AFM) topography images of the patterned graphite gates usedfor each device. The scale bars are 50nm. e Longitudinal resistivity (red trace) andHall resistance at B=0:1 T (green trace) as a function of the electron density per SLunit cell for Dev 1 (silicon backgate voltage VBG = 70 V). Gray dashed traces displaylongitudinal resistivity and Hall resistance for VBG =0 V, i.e., when there is no SLmodulation. In the first situation, clear satellite peaks can be observed when thenormalized density n=n0 is a multiple of 4, with n0 corresponding to the densitywhere each SL unit cell is filled with one electron. This is consistent with the gra-phene´s four-fold degeneracy. f Longitudinal resistivity for Dev 2 as a function ofthe patterned bottom gate (PBG) applied. Satellite peaks emerge as well at nor-malized densities n=n0 = ±4:Gray dashed line indicates VPBG =0 V, for which nosatellite peak is observed.Article https://doi.org/10.1038/s41467-022-34734-3Nature Communications |         (2022) 13:6926 3modulation along the graphene layer for the formation of the SL, weconsider a periodic one-dimensional system with a patterned bottomgate, global top gate (more details in Supplementary Note 4), and 50%duty cycle gate/vacuum. Due to the linearity of the Poisson equation,the inducedmodulation of the electrostatic potentialU scales with theratio of the dielectric thickness tBN and the SL period aSL. We estimatefor Dev 1 (tBN=aSL =0:13) U ∼ 200meV, while for Dev 2 (tBN=aSL =0:18)U ∼ 120 meV. Furthermore, we need to consider the scaling of theDirac equation (Eq. 1). The larger the external potential term Uðx,yÞ iscompared to the unperturbed graphene HamiltonianH0, the strongerSL effects in the band structure will be:H=H0 +Uðx,yÞI ð1ÞSince themomentum at themini-Brillouin zone edge is inverselyproportional to the SL period aSL, decreasing aSL by a factor αenhances the unperturbed graphene term compared to the elec-trostatic potential term. In order to compensate for this enhance-ment, the external potential U x,yð Þ would need to be larger by thefactor α. At the same time, the energy of the system will scaleinversely proportional to α. As a result, the comparatively small Uand small aSL in Dev 2 makes that the effect of the electrostaticmodulation and, thus, the band structure modification in Dev 2 isweaker than that in Dev 1. Figure 3b displays the importance of theDirac invariant parameterU � aSL (∼9:4 for Dev 1 and ∼ 2:2 for Dev 2)on the density of states.Magneto-transport measurementsFurther evidence of the modified band structure is given in Fig. 4,where the gate voltage configurations are the same as in Fig. 3. For Dev1 (aSL =47 nm), Landau fans emerge from the satellite peaks at fillingfractions n=n0 =0, ± 4, ± 8. Given the relatively large period comparedto typical moiré systems, it is possible to reach one quantum of mag-netic flux inside the SL unit cell. We also observe resistance dips atinteger fractions of the flux quanta ϕ=ϕ0 = 1=3,1=2,1, indicated by redarrows. They could be attributed Brown-Zak oscillations35,36, but fur-ther investigation would be needed in order to confirm this. For Dev 2(aSL = 18 nm), apart from the LL spectra emerging from chargeneutrality, twoother fans converge to densities n=n0 = ± 4. This is solidevidence for our device’s 18 nm period SL formation. Understandingthe origin of additional oscillations between n=n0 =0 and n=n0 = � 4at finite magnetic field is subject of future work.DiscussionTo conclude, we have successfully demonstrated a nanofabricationtechnique that strongly alleviates proximity effects allowing to gobeyond the spatial resolution limits of EBL. We used this technique toinduce a SL potential in single layer graphene devices. To demonstratethe formation of the SL, we have presented electron transport datashowing satellite peaks corresponding to cloned Dirac cones, Hof-stadter butterfly spectrum, and Landau levels emerging from thesatellite peaks. To the best of our knowledge, the dimension of oursmaller SL with aSL = 18 nm sets a record, enhancing by a factor of fourthe relevant Coulomb interaction strength / 1=a2SL12,30–32.However, there are limitations in the nanopatterning process thatremain to be improved in future works. In particular, it remains chal-lenging to pattern long lines or closed shapes, such as rings, due to thesuspended nature of the masks. Furthermore, the use of a PMMAsacrificial layer and the substrate back-scattered ions during the RIEcould be sources of damage and contamination in our samples,despite the cleaning efforts. Possible routes, such as adding anhBN flake at the bottomof the patterned gate12, or integrate the siliconmask directly in the heterostructure, could improve the processquality.The ability to engineer arbitrary lattice geometries opens the pathtoward studying non-bipartite lattices37 and flat bands in Dirac andgapped Dirac systems, such as the Lieb or Kagomé lattices, whichrequire superior spatial resolution compared to patterned SLsachieved thus far. Furthermore, our technique enables a new genera-tion of Fermi-Hubbard model simulators38 when combining our pat-terned gate electrodes with 2D tunable semiconductors such astransitions metal dichalcogenides39 or bilayer graphene40,41. Combin-ing the patterned gate with a second gate allows the carrier filling andthe Hubbard on-site interaction strengthU to be tuned independently.The superior quality of our nanopatterning process will make it pos-sible to engineer lattices where the Hubbard U can reach theDev 2 - Square aSL = 18 nm Dev 1 - Square aSL = 47 nm (4,2)(4,10)(4,6)(-4,-2)(-4,-10)(-4,-6)(4,-2) (4,2) (4,6)(4,10)(-4,-2)(-4,-6)(-4,-10)(-8,-10)(-8,-6)ϕ/ϕ0=1 ϕ/ϕ0=1/2 ϕ/ϕ0=1/3 Fig. 4 | Longitudinal magneto-resistance measurements of devices Dev 1 andDev 2. For Dev 1 (VBG = 70 V), we observe a rich Hofstadter butterfly where Landaufans emerge from filling fractions n=n0 = 0, ± 4, ± 8. Red arrows indicate resistancedips corresponding to an integer fraction of the flux quantumϕ=ϕ0 = 1=3,1=2,1. ForDev 2 (VPBG = 1:4 V), Landau fans emerge from n=n0 =0, ± 4. These are solid evi-denceof the formationof an 18 nmperiod superlattice (SL). Colored linesbelowthemagneto-resistancemaps indicate the observed Landau fans. Labels indicate the SLfilling fraction and Landau level ðn=n0,LLÞ.Article https://doi.org/10.1038/s41467-022-34734-3Nature Communications |         (2022) 13:6926 410–100meV range, such that exotic correlated phenomena can beengineered at comparatively high temperatures.MethodsHard mask FIB millingFabrication of the devices begins with commercially available poly-crystalline silicon membranes (US100-A05Q00, SiMPore). Prior tomilling in FIB, the membranes are annealed in a H2:Ar atmosphere, at400C, for 3 h. We find that this step of annealing greatly reducesmechanical strain in the Si membranes. On inspection in opticalmicroscope, the membranes appear slightly wrinkled before theannealing process, whereas after annealing themembranes noticeablyflatten.The membranes are mounted on a hole in the sample holder, toimprove imaging contrast and loaded into the He focused-ion beammicroscope (HIM). The HIM is then aligned to high precision onmetallic features in the sample, with typical parameters being 5μT Hepressure, 10 or 20 μm aperture and spot control between 3 and 5. Thisyields a beam current between 2 and 12 pA and resolution between∼ 2 and 10 nm (determined by visualizing sharp edges and features),with the exactmilling parameters determined tomatch the achievableresolution with the desired periodicity of the pattern. Notably, the useof relatively high currents allows fastermilling and reducesmechanicaldrift and similar undesirable effects.After initial alignment, the membrane area is located in the HIM(the thin membrane shows clear contrast with the thicker, more con-ductive, background surrounding it). The sample is usually allowed torest for 30–90min (overnight when time allows), to minimize theeffects of piezo drift in the sample stage. Following this resting periodand additional finer alignment, the membrane is milled using a pre-programmedpoint-by-point deflection list. For large features, amillingdose comparable to 0.9 nCμm�2 is used. For smaller features, andespecially when the lattice period approaches the HIM resolution (forthe specific parameters used), the milling dose is optimized via demopatterns, wheremilling is typically sequential (single repeat rather thanmultiple repeats). The size of the milled area is typically kept on theorder of 3 × 3 μm2 in accordance with experimental needs. After mil-ling the desired patterns, 20 nm wide cuts are made to the side of themembrane, leaving it partially connected to the frame via 3–4μmwideconnecting bridges. These cuts facilitate breaking the membrane laterduring the transfer process.In addition to the majority of the samples produced during ourresearch, using He-FIB, we were also able to produce similar results(but with larger milling periods) using a Gallium focused-ion beammicroscope (Ga FIB). These samples were processed similarly to theabove described samples milled by HIM, with the exception being thatthe membrane was mounted with the window facing down (situatedabove a hole in the sample holder), in order to facilitate locating theintendedmilling areawith the FIB. The resolution of the specific Ga FIBmicroscope used in our experiments was restricted by various tech-nical issues, limiting the size of the spot effected by the Ga ions toabout 20 nm and the lattice period to the order of 50nm. With a morenarrowely focused FIB, we estimate, based on our experience, that a~10 nm single feature and ~30 nm lattice period should be achievable.Device fabricationThe fabrication process of the patterned graphite gate is explained inthe main text. After the cleaning process, we prepared an hBN/gra-phene/hBN (hBN/graphene/hBN/graphite/hBN in the case of Dev 2)heterostructure. We first dropped it on a clean Si/SiO2 substrate at atemperature of 158 °C to clean its interfaces, and subsequently tem-perature was increased to 180 °C to melt the poly (bisphenol A car-bonate) (PC) film42. After dissolving the PC film in chloroform, theheterostructure quality is checked through AFM imaging and Ramanspectroscopy. Finally, the heterostructure is again picked up andreleased following the sameprocedureon the patterned graphite gate.It is important to note that the hBN flakes between the graphene layerand the patterned gate electrode must be thin to allow for efficientdoping modulation.Standard EBL is used to pattern the Hall bar geometry and makeone-dimensional edge contacts43 to our heterostructure. In the case ofthe contacts, since they are right on topof thepatternedgraphiteflake,we perform first an SF6 etching process44 to remove only the top hBN,followed by anO2/Ar etching to remove the graphene, but not the thinbottom hBN that will prevent leakage current between the bottomgraphite gate and the electrodes. We deposit Cr(3 nm)/Au(40nm)followed by a lift-off in acetone.Electronic transport measurementsElectrical measurements were performed in a He flow cryostat fromICE Oxford operating at T = 1:45 K. Measurements were taken usingstandard lock-in techniques. A constant current of 5–20 nA wassourced by using a 10 MOhm resistor in series with our device atfrequencies 11–18Hz. Si BG, PBG, TG were controlled independentlywith a source meter.AFM images processingTo remove substrate height variations,we apply a highpassfilterwith acut off frequency f = 1=3�f aSLby performing a 2D fast Fourier trans-form. See Supplementary Note 8 for an example of the pre-processedand post-processed images.Data availabilityRelevant data supporting the key findings of this study are availablewithin the article and the Supplementary Information file. All raw datagenerated during the current study are available from the corre-sponding author upon request.References1. Theis, T. N. & Wong, H.-S. P. The End of Moore’s Law: a newbeginning for information technology. Comput. Sci. Eng. 19,41–50 (2017).2. Polini, M. et al. Materials and devices for fundamental quantumscience and quantum technologies. Preprint at http://arxiv.org/abs/2201.09260 (2022).3. Lemme, M. 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H.H.S. acknowledgesfunding from the European Union’s Horizon 2020 programmeunder the Marie Skłodowska-Curie grant agreement Ref. 843830.H.A. acknowledges funding from the European Union’s Horizon2020 research and innovation program under the MarieSkłodowska-Curie grant agreement no. 665884. R.K.K. acknowl-edges the EU Horizon 2020 program under the Marie Skłodowska-Curie grants 754510 and 893030. L.V. acknowledges funding fromthe H2020-MSCA-IF-2019 [887367-NanoMagnO]. A.B. acknowl-edges support from ERC Advanced Grant No. 692876 and MICINNGrant No. RTI2018-097953-B-I00, the European Union’s Horizon2020 research and innovation programme under the MarieSkłodowska-Curie grant agreement No. 847517 and 101023289,AGAUR (Grant No. 2017SGR1664), the Quantera grant (PCI2022-132951), the Fondo Europeo de Desarrollo, Recovery, Transforma-tion and Resilience Plan-Funded by the European Union-NextGenerationEU and Quantum CCAA. F.H.L.K. acknowledgessupport by the ERC TOPONANOP (726001), the Government ofSpain (PID2019-106875GB-I00), and Generalitat de Catalunya(AGAUR, SGR 1656). Furthermore, the research leading to theseresults has received funding from the European Union’s Horizon2020 under grant agreement no. 881603 (Graphene flagship Core3) and 820378 (Quantum flagship).Author contributionsAll authors contributed to writing the manuscript. H.H.S. fabricated thesiliconmasks, and D.B.R. and R.H. fabricated the devices, with help fromH.A. Measurements were taken by D.B.R. with help from R.K.K., L.V., andH.H.S. D.B.R. and H.H.S. performed the data analysis. T.T. and K.W.provided the hBN crystals. I.T. performed the electrostatics and bandstructure calculations. F.H.L.K. and A.B. supervised the work.Competing interestsThe authors declare no competing interests.Article https://doi.org/10.1038/s41467-022-34734-3Nature Communications |         (2022) 13:6926 6http://arxiv.org/abs/2206.13501https://arxiv.org/abs/2210.05827https://arxiv.org/abs/2210.05827Additional informationSupplementary information The online version containssupplementary material available athttps://doi.org/10.1038/s41467-022-34734-3.Correspondence and requests for materials should be addressed toFrank H. L. Koppens.Peer review information Nature Communications thanks Carlos For-sythe and the other, anonymous, reviewer(s) for their contribution to thepeer review of this work. 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To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.© The Author(s) 2022Article https://doi.org/10.1038/s41467-022-34734-3Nature Communications |         (2022) 13:6926 7https://doi.org/10.1038/s41467-022-34734-3http://www.nature.com/reprintshttp://creativecommons.org/licenses/by/4.0/http://creativecommons.org/licenses/by/4.0/ Engineering high quality graphene superlattices�via ion milled ultra-thin etching�masks Results and discussion Ion-milled hard mask lithography Electronic transport measurements Magneto-transport measurements Discussion Methods Hard mask FIB milling Device fabrication Electronic transport measurements AFM images processing Data availability References Acknowledgements Author contributions Competing interests Additional information