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Matthew Yankowitz, [K. Watanabe](https://orcid.org/0000-0003-3701-8119), [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), Pablo San-Jose, Brian J. LeRoy

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[Pressure-induced commensurate stacking of graphene on boron nitride](https://mdr.nims.go.jp/datasets/3ad78191-c383-4e1e-acca-800740ff9222)

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Pressure-induced commensurate stacking of graphene on boron nitrideARTICLEReceived 25 Apr 2016 | Accepted 8 Sep 2016 | Published 20 Oct 2016Pressure-induced commensurate stacking ofgraphene on boron nitrideMatthew Yankowitz1,w, K. Watanabe2, T. Taniguchi2, Pablo San-Jose3 & Brian J. LeRoy1Combining atomically-thin van der Waals materials into heterostructures provides apowerful path towards the creation of designer electronic devices. The interactionstrength between neighbouring layers, most easily controlled through their interlayerseparation, can have significant influence on the electronic properties of these compositematerials. Here, we demonstrate unprecedented control over interlayer interactions by locallymodifying the interlayer separation between graphene and boron nitride, which we achieve byapplying pressure with a scanning tunnelling microscopy tip. For the special case of aligned ornearly-aligned graphene on boron nitride, the graphene lattice can stretch and compresslocally to compensate for the slight lattice mismatch between the two materials. We findthat modifying the interlayer separation directly tunes the lattice strain and inducescommensurate stacking underneath the tip. Our results motivate future studies tailoringthe electronic properties of van der Waals heterostructures by controlling the interlayerseparation of the entire device using hydrostatic pressure.DOI: 10.1038/ncomms13168 OPEN1 Physics Department, University of Arizona, Tucson, Arizona 85721, USA. 2 National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.3 Instituto de Ciencia de Materiales de Madrid (ICMM-CSIC), Cantoblanco, 28049 Madrid, Spain. w Present Address: Department of Physics, ColumbiaUniversity, New York, NY 10027, USA. Correspondence and requests for materials should be addressed to B.J.L. (email: leroy@physics.arizona.edu).NATURE COMMUNICATIONS | 7:13168 | DOI: 10.1038/ncomms13168 | www.nature.com/naturecommunications 1mailto:leroy@physics.arizona.eduhttp://www.nature.com/naturecommunicationsThe electronic properties of heterostructures of van derWaals (vdW) materials are expected to depend on theexact nature of the interactions between the compositelayers. Previous work has focused on controlling the propertiesof these systems through the choice and ordering of thematerials in the heterostructure, as well as the rotationalalignment between layers1, but little has been done to explorethe interlayer separation degree of freedom. In bilayer graphene,for example, the electronic coupling between the two layersdepends exponentially on their separation2, controlling theeffective mass of the charge carriers and the magnitude of thefield-tunable band gap3. For graphene on atomically-heavymaterials, such as WSe2 or topological insulators, the strongsubstrate spin–orbit interaction (SOI) is predicted to stronglyenhance the SOI in the graphene and possibly inducetopologically non-trivial insulating states4,5. The predictedmagnitude of the SOI in the graphene also depends criticallyon the interlayer separation in such structures. Less immediatelyapparent, modifying the interlayer separation through pressurecan also induce a commensurate match between two crystals withslight lattice mismatch at equilibrium.Graphene on hexagonal boron nitride (hBN) is an excellenttestbed for this effect, as a long-wavelength periodic interactionemerges when the two crystals are in near-rotational alignmentdue to their small lattice mismatch (dB1.8%) (refs 6–8).This moiré pattern spatially modulates both the electroniccoupling, and the vdW adhesion between the graphene andhBN lattices. The periodic modulation of the electronic potentialleads to secondary Dirac cones in the graphene spectrum9, whilethe modulation of the adhesion potential is expected to produceperiodic in-plane strains of the graphene lattice. The latter arisebecause the adhesion potential is stronger for carbon–boron(CB) stacking than for any other lattice alignment. As a result,the graphene lattice expands locally around CB-stacked regionsto increase the area of this favored stacking. This occurs atthe expense of other stacking configurations, so that thetotal adhesion plus elastic energies is minimized10. A smallout-of-plane lattice corrugation matching the moiré also developsto minimize the total potential energy of the system11–13(Supplementary Note 4; Supplementary Fig. 7). Small electronicband gaps are expected to emerge for such a scenario, asthe sublattice symmetry of the graphene is slightly broken dueto the in-plane strain field10,12,14,15. A large enough enhancementof the adhesion modulation should cause the graphene tosnap into a globally commensurate CB-stacked phase (that is,graphene stretching uniformly to compensate for the latticemismatch with hBN). The resulting heterostructure is expectedto become a very high-mobility semiconductor with a sizable(B50–200 meV) band gap6,14. Importantly, the strength ofthe adhesion modulation is controlled directly by the interlayerseparation.Here we demonstrate a path towards achieving control overthis degree of freedom by demonstrating that pressure exertedby a scanning tunnelling microscope (STM) tip16–20 is capableof compressing or relaxing the interlayer separation locallybetween graphene and hBN. We also show that by modulatingthe interlayer separation we can control the degree of localcommensurate stacking and the in-plane strain of graphene. Thistechnique provides unprecedented control over the crystalstructure of a two-dimensional (2D) vdW heterostructure.ResultsLifting graphene with an STM tip. We first present evidenceof the out-of-plane movement of the graphene lattice producedby the tip, depicted schematically in Fig. 1b,c. We monitorthe tunnel current I as a function of the relative tip-sampleseparation Dz. The tunnelling current is expected to scaleexponentially with Dz asI / e�Dzffiffiffiffiffi8mf‘2p; ð1Þwhere m is the electron mass and f is the tunnel barrier height.This exponential approximation holds well for graphene on SiO2,but fails for graphene on hBN (Fig. 2a), independent of relativerotation angle (Supplementary Note 2 and Supplementary Fig. 3).In the latter case, I(Dz) becomes strongly dependent on thespecific tunnelling parameters, with the tunnel current decay(AA/CN)Contracted(CB)Expanded(AA/CN)ContractedhcorrhmaxhmaxabcdFigure 1 | Schematic of graphene on hBN and the influence of an STM tip.(a) Schematic of an aligned graphene on hBN heterostructure. Due to thespatially modulated vdW adhesion potential, the graphene lattice periodicallyexpands and contracts in-plane. An out-of-plane corrugation profile alsodevelops, both matching the moiré. (b) In the presence of an STM tip, a vdWadhesion between the tip and graphene lifts the graphene off the surface ofthe hBN, modifying the strain field. (c) For an STM tip very close to thesurface, the graphene is pushed closer to the hBN, enhancing the differencein the adhesion potential for different stacking configurations. The graphenelattice then expands to match the slightly longer lattice constant of the hBN.(d) Top view of (c), where the STM tip sits in the centre of a moiré period(that is, over a CB stacking configuration). The graphene lattice expandslocally (red) to match the hBN lattice. Both the lattice constant and thespatial deformation have been scaled up for better visibility.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms131682 NATURE COMMUNICATIONS | 7:13168 | DOI: 10.1038/ncomms13168 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsgrowing slower as the tip distance is brought closer to the surface.Furthermore, the decay is initially quadratic rather thanexponential. Figure 2b shows a similar measurement with thetunnel current plotted on a logarithmic scale, further highlightingthe initial regime of non-exponential decay. The departure fromequation 1 implies that the graphene is moving with the STMtip as it retracts from the sample, owing to a vdW attractionbetween the graphene and the tip. The vdW adhesion isapparently stronger between the tip and graphene than betweenthe graphene and hBN, as evidenced by a visible I(Dz) hysteresisbetween tip approach and tip retraction (Supplementary Fig. 3).This allows the tip to modify the interlayer separation (whileconversely, the graphene is more strongly adhered to the SiO2substrate and is relatively immobile).To account for the additional out-of-plane movement of thegraphene sheet, we substitute Dz in equation 1 with Dz� zg(z),where zg(z) represents the movement of the graphene relative tothe hBN substrate as a function of the tip position z. We plot therelative movement of the graphene in Fig. 2c, assuming aneffective barrier height f¼ 4 eV, as extracted from measurementsacquired at large tip-sample separations. The tip initially lifts thegraphene away from the hBN as it retracts. After around 2 Å ofretraction, the tip is no longer able to continue pullingthe graphene, which then begins to slowly relax back towardsthe hBN substrate, as it is still under the influence of a vdW forcefrom the tip19. It is important to note that the graphene is initiallypushed towards the hBN by the tip, so the equilibrium separationlies somewhere at zg40. The blue and black curves in Fig. 2b,care taken in the centre and along the boundaries of the moiré,respectively, and exhibit a spatial variation in the maximumpulling amplitude of the tip. The variations can be furtherhighlighted by plotting a spatial map of the tunnelling current at afixed tip retraction distance Dz, as in Fig. 2d. The spatial variationin the current matches the topographic moiré pattern, suggesting120100806040200z g (pm)43210Δz (Å)110100I (pA)43210Δz (Å)a bc d100806040200I (pA)1086420Δz (Å)Figure 2 | Tunnelling current as a function of tip-sample separation. (a) Measurement of the tunnel current I versus tip retraction distance Dz fornearly-aligned graphene on hBN, starting with the tip in close proximity to the sample. The dot-dashed blue curve is taken on graphene on SiO2 forreference, and exhibits the anticipated exponential decay. The remaining curves, from gold to black, represent decreasing sample bias (that is, moving thetip closer to the surface), from 1 to 0.05 V. The decay is initially parabolic, and the crossover point to exponential decay grows to larger Dz as the samplebias is lowered. (b) Similar decay measurement plotted on a log scale on a CB (blue) and CN/AA (black) region. The transition from parabolic to linearoccurs at Dz of about 2 Å. (c) Out-of-plane graphene movement relative to the hBN (zg) as a function of tip separation Dz. As the tip is initially retracted,the graphene moves with it, lifting away from the hBN. At just over 2 Å, a maximum pulling distance is reached, and on further tip retraction the grapheneslowly relaxes back towards the hBN. (d) Spatial map of the tunnelling current (dark is low and bright is high). The data are taken from the same set as in(b), at Dz¼ 3 Å. The inset displays the simultaneously acquired topography. The tunnelling current is smaller in the moiré centres than along theboundaries, suggesting a spatial modulation in the ability of the tip to pull the graphene off the hBN substrate. The maps have been spatially-averaged(see main text). Note that a similar pattern is exhibited at all Dz, as the blue curve is always below the black in (b). The scale bar is 5 nm for the main paneland 10 nm for the inset.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13168 ARTICLENATURE COMMUNICATIONS | 7:13168 | DOI: 10.1038/ncomms13168 | www.nature.com/naturecommunications 3http://www.nature.com/naturecommunicationsmodulations in the magnitude of the out-of-plane graphenepulling by the tip due to the underlying spatial modulations in theadhesion potential between the graphene and the hBN.Modifying commensuration with interlayer spacing. Therelative adhesion potentials between the CB, CN (carbon–nitrogen) and AA (hexagons atop one another) stacking config-urations depend on the interlayer separation between the twomaterials (Supplementary Note 4 and Supplementary Fig. 6).To understand how the in-plane strains in the graphene latticedepend on the interlayer separation, and to show how they canbe controlled through tip pressure, we have acquiredatomically-resolved topographic maps of nearly-aligned grapheneon hBN heterostructures (Fig. 3a) with varying tunnel resistance(which controls tip-sample separation and therefore the interlayerseparation). All measurements were performed in ultra-highvacuum at a temperature of 4.5 K. From a topographic map, wetake small (4� 4 nm2) areas, perform a Fourier transform(Fig. 3b), and extract the average length a of the three resonancesdue to the hexagonal graphene lattice. We then create a mapof the average graphene lattice constant normalized by theequilibrium length (a/a0, with a0¼ 2.46 Å) as a function ofposition (Fig. 3c). Finally, to enhance the clarity of these strainimages we average each point in the moiré unit cell with all otherequivalent sites in the strain image (Fig. 3d).Figure 4a–c shows spatially-averaged STM topography imagestaken over the same area of a nearly-aligned graphene on hBNsample with decreasing tip-sample separation. The hexagonalstacking boundaries in the measured moiré pattern grow sharperas the tip moves closer to the surface, exerting an increasingpressure. Below a critical tip separation, the stacking boundariesappear atomically and sub-atomically sharp, and a hysteresiseventually develops in their positions between the forward andbackward scan directions (Fig. 4c; Supplementary Fig. 1).This observation clearly points to a strong influence of the tipa bc dΔz (pm)0 18012060FFT (arb.)0 1a/a00.97 1.02Figure 3 | Method for generating strain maps. (a) Atomically-resolved topography of nearly-aligned graphene on hBN. The topography was acquired witha sample voltage of Vs¼0.3 V and a tunnelling current of It¼ 200 pA. (b) Fourier transform of a 4�4 nm2 region of (a), showing six resonancesrepresenting the hexagonal graphene lattice (red circles). The red arrows depict the measurement of the lattice constant in each direction. (c) Plot of theaverage length of the three lattice directions, as measured in (b) for each point in the topographic map. The points are normalized by the equilibriumgraphene lattice constant a0. (d) Spatially-averaged strain map, generated by averaging (c) over a few moiré unit cells. The scale bars are 10 nm for(a,c,d) and 10 nm� 1 for (b).ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms131684 NATURE COMMUNICATIONS | 7:13168 | DOI: 10.1038/ncomms13168 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationson the graphene lattice. If the sample were unperturbed bythe tip, the appearance of the topography, and in particular themeasured thickness of the stacking boundaries would correspondto the equilibrium sample configuration, and should not dependon the tip pressure except for a local density of states componentwhich can be eliminated (Supplementary Note 1). The graphenelattice strain maps for the different characteristic profiles of themoiré topography are shown in Fig. 4d–f. Like the topography,these are not equilibrium strain fields but rather local strainsunder the tip that dynamically evolve during the scan in responseto the moving tip interaction. We identify three typical andqualitatively different spatial patterns in this dynamical strain.Stacking boundaries can appear thick, but are expanded relativeto the CB regions (large tip-sample separations, Fig. 4d). This isopposite to the equilibrium expectation. Alternatively, boundariescan appear thin, and are compressed relative to CB regions(intermediate tip separations, Fig. 4e). Finally, boundaries canexhibit hysteretic behaviour and broken three-fold symmetry, andafedb cihg1.031.010.990.97a/a01007550250Δz(pm)Figure 4 | Topography and strain maps in different interaction regimes. (a–c) Spatially-averaged topography maps acquired over the same region of anearly-aligned sample, with the tip moving progressively closer to the sample. The appearance of the stacking boundaries becomes sharper as the tipmoves closer, and becomes hysteretic and asymmetric in (c). (d–f) Experimental spatially-averaged strain maps generated from the topographic maps of(a–c). In (d) the graphene lattice is compressed in the moiré centres and expanded along the boundaries. The opposite behaviour is observed in (e). In (f),the graphene lattice constant for the entire map is expanded, as the system is in a strongly interacting, hysteretic regime. (g–i) Simulated strain maps,showing excellent agreement with the experimental results. The disagreement in the dynamical strain at the stacking boundaries between (f) and (i) isattributed to the absence of out-of-plane buckling in the simulation. The tunnelling parameters are (a) Vs¼0.5 V and It¼ 50 pA, (b) Vs¼0.5 V andIt¼ 900 pA and (c) Vs¼0.05 V and It¼ 100 pA. All scale bars are 10 nm.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13168 ARTICLENATURE COMMUNICATIONS | 7:13168 | DOI: 10.1038/ncomms13168 | www.nature.com/naturecommunications 5http://www.nature.com/naturecommunicationsthe entire graphene lattice is expanded relative to equilibrium(smallest tip separations, Fig. 4f). The response of the sample tothe tip is so strong that, within the limits of our STMmeasurements, it is never possible to measure the equilibriumconfiguration of the heterostructure (that is, even at very largetip-sample separations, the graphene is still lifted off the hBN).The apparently sharp boundaries in Fig. 4c in particular, alsoobserved in our previous work21, are therefore not an equilibriumconfiguration.Interestingly, we observe qualitatively similar behaviour inslightly misaligned samples as well. Specifically, we observe thethree different strain profiles as a function of tip-sampleseparation in all moiré areas studied with periods varying from14 nm (essentially perfect alignment) down to about 6 nm(below which the behaviour may persist, but our analysis is nolonger sensitive as the size of our Fourier transform windowbecomes comparable to the entire moiré unit cell). As an example,Supplementary Fig. 2 shows strain maps for an 8 nm moiréperiod. This observation is in stark contrast to the results of ref.22, the reasons for which will be discussed in our model belowand in Supplementary Note 6.Theoretical analysis. We have simulated the dynamical strain ofthe graphene lattice under a scanning tip using a simpleadhesion model between graphene and hBN (see Methods andSupplementary Note 4 for full details, as well as SupplementaryMovies 1–4 for animations). In our model, the graphene sticks toa parabolic tip, and can thus be locally compressed against orseparated away from the hBN substrate. Figure 4g–i shows thestrain maps obtained for decreasing tip-sample separations,which exhibit excellent agreement overall, both qualitatively andquantitatively with their experimental counterparts. The threecharacteristic spatial patterns arise naturally when the effectiveinteraction between the tip and the equilibrium stackingboundaries changes with z from attractive, to repulsive, and tostrongly repulsive. In the attractive regime, the graphene underthe tip is lifted off the hBN surface, lowering the adhesionpotential. The stacking boundaries are then attracted to thescanning tip, and as a result the graphene lattice appears to beexpanded along the stacking boundaries (Fig. 4g). In the repulsiveregime, the tip is pushing down on the sample, increasing theadhesion energy modulation. The CB-stacked regions thenbecome expanded under the tip, up to the maximum static valuea/a0¼ 1þ d (local commensurate stacking) at high pressure, andthe stacking boundaries are pushed away (Fig. 1d for a schematicof the graphene lattice strain when the tip sits above theCB centre of the moiré). As the tip scans the sample, thecommensurate area underneath (red in the schematic) moveswith it, and the stacking boundaries are likewise pushed along(Fig. 4h). If the tip pressure is strong enough, the stackingboundaries are pushed until, eventually, they irreversibly snapback under the tip (Fig. 4i). This abrupt snapping results in theobserved hysteretic behaviour with tip scan direction, and abreaking of the characteristic three-fold symmetry of the moirépattern (note that the expanded hysteretic boundaries thatdevelop in this regime may be explained by sudden out-of-planedelamination of graphene in front of the tip, a possibility notincluded in our model, see Supplementary Note 4).The notable success of our simulations in reproducing theexperimental dynamical strain maps allows us to confidentlyremove the tip from the simulations, to understand theequilibrium configuration of the graphene lattice. We find thatthe observed phenomenology is consistent with intrinsic adhesionpotential differences23,24 of VAA�VCB¼ 16 meV per grapheneunit cell, similar to the values from ab-initio calculations11.Importantly, our results are not consistent with an adhesionpotential difference of zero (nor an infinitely stiff graphenelattice). The corresponding strain of the graphene at equilibrium(without a tip) is rather weak, and varies almost sinusoidallybetween ±0.3% (Supplementary Fig. 10). This is in stark contrastto the dynamical strain maps, which may appear much sharperspatially and in excess of ±1%. These dynamical strain effects areimportant to consider in all scanning probe measurements ofgraphene on hBN (refs 9,22) (Supplementary Note 6).DiscussionWe have demonstrated unprecedented control of the atomicstructure of graphene by locally modifying the interactionstrength with an hBN substrate through pressure appliedwith an STM tip. This allowed us in particular to induce anddirectly image tunable in-plane strains and local commensuratestacking. While a globally commensurate graphene on hBNstructure is expected to exhibit an electronic band gap, we do notobserve any signatures of a gap in our tunnelling spectroscopymeasurements of the local density of states (SupplementaryNote 3) for any applied tip pressure. When the tip is far from thesample, such that it remains incommensurate, the tip likelyscreens the many-body interactions responsible for thedevelopment of the band gap typically observed in transportexperiments14,25,26. When the graphene is commensurate withthe hBN, the gap is expected to be of order 50 meV even beforethe consideration of potential many-body enhancement6.Therefore, it may seem surprising that we also do not observe aband gap in tunnelling spectroscopy even in the case where thetip is very close to the sample, such that the graphene iscommensurate with the hBN underneath the tip. However, thelack of observed band gap is a consequence of the local nature ofthe applied pressure in our experimental setup. A gap ofmagnitude D corresponds to the localization of states of typicalwavelength lD¼ hvF /D2. For the anticipated band gap DE50 meV,states must be localized on length scales of order 100 nm. In ourwork, our model predicts that the area of the graphene forced intoa commensurate state with the hBN is confined to approximatelyone moiré period, of order 10 nm (Fig. 1d). Thus, the lack of aband gap in tunnelling spectroscopy is to be expected because thecommensurate area is considerably smaller than the requisitelocalization area (Supplementary Notes 3 and 5 for further detailsabout the tunnelling spectroscopy measurements and theirtheoretical modelling).This suggests a natural extension of our work, where agraphene sheet is forced into a commensurate state with hBNover the entire sample area. Fortunately, the technique ofapplying pressure to a vdW heterostructure is very easilygeneralizable to the scale of the entire device using hydrostaticor diamond anvil pressure cells. In graphene on hBN inparticular, we anticipate a globally commensurate state to emergeunder a hydrostatic pressure of roughly 150 MPa (SupplementaryNote 4 and Supplementary Fig. 8), characterized by the absence ofa moiré pattern and a large band gap due to globally brokensublattice symmetry in the graphene. More generally, globalcontrol of the interlayer separation through pressure in othervdW heterostructures should enable exciting new experimentaldesigns, and result in the emergence of many novel electronicdevice properties.MethodsSample preparation and measurement details. Chemical vapour depositiongrown graphene was transfered onto mechanically exfoliated hexagonalboron nitride resting on a Si/SiO2 substrate. The devices were annealed at 350 �C ina mixture of argon and hydrogen, then at 300 �C in air. Similar results toARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms131686 NATURE COMMUNICATIONS | 7:13168 | DOI: 10.1038/ncomms13168 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsthose reported here were observed in preliminary work with exfoliated grapheneflakes as well.All the STM measurements were performed in ultra-high vacuum at atemperature of 4.5 K using a tungsten tip. The tunnelling resistance was varied overfive orders of magnitude by controlling the sample bias and tunnelling current.We note that tip geometries are somewhat random between different tips, andbetween different tip shaping procedures on the same tip. Because the nature of thetip ending is also important for determining the interaction strength with thesubstrate, comparing tunnelling resistances between different measurements isnot itself a sufficient metric for determining the amount of compression orrelaxation of the graphene relative to the hBN.Tip preparation. Tungsten tips were prepared by electrochemical etching, andfurther shaped in situ when necessary by applying electrical pulses of 5–10 Von the Au contacts far from the graphene sample. The lattice deformation effectsdetailed here have been observed with every tip (tens of tips measured in total)and over tens of pulse cycles per tip. We note that qualitatively similar moiré scalelattice deformations have been observed in graphene on Ir(111) with AFMusing a tip intentionally terminated with a carbon monoxide molecule27. While wecannot rule out that a deformable tip could have some influence on our results,we are confident that the primary source of the effects we present can be explainedby our proposed model for a number of reasons. First, because we do notintentionally terminate our tips with a deformable molecule, it is very unlikely thatwe would observe similar results across all of our tips and pulse cycles if such adeformable tip ending were being randomly picked up every time. Second, thedeformable tip ending would have to be metallic to be relevant for our tunnellingmeasurements. While our samples may have water, hydrogen or other smallmolecule adsorbates, they should certainly be free of metallic contaminants tounintentionally attach to the end of every tip. Further, we observe our reportedbehaviour even with brand new tips, which are landed directly onto the graphene.Third, we observe sub-atomically sharp discontinuities in the topography only onthe moiré length scale (in contrast to previous reports showing such behaviour onthe atomic scale using a cobalt atom dragged across the surface of the sample28).No similar model can easily explain our observation of smooth atoms except atmoiré boundaries in the hysteretic regime, which would require a much longerdeformation length scale and a strong preference for irreversible topographicdiscontinuities only at special sites on the moiré. This suggests the discontinuitiesinstead arise from lattice deformations in the graphene at moiré boundariesas we argue in our model. Finally, we observe a saturation of the graphene latticeconstant expansion at just under 2% in the hysteretic regime (excluding theboundaries, which exhibit irreversible discontinuities), consistent with acommensurate structural transition (as this is roughly the lattice mismatchbetween graphene and hBN). We have never observed significantly larger latticedeformations. We would not anticipate such a bound if this effect were dueto a deformable tip, providing further compelling evidence that the apparentlattice deformations we observe are primarily due to a modification of the graphenelattice itself, as proposed in our model.Theoretical model. An overview of our theoretical model is as follows (seeSupplementary Note 4 for full details). The STM tip is approximated by a para-boloid of radius R around its apex, hovering at height h0 relative to a relaxedreference plane (taken as the graphene position at the CB-stacked regions—recallthat graphene is slightly corrugated due to non-uniform adhesion to hBN). Weassume that the vertical graphene displacement conforms to the tip profile as longas it does not exceed a certain height, hmax, see Fig. 1c. Otherwise graphene takes onthe equilibrium vertical displacements at each stacking. We assume a certain in-plane distortion u(r) of the sample, relative to the relaxed moiré pattern, which wewant to determine. We construct a smooth interpolation of the ab-initio adhesionpotentials VS(z) between different graphene/hBN stackings, where z is theseparation between the two crystals. Using the interpolated potential, we evaluatethe total adhesion energy per unit area for a given field u(r). At each r, the value ofz is constrained by the tip profile, as described above. To this adhesion energy, weadd the corresponding elastic energy associated to u(r). We discretize r, andexpress the total energy as a function of the finite set of u on the discrete mesh.We minimize the total energy, using conjugate gradient methods, and find thedeformation u(r) at equilibrium. We then obtain the dynamical strain as measuredby the tip by performing this sample relaxation as the tip moves across the sampleat a constant height h0. The model has no unconstrained free parameters, as all canbe roughly estimated experimentally.Data availability. The data that support the findings of this study are availablefrom the corresponding author on request.References1. Geim, A. K. & Grigorieva, I. V. Van der waals heterostructures. Nature 499,419–425 (2013).2. Trambly De, L. G., Mayou, D. & Magaud, L. Localization of Dirac electrons inrotated graphene bilayers. Nano Lett. 10, 804–808 (2010).3. McCann, E. & Koshino, M. The electronic properties of bilayer graphene.Rep. Prog. 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Controlling the dynamics of a single atom inlateral atom manipulation. Science 306, 242–247 (2004).AcknowledgementsWe thank J. Sanchez-Yamagishi and P. Jarillo-Herrero for a device measured during theearly development stages of this work. The work at Arizona was partially supported bythe U.S. Army Research Laboratory and the U.S. Army Research Office under contract/grant number W911NF-14-1-0653 and the National Science Foundation DMR-0953784.P. S.-J. was supported by the Spanish Ministry of Economy and Innovation through grantno. FIS2011-23713 and the Ramón y Cajal programme through grant no. RYC-2013-14645.Author contributionsM.Y. and B.J.L. designed the experiments. M.Y. fabricated the graphene on hBN devicesand performed the STM experiments. K.W. and T.T. provided the single crystal hBN.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms13168 ARTICLENATURE COMMUNICATIONS | 7:13168 | DOI: 10.1038/ncomms13168 | www.nature.com/naturecommunications 7http://www.nature.com/naturecommunicationsP.S.-J. performed the theoretical calculations. All authors participated in the datadiscussion and writing of the manuscript.Additional informationSupplementary Information accompanies this paper at http://www.nature.com/naturecommunicationsCompeting financial interests: The authors declare no competing financial interests.Reprints and permission information is available online at http://npg.nature.com/reprintsandpermissions/How to cite this article: Yankowitz, M. et al. Pressure-induced commensurate stackingof graphene on boron nitride. Nat. Commun. 7, 13168 doi: 10.1038/ncomms13168(2016).This work is licensed under a Creative Commons Attribution 4.0International License. The images or other third party material in thisarticle are included in the article’s Creative Commons license, unless indicated otherwisein the credit line; if the material is not included under the Creative Commons license,users will need to obtain permission from the license holder to reproduce the material.To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/r The Author(s) 2016ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms131688 NATURE COMMUNICATIONS | 7:13168 | DOI: 10.1038/ncomms13168 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationshttp://npg.nature.com/reprintsandpermissions/http://npg.nature.com/reprintsandpermissions/http://creativecommons.org/licenses/by/4.0/http://www.nature.com/naturecommunications title_link Results Lifting graphene with an STM tip Figure™1Schematic of graphene on hBN and the influence of an STM tip.(a) Schematic of an aligned graphene on hBN heterostructure. Due to the spatially modulated vdW adhesion potential, the graphene lattice periodically expands and contracts in-plane. An o Figure™2Tunnelling current as a function of tip-sample separation.(a) Measurement of the tunnel current I versus tip retraction distance Deltaz for nearly-aligned graphene on hBN, starting with the tip in close proximity to the sample. The dot-dashed blue Modifying commensuration with interlayer spacing Figure™3Method for generating strain maps.(a) Atomically-resolved topography of nearly-aligned graphene on hBN. The topography was acquired with a sample voltage of Vs=0.3thinspV and a tunnelling current of It=200thinsppA. (b) Fourier transform of a 4time Figure™4Topography and strain maps in different interaction regimes.(a-c) Spatially-averaged topography maps acquired over the same region of a nearly-aligned sample, with the tip moving progressively closer to the sample. The appearance of the stacking b Theoretical analysis Discussion Methods Sample preparation and measurement details Tip preparation Theoretical model Data availability GeimA. K.GrigorievaI. V.Van der waals heterostructuresNature4994194252013Trambly DeL. G.MayouD.MagaudL.Localization of Dirac electrons in rotated graphene bilayersNano Lett.108048082010McCannE.KoshinoM.The electronic properties of bilayer grapheneRep. Pro We thank J. Sanchez-Yamagishi and P. Jarillo-Herrero for a device measured during the early development stages of this work. The work at Arizona was partially supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under contracts ACKNOWLEDGEMENTS Author contributions Additional information