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C. R. Woods, F. Withers, M. J. Zhu, Y. Cao, G. Yu, A. Kozikov, M. Ben Shalom, S. V. Morozov, M. M. van Wijk, A. Fasolino, M. I. Katsnelson, [K. Watanabe](https://orcid.org/0000-0003-3701-8119), [T. Taniguchi](https://orcid.org/0000-0002-1467-3105), A. K. Geim, A. Mishchenko, K. S. Novoselov

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[Macroscopic self-reorientation of interacting two-dimensional crystals](https://mdr.nims.go.jp/datasets/e5b0df09-8f0c-4853-9ef8-e283facf8464)

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Macroscopic self-reorientation of interacting two-dimensional crystalsARTICLEReceived 5 Aug 2015 | Accepted 20 Jan 2016 | Published 10 Mar 2016Macroscopic self-reorientation of interactingtwo-dimensional crystalsC.R. Woods1, F. Withers1, M.J. Zhu1, Y. Cao1, G. Yu1, A. Kozikov1, M. Ben Shalom1, S.V. Morozov1,2,3,M.M. van Wijk4, A. Fasolino4, M.I. Katsnelson4, K. Watanabe5, T. Taniguchi5, A.K. Geim6, A. Mishchenko7& K.S. Novoselov1,7Microelectromechanical systems, which can be moved or rotated with nanometre precision,already find applications in such fields as radio-frequency electronics, micro-attenuators,sensors and many others. Especially interesting are those which allow fine control over themotion on the atomic scale because of self-alignment mechanisms and forces acting on theatomic level. Such machines can produce well-controlled movements as a reaction to smallchanges of the external parameters. Here we demonstrate that, for the system of grapheneon hexagonal boron nitride, the interplay between the van der Waals and elastic energiesresults in graphene mechanically self-rotating towards the hexagonal boron nitride crystal-lographic directions. Such rotation is macroscopic (for graphene flakes of tens of micrometresthe tangential movement can be on hundreds of nanometres) and can be used for repro-ducible manufacturing of aligned van der Waals heterostructures.DOI: 10.1038/ncomms10800 OPEN1 School of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, UK. 2 Institute of Microelectronics Technology and HighPurity Materials RAS, Chernogolovka 142432, Russia. 3 National University of Science and Technology ‘MISiS’, Moscow 119049, Russia. 4 Institute forMolecules and Materials,Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands. 5 National Institute for Materials Science,1-1 Namiki, Tsukuba 305-0044, Japan. 6 Centre for Mesoscience and Nanotechnology, University of Manchester, Oxford Road, Manchester M13 9PL, UK.7 National Graphene Institute, University of Manchester, Oxford Road, Manchester M13 9PL, UK. Correspondence and requests for materials should beaddressed to K.S.N. (email: kostya@manchester.ac.uk).NATURE COMMUNICATIONS | 7:10800 | DOI: 10.1038/ncomms10800 | www.nature.com/naturecommunications 1mailto:kostya@manchester.ac.ukhttp://www.nature.com/naturecommunicationsIn many layered crystals, it is the van der Waals interactionwhich is responsible for perfect stacking of individual layers.Once such perfect stacking is lost (for instance through arotational fault), the van der Waals interaction tends to restorethe perfect stacking—the effect known as self-rotation. This effecthas been seen for nanometre-sized graphene flakes when drivenby an atomic force microscopy (AFM) tip on the surface ofgraphite1. However, up to now, such phenomena has not beenobserved at micrometre or larger sizes, apart for the cases whensuch self-rotation was driven by surface free energy in displacedgraphite mesa structures2,3.One of the reasons why self-rotation is hard to observe inhomogeneous systems (where the two surfaces are represented bythe same crystals) is because both the self-rotating forces (whichtry to return the crystals to perfect stacking), and the frictionforces are essentially determined by the same van der Waalspotential. So, even when close to the perfect commensurate state(where the self-retracting forces should be the strongest), the vander Waals potential would exhibit a number of local potentialminima (which correspond to strong friction), where the systemmay get localized.The situation is very different when the two crystals are notidentical (for instance, have different lattice constants). In thiscase, the local minima in the van der Waals potential are notexpected to play such a significant role, because of strongincommensurability. In addition, if at least one of the crystals hasthe freedom to relax elastically, the van der Waals potential startsto compete with elastic energy, forming more complex potentiallandscape. Thus, it is interesting to investigate if the self-rotationcan be achieved in such heterogeneous structures.Such interfaces can be created by stacking severaltwo-dimensional (2D) atomic crystals into van der Waalsheterostructures4–6, with one of the most interesting systemsbeing graphene on hexagonal boron nitride (hBN)7, as the latticeconstants of the two crystals are different only by 1.8%. It hasbeen shown that graphene on hBN has an observable moirépattern, whose period depends on the misorientation angle8,9.Because of the difference in the interatomic distances for the twocrystals, the maximum moiré period (of B14 nm) is achievedwhen the crystallographic lattices are perfectly aligned. At smalldeviations from the alignment, graphene on hBN undergoes anincommensurate to commensurate transition10. In thecommensurate state, graphene splits into domains (where itslattice is stretched to gain in van der Waals interaction energywith hBN) separated by sharp domain walls (where graphenelattice is relaxed)10,11. Within the domain, the stretching isgradual, ranging11 from more than 1%, down to 0%. Thus, theaverage stretching of graphene is quite small (well below 1.8%),resulting in only a small lost in the elastic energy, which iscompensated by the gain in the van der Waals energy.Such stretching of graphene, even so being small, leads toglobal breaking of the sublattice symmetry12–14. Thus, thepossibility to align graphene and hBN is extremely important,and already led to the observation of a number of excitingphysical phenomena, such as Hofstadter butterfly15–17 andtopological currents18. Furthermore, the concept of self-alignment could be extended to other interfaces and utilized forthe formation of novel devices19–26, which rely on such alignedcrystals (for example, resonant tunnelling diodes27).Typically, the commensurate state is identified by a small (ofthe order of 0.1) ratio between the width of the domain walls (d)and the moiré period (L), whereas d/LE0.5 in the incommensu-rate phase.In the following, we demonstrate that, despite the strongcompetition between the elastic and van der Waals energies,graphene can reorient itself on top of hBN towards acommensurate state (where the crystallographic axis of the twocrystals are aligned better thanB0.7�).ResultsDemonstration of self-rotation for graphene on hBN.Graphene flakes, studied in this work, were transferred onto hBNby the dry transfer method28,29, to produce a clean interface(Fig. 1a). During the transfer procedure, we ensure (by directoptical observation of the crystallographic facets in the transferset-up) that the crystallographic directions of graphene and hBNare misoriented by y¼ 1–2�. We further confirmed themisorientation angle by measuring the period of the moirépattern in scanning probe experiments8–10 (Fig. 1b) as well as bythe width of Raman 2D peak (Fig. 2a), which can be related to theperiod of the moiré superstructure30 and the misorientationangle30 (Fig. 2b). Moiré patterns can be observed in variouschannels in AFM, including topography, friction and so on, aswell as in scanning tunnelling experiments8,9 and conductiveAFM15. Here we mainly used PeakForce Tapping mode31 andevaluated the point Young’s modulus channel with a typicalresolution better than 2 nm.282785800 10 20 3026250 10 20 30Position, nmedb caPosition, nmYoung's modulus, MPaYoung's modulus, MPaFigure 1 | Optical and atomic force microscopy of a self-rotating flake.(a) Optical microscopy image of the flake, demonstrating a very cleaninterface (bubble free) between graphene and hBN (the scale bar is 20mm).Different colours correspond to different thicknesses of hBN. Graphene ispractically invisible and is marked by red dashed line. The hatched area isbilayer graphene. (b,c) Young modulus distributions obtained in PeakForceTapping mode of the moiré superlattice before (b) and after (c) self-alignment. The scale bar in b and c is 10 nm. (d,e) Line profiles across therespective Young’s modulus distribution images, which indicates thesmaller width of the Young’s modulus peaks in the annealed (self-rotated)sample. Symbols—experimental data, solid curves—fitted peaks.ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms108002 NATURE COMMUNICATIONS | 7:10800 | DOI: 10.1038/ncomms10800 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsFigure 1a shows an optical image of one of our graphene onhBN structures (another example is given in SupplementaryNote 1). Originally, it has been aligned by yE1.0� with respect tothe hBN flake, as confirmed by AFM (Fig. 1b) and Raman(Fig. 2a,b). We would like to note that, even before annealing, thisflake approaches the commensurate state (d/L¼ 0.35, Fig. 1d).The sample was annealed at 200 �C for 4 h in forming gas(90% Arþ 10% H2). After annealing, L increases by 15%(from 10 to 11.5 nm, Fig. 1c), which indicates greater alignment(misalignment angle yE0.7�). Importantly, d/L¼ 0.20 afterannealing, which demonstrates an increased level of commen-suration (also confirmed by Raman, Fig. 2c,d). The alignment isuniform across the flake, which could be seen from the Ramansignal (Fig. 2b,d) or from the observation of the uniform moiréperiod by AFM measurements in different parts of the sample(see Supplementary Note 2 for details, and similar data foranother sample in Supplementary Note 1).We would like to stress that neither formation of creases norstrain accumulation have been observed after the annealing(as follows from our AFM and Raman measurements, respec-tively). To achieve such uniform alignment, the graphene flakeshould have uniformly rotated by Dy¼ 0.3�. It means that someparts of the flakes should have moved by d¼DylE0.15 mm(here lB30mm is the characteristic size of the flake). This is asignificant macroscopic movement, which can be used to drivecertain nanomachines (such a macroscopic motion is demon-strated in Supplementary Note 1, as well as has recently been seenby other groups as well32).Theoretical analysis. What pushes such macroscopic movementis the gradient in the van der Waals forces. To analyse their role,we compare, in Fig. 3, the interlayer van der Waals energy to theelastic intralayer contribution to the total energy after energyminimization for different alignments, relative to the values at 0�.The total energy does not vary up to 0.7�, after which theinterlayer energy interaction increases while the intralayer energydecreases, resulting in an increase of total energy. As all values areobtained from energy minimization for a given angle, thisfigure does not give information about the barriers betweendifferent angles.This picture fits remarkably well with our experimentalobservation. Our graphene flakes rotated to within 0.7� to thecrystallographic orientation of hBN, which correspondsnicely to the plateau in van der Waals energy misalignmentdependence for yo0.7�. Still, we note that in many previousexperiments8–10,15–17 the graphene flakes exhibit much betteralignment than 0.7�, which we would like to also attribute to theself-rotation mechanism.Appearance of one-dimensional wrinkling. We would like tostress that not all the flakes become aligned after annealing. Wehad a number of flakes that do not self-align. At the same time,those which do not undergo the self-rotation would typicallyform one-dimensional network of wrinkles (Fig. 4b), similar tothat reported previously33 (although in that case such wrinklesare formed upon cooling). Similar to the moiré pattern, thewrinkles could be observed in several AFM modes, although theyare most clearly visible in the local Young modulus and heightchannels (see Supplementary Note 3 for more examples). The factthat they are readily observable in the Young’s modulus channel,suggests strain accumulation around the wrinkles, which is alsoconfirmed by an increase in the full-width at half-maximum ofthe Raman 2D peak (Fig. 4e; in this case, the broadening isuniaxial, which reflects the fact that wrinkles predominantlycreate strain only in one direction, see Supplementary Note 4).Figure 4a,b shows the contrasting images in Young’s modulus ofthe moiré pattern before and after annealing to high temperature,respectively. The one-dimensional network of wrinkles is clearlyvisible on the sample after annealing to be superimposed on themoiré structure (Fig. 4b). At the same time, the period of themoiré structure has not changed. We would also like to suggestthat the wrinkles are most likely linked to the moiré structure, asseen from the orientation and the position of the peaks in theFourier transform patterns.The proposed mechanism for their formation is the following.At high temperature, because of the difference in the thermalexpansion coefficients between the hBN and graphene, the latticemismatch increases, favouring the incommensurate phase.Upon cooling, the same difference in thermal expansioncoefficient acts as a compression for graphene, possibly leadingto wrinkles (Fig. 4f). Also, the reconstructed moiré patternrecovers upon cooling, making the two structures (wrinkles and1.021FWHM of2D peak26 31ac21FWHM of2D peak26 310.5Counts, a.u.Counts, a.u.0.01.0db0.50.00.0 0.5 1.0�, degree�, degree1.50.0 0.5 1.0 1.5Figure 2 | Raman spectroscopy before and after self-rotation. (a,c) Mapsof the full-width at half-maximum of Raman 2D peak before and afterannealing, respectively (the scale bars are 10mm). (b,d) Histograms ofalignment angles, as recalculated from a and c, respectively.4Interlayer energyIntralayer energyTotal energy20210–10 2 4–20 10 20 30�, degree�, degreeEnergy, meV per atomEnergy, meV per atomFigure 3 | Calculated interaction energies for graphene on hexagonalboron nitride. Total energy (red circles) contributions from intralayer(elastic changes/blue triangles) and interlayer (adhesive/black squares)interactions, as a function of alignment angle, relative to the value at y¼0.Points are calculated by minimizing energy for a given angle. Inset: thesame curves for low misalignment angles.NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10800 ARTICLENATURE COMMUNICATIONS | 7:10800 | DOI: 10.1038/ncomms10800 | www.nature.com/naturecommunications 3http://www.nature.com/naturecommunicationsthe reconstructed moiré pattern) to coexist (Fig. 4g). However, asboth the domain walls of the reconstructed moiré pattern and thewrinkles carry strain field, it becomes energetically favourable tomake the two commensurate, overlapping the wrinkles and thedomain walls (Fig. 4h). Furthermore, the wrinkles can undergofurther reconstruction within the domains of stretched graphenethemselves (Fig. 4i). In this model, wrinkles should carryadditional strain, which indeed has been observed by strongbroadening of the Raman 2D peak (Fig. 4e). Such contribution tothe strain energy changes the potential landscape and, as it turnsout, prevents the self-alignment process.Finally, the presence of contamination bubbles and creasesseems to prevent the possibility of self-alignment. Self-alignmentwas not observed in any sample with more than a few bubbles.The detrimental influence of the bubbles can be twofold: itreduces the interaction area between graphene and hBN, makingthe van der Waals potential landscape shallower; also, thecontamination concentrated in such bubbles29 can act as pinningcentres, preventing any macroscopic movements of graphene.DiscussionOur observation opens a new direction in the physics andapplications of van der Waals heterostructures—self alignedstacks. Already now this effect is being used to produce graphenealigned on hBN for transport experiments (such as theobservation of Hofstadter effect15–17, topological currents dueto Berry curvature18 and so on). In such devices, the self-rotation could be in principle observed directly as shifting of thesecondary Dirac point and the associated with it resistance peak(see Supplementary Note 5 for details). We also expect that suchself-rotation is not unique to graphene/hBN stacks and that otherlayered materials should exhibit similar behaviour. For instance,in Supplementary Note 6, we present an example of theobservation of self-rotation in graphene/graphene stack beingseen via direct measurements of the electronic density of states intunnelling experiments. Furthermore, one can utilize themechanical motion of the crystals to produce nanomechanicaldevices. It is still unclear to what extent the surface reconstructionof the crystal influences the van der Waals potential—a subjectstill to be explored further both through experimental andtheoretical investigations.MethodsSample fabrication. Our samples were produced by the dry (‘stamp’) transfertechnique described in detail previously28,29,34. In brief, the method involves usinga double polymer layer to identify and isolate graphene flakes on a membrane,before bringing the graphene into contact with the hBN. Importantly, this methoddoes not require the use of any solvents, which minimizes the contamination.Sample characterization. AFM measurements were performed on a BrukerFastScan AFM, in the PeakForce31 feedback mode, which allows the extraction andanalysis of individual force curves for each pixel at regular scanning speeds(0.5–4 Hz). Typically, fast and large area scans are used to determine the period,whereas slower and smaller area scans are used to calculate the ratio d/L. Ramanspectroscopy measurements were taken with the Witec confocal Ramanspectrometer with a wavelength of 514 nm and 1 mW power.Details of theoretical analysis. For the calculation of the interaction energies, weconstructed a model of graphene on hBN with their crystallographic axis rotatedwith respect to each other. The hBN is kept fixed to mimic a bulk substrate. Notethat a different supercell has to be constructed at each misorientation angle(see Supplementary Note 7 for details). The size of the supercells with periodicboundary conditions demands the use of an empirical potential. The grapheneatoms interact through the reactive empirical bond order potential35, asimplemented in the molecular dynamics code large-scale atomic/molecularmassively parallel simulator (LAMMPS)36. This potential is widely used insimulations of carbon materials in view of its excellent description of structure andelastic properties of all carbon allotropes. As no potential for graphene/hBNinteraction is currently available, the interlayer interaction is assumed to be of theform of a registry-dependent potential for interlayer interactions in graphene37,without the correction for bending. We scale this potential to the lattice constant ofhBN and use different scaling factors for C–B and C–N interactions as was done inref. 11 because this leads to a good agreement with experimental results10 and ab-c dh32302826FWHM (2D), cm–1240 200Annealing temperature, °C400 600a bef giFigure 4 | Evidence of uniaxial straining in graphene on hexagonal boronnitride. (a,b) AFM images of the moiré superstructure in a sample whichdid not rotate before and after annealing to 600 �C, respectively. The scalebar in a and b is 10 nm. (c,d) The Fourier transformations of a and b areshown, respectively. The scale bar in c and d is 0.2 nm� 1. (e) Width of the2D peak in the Raman scattering spectrum as a function of annealingtemperature, the increase is linked to the formation of one-dimensional(1D) wrinkles. (f–i) Proposed structure of the superposition between themoiré pattern and the 1D wrinkles. At high temperatures, 1D wrinkles areformed due to difference in thermal expansion coefficients of graphene andhBN (f). Upon cooling, the moiré structure appears, which coexists with thewrinkle (g). It is more energetically favourable, however, for the 1D wrinklesto coincide with the domain walls of the moiré structure (h). Part of thewrinkle can be flattened because of commensurate–incommensuratetransition (i).ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms108004 NATURE COMMUNICATIONS | 7:10800 | DOI: 10.1038/ncomms10800 | www.nature.com/naturecommunicationshttp://www.nature.com/naturecommunicationsinitio calculations38,39. We have further refined this approach13 leading to a choiceof the B–C interaction of 60% of the C–C value, whereas the N–C interaction is setto 200% of the C–C value in the original form37. We minimize the total potentialenergy by relaxing the graphene layer by means of FIRE40, a damped dynamicsalgorithm. For samples close to alignment, this leads to significant changes in bondlength along the moiré pattern.References1. Filippov, A. E., Dienwiebel, M., Frenken, J. W. M., Klafter, J. & Urbakh, M.Torque and twist against superlubricity. Phys. Rev. Lett. 100, 046102 (2008).2. Liu, Z. et al. Observation of microscale superlubricity in graphite. Phys. Rev.Lett. 108, 205503 (2012).3. Yang, J. R. et al. Observation of high-speed microscale superlubricity ingraphite. Phys. Rev. Lett. 110, 255504 (2013).4. Novoselov, K. S. Nobel lecture: graphene: materials in the Flatland. Rev. Mod.Phys. 83, 837–849 (2011).5. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499,419–425 (2013).6. Novoselov, K. S. & Neto, A. H. C. Two-dimensional crystals-basedheterostructures: materials with tailored properties. Phys. Scr. T146, 014006(2012).7. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics.Nat. Nanotechnol. 5, 722–726 (2010).8. Xue, J. M. et al. Scanning tunnelling microscopy and spectroscopy of ultra-flatgraphene on hexagonal boron nitride. Nat. Mater. 10, 282–285 (2011).9. Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene onhexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).10. Woods, C. R. et al. Commensurate-incommensurate transition in graphene onhexagonal boron nitride. Nat. Phys. 10, 451–456 (2014).11. van Wijk, M. M., Schuring, A., Katsnelson, M. I. & Fasolino, A. Moire patternsas a probe of interplanar interactions for graphene on h-BN. Phys. Rev. Lett.113, 135504 (2014).12. Song, J. C. W., Shytov, A. V. & Levitov, L. S. Electron interactions and gapopening in graphene superlattices. Phys. Rev. Lett. 111, 266801 (2013).13. Slotman, G. J. et al. Effect of structural relaxation on the electronic structure ofgraphene on hexagonal boron nitride. Phys. Rev. Lett. 115, 186801 (2015).14. Wang, Z. et al. Strong interface-induced spin-orbit interaction in graphene onWS2. Nat. Commun. 6, 8339 (2015).15. Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices.Nature 497, 594–597 (2013).16. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect inmoire superlattices. Nature 497, 598–602 (2013).17. Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van derWaals heterostructure. Science 340, 1427–1430 (2013).18. Gorbachev, R. V. et al. Detecting topological currents in graphene superlattices.Science 346, 448–451 (2014).19. Yao, J. J. RF MEMS from a device perspective. J. Micromech. Microengin. 10,R9–R38 (2000).20. Suzuki, K. Micro electro mechanical systems (MEMS) micro-switches for use inDC, RF, and optical applications. Jpn J. Appl. Phys 41, 4335–4339 (2002).21. Cumings, J. & Zettl, A. Low-friction nanoscale linear bearing realized frommultiwall carbon nanotubes. Science 289, 602–604 (2000).22. Kim, S. H., Asay, D. B. & Dugger, M. T. Nanotribology and MEMS. NanoToday 2, 22–29 (2007).23. Hsu, S. M. Nano-lubrication: concept and design. Tribol. Int. 37, 537–545 (2004).24. Hedgeland, H. et al. Measurement of single-molecule frictional dissipation in aprototypical nanoscale system. Nat. Phys. 5, 561–564 (2009).25. Guerra, R., Tartaglino, U., Vanossi, A. & Tosatti, E. Ballistic nanofriction. Nat.Mater. 9, 634–637 (2010).26. Delrio, F. W. et al. The role of van der Waals forces in adhesion ofmicromachined surfaces. Nat. Mater. 4, 629–634 (2005).27. Mishchenko, A. et al. Twist-controlled resonant tunnelling ingraphene/boron nitride/graphene heterostructures. Nat. Nanotechnol. 9,808–813 (2014).28. Wang, L. et al. One-dimensional electrical contact to a two-dimensionalmaterial. Science 342, 614–617 (2013).29. Kretinin, A. V. et al. Electronic properties of graphene encapsulated withdifferent two-dimensional atomic crystals. Nano Lett. 14, 3270–3276 (2014).30. Eckmann, A. et al. Raman fingerprint of aligned graphene/h-BN superlattices.Nano Lett. 13, 5242–5246 (2013).31. Pittenger, B. B., Erina, N. & Su, C. in Application Note #128 (Bruker, 2012).32. Wang, L. et al. Evidence for a fractional fractal quantum Hall effect in graphenesuperlattices. Science 350, 1231–1234 (2015).33. Gallagher, P. et al. Switchable friction enabled by nanoscale self-assembly ongraphene. Nat. Commun. 7, 10745 (2016).34. Withers, F. et al. Light-emitting diodes by band-structure engineering in vander Waals heterostructures. Nat. Mater. 14, 301–306 (2015).35. Brenner, D. W. et al. A second-generation reactive empirical bond order(REBO) potential energy expression for hydrocarbons. J. Phys. Condens. Matter14, 783–802 (2002).36. Plimpton, S. Fast parallel algorithms for short-range molecular-dynamics. J.Comput. Phys. 117, 1–19 (1995).37. Kolmogorov, A. N. & Crespi, V. H. Registry-dependent interlayer potential forgraphitic systems. Phys. Rev. B 71, 235415 (2005).38. Sachs, B., Wehling, T. O., Katsnelson, M. I. & Lichtenstein, A. I. Adhesion andelectronic structure of graphene on hexagonal boron nitride substrates. Phys.Rev. B 84, 195414 (2011).39. Bokdam, M., Amlaki, T., Brocks, G. & Kelly, P. J. Band gaps inincommensurable graphene on hexagonal boron nitride. Phys. Rev. B 89,201404 (2014).40. Bitzek, E., Koskinen, P., Gahler, F., Moseler, M. & Gumbsch, P. Structuralrelaxation made simple. Phys. Rev. Lett. 97, 170201 (2006).AcknowledgementsThis work was supported by the Royal Society, US Army, European Research Council,EC-FET European Graphene Flagship, Engineering and Physical Sciences ResearchCouncil (UK), US Office of Naval Research, US Air Force Office of Scientific Research,FOM (The Netherlands). S.V.M. is supported by NUST ‘MISiS’ (grant K1-2015-046) andRFBR (14-02-00792). M.J.Z. acknowledges the National University of Defense Tech-nology (China) overseas PhD student scholarship.Author contributionsC.R.W. produced experimental devices, measured device characteristics, analysedexperimental data, participated in discussions, contributed to writing the manuscript;F.W., M.B.S. and Y.C. produced experimental devices; M.J.Z., S.V.M. and G.Y performedtransport measurements; A.K. contributed to Raman studies; M.M.vanW., A.F., M.I.K.provided theoretical support; K.W. and T.T. provided hBN. A.K.G. analysed experi-mental data, participated in discussions, contributed to writing the manuscript; K.S.N.initiated the project, analysed experimental data, participated in discussions, contributedto writing the manuscript; A.M. analysed experimental data, participated in discussions,contributed to writing 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: Woods, C. R. et al. Macroscopic self-reorientation of interactingtwo-dimensional crystals. Nat. Commun. 7:10800 doi: 10.1038/ncomms10800 (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/NATURE COMMUNICATIONS | DOI: 10.1038/ncomms10800 ARTICLENATURE COMMUNICATIONS | 7:10800 | DOI: 10.1038/ncomms10800 | www.nature.com/naturecommunications 5http://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 Demonstration of self-rotation for graphene on hBN Figure™1Optical and atomic force microscopy of a self-rotating flake.(a) Optical microscopy image of the flake, demonstrating a very clean interface (bubble free) between graphene and hBN (the scale bar is 20thinspmgrm). Different colours correspond to di Theoretical analysis Appearance of one-dimensional wrinkling Figure™2Raman spectroscopy before and after self-rotation.(a,c) Maps of the full-width at half-maximum of Raman 2D peak before and after annealing, respectively (the scale bars are 10thinspmgrm). (b,d) Histograms of alignment angles, as recalculated from  Figure™3Calculated interaction energies for graphene on hexagonal boron nitride.Total energy (red circles) contributions from intralayer (elastic changessolblue triangles) and interlayer (adhesivesolblack squares) interactions, as a function of alignment  Discussion Methods Sample fabrication Sample characterization Details of theoretical analysis Figure™4Evidence of uniaxial straining in graphene on hexagonal boron nitride.(a,b) AFM images of the moiré superstructure in a sample which did not rotate before and after annealing to 600thinspdegC, respectively. The scale bar in a and b is 10thinspnm.  FilippovA. E.DienwiebelM.FrenkenJ. W. M.KlafterJ.UrbakhM.Torque and twist against superlubricityPhys. Rev. Lett.1000461022008LiuZ.Observation of microscale superlubricity in graphitePhys. Rev. Lett.1082055032012YangJ. R.Observation of high-speed microscal This work was supported by the Royal Society, US Army, European Research Council, EC-FET European Graphene Flagship, Engineering and Physical Sciences Research Council (UK), US Office of Naval Research, US Air Force Office of Scientific Research, FOM (The ACKNOWLEDGEMENTS Author contributions Additional information