Twistable electronics with dynamically rotatable heterostructures
Rebeca Ribeiro-Palau, Changjian Zhang, Kenji Watanabe, Takashi Taniguchi, James Hone, Cory R. Dean
TTwistable electronics with dynamically rotatable heterostructures
Rebeca Ribeiro-Palau,
1, 2, ∗ Changjian Zhang ∗ ,
2, 3
KenjiWatanabe, Takashi Taniguchi, James Hone, and Cory R. Dean Department of Physics, Columbia University, New York, NY, USA Department of Mechanical Engineering, Columbia University, New York, NY, USA Department of Electrical Engineering, Columbia University, New York, NY, USA National Institute for Materials Science, 1-1 Namiki, Tsukuba, Japan
The electronic properties of two-dimensionalmaterials and their heterostructures can be dra-matically altered by varying the relative anglebetween the layers. This makes it theoreticallypossible to realize a new class of twistable elec-tronics in which device properties can be manip-ulated on-demand by simply rotating the struc-ture. Here, we demonstrate a new device archi-tecture in which a layered heterostructure can bedynamically twisted, in situ . We study grapheneencapsulated by boron nitride where at small ro-tation angles the device characteristics are dom-inated by coupling to a large wavelength Moir´esuperlattice. The ability to investigate arbitraryrotation angle in a single device reveals new fea-tures in the optical, mechanical and electronic re-sponse in this system. Our results establish thecapability to fabricate twistable electronic deviceswith dynamically tunable properties.
The weak van der Walls forces between the atomicplanes in 2D materials makes it possible to fabricate de-vices with arbitrary rotational order. This provides a newopportunity in device design where electronic propertiesare controlled by varying the relative twist angle betweenlayers [1]. Indeed several studies have established thatin heterostructures assembled from 2D crystals, electrontunneling between layers varies strongly with rotation[2–8]. In twisted bilayer graphene (two monolayers in directcontact but with an angle mismatch between the lay-ers) several novel phenomenon have been predicted andobserved, including topological valley transport [9–13],and superconductivity[14], as a consequence of angle-dependent interlayer coupling. Likewise, the formationof interlayer excitons in transition metal dichalcogenideheterostructures is highly sensitive to angle[15–17].The effect of rotational alignment between conduct-ing and insulating 2D layers can be equally significant.A remarkable example is provided by graphene coupledto hexagonal boron nitride (BN). Owing to the closelymatched lattice constants a large Moir´e superlattice de-velops near zero angle mismatch[18, 19]. This substan-tially alters the graphene band structure opening an en-ergy gap at the charge neutrality point (CNP) and cre-ating replica Dirac points at higher energies[20–22].Several techniques have been developed to fabricatelayered heterostructures with controlled rotation between the layers, including optical alignment of crystal edges[18, 20–22], rotational alignment [23] during assembly,and self-alignment through thermal annealing [24, 25]).However, in each case a priori understanding of the crys-tallographic orientation of each layer is required beforeassembly; motion between the layers during assemblymakes it difficult to achieve precise angle control; andmost significantly, once assembled the angle can not befurther modified. Here, we present a new experimentaltechnique that provides on-demand control of the orien-tation between layers in a van der Waals heterostruc-ture. We study a BN/graphene/BN structure where wedemonstrate in situ control over the length of the Moir´epotential and consequently achieve dynamic tunabilityof the optical, mechanical and electrical properties of thesystem.Figure 1a shows a cartoon schematic of our devicedesign. Using the mechanical assembly technique[26],graphene is placed on top of a large flake of BN, andthen etched into a Hall bar shape using oxygen plasma.The graphene layer is intentionally misaligned to this BN,producing a short-wavelength Moir´e potential that doesnot significantly alter the intrinsic graphene band struc-ture [27]. Next, a pre-shaped BN structure is transferredon top of the graphene. Finally, electrical contacts arepatterned onto the exposed leads of the graphene (seesupplementary information). Due to the low mechanicalfriction between graphene and BN, we are able to freelyrotate and translate this top BN layer using an atomicforce microscope (AFM). Pushing on one of the arms ofthe uppermost BN structure rotates this layer (Fig. 1b-d)changing its crystallographic orientation with respect tothe graphene layer. The Moir´e superlattice wavelength, λ , generated between these crystals is given by: λ = (1 + δ ) a (cid:112) δ )(1 − cos ( θ )) + δ (1)where δ = 0 .
017 is the lattice mismatch betweengraphene and BN, a is the lattice constant of grapheneand θ is the rotational mismatch between the layers. Byrotating the top BN layer, the wavelength of the resultingMoir´e superlattice can therefore be dynamically varied.Imaging with the same AFM provides a real-time mea-surement of the orientation of the rotatable BN layerrelative to the reference frame of the AFM, which we a r X i v : . [ c ond - m a t . m e s - h a ll ] A ug FIG. 1.
Rotatable heterostructures a , Schematic cartoon of the device structure and the experimental technique. b-d ,AFM image of a fabricated device showing three different orientations of the top BN. The angles identified in each panel isthe absolute angle referenced to the AFM coordinate system (labelled θ A in the text). The images were acquired by the sameAFM used to rotate the BN layer. e Schematic illustration of the Moire superlattice arising between graphene (Red) and BN(Blue) at zero angle. The moire wavelength is identified by λ . f , Raman spectrum of the device shown in (b-c) for θ A between34.2 ± ± .
2. Black curve shows an additional measurement acquired at ≈
64 degrees. g , FWHM of the 2Dpeak as a function of the absolute angle. All Raman measurements were taken with the gate bias held at V G = 0 V. The peakFWHM position identifies zero angle crystallographic alignment (see text). Dashed line represents the FWHM measured forall angles larger than approximately 2 degrees away from perfect alignment with the shaded region representing the associateduncertainty. label by the absolute angle ( θ A ) (see for example Fig.1b-d). More significant is the relative angle , θ , betweenthe rotatable BN and encapsulated graphene crystal lat-tices. To determine this we identify and measure angle-dependent features in the optical Raman spectrum of theheterostructure.Figure 1f shows a series of Raman spectra measuredfrom θ A = 34 −
64 degrees. The most striking variation inthe Raman spectra is an increase in the full width at halfmaximum of the 2D peak (FWHM ) [19, 28]. Plottingthis as a function of absolute angle (Fig. 1g) we see a welldefined maximum, occurring for this device at θ A ∼ . θ forany orientation of the BN layer.Our result highlights the robustness of Raman spec-troscopy as a tool to characterize the rotational order inthese van der Waals heterostructures. Moreover, we em- phasize that previous efforts to study effects of twist anglein this system required numerous samples with differentfixed angles whereas here we demonstrate a mapping ofthe angular dependence with better than 0.2 degree pre-cision, in a single tunable device.One notable disagreement with previous results[28] isan overall narrower 2D line-width in our devices. In pre-vious work this reduced linewidth was proposed to bea consequence of a reduction of the in-plane strain infully-encapsulated structures, such that areas of full com-mensuration to the aligned BN disappear [19]. However,our observation of the same linear trend and a reducedlinewidth for the misaligned position - for which no com-mensurate regions are expected - suggests a different ori-gin. We speculate that the real origin of this linewidthreduction is the change of dielectric environment of thegraphene by the presence of the second BN, as proposedin ref. [29]. Therefore, our results re-open the questionof the existence of commensurate states in encapsulatedgraphene devices. We additionally have identified a shift T i p de f l e c t i on ( V ) Time (s) B -30 -20 ∆ T i p de f l e c t i on ( V ) θ A (degree)
60 degrees
Si/SiO BNBN
Graphene
Photodetector
AFM tip AC motion (i) (ii) (iii) FIG. 2.
Mechanical properties versus angle. a , Schematic description of friction measurements. When the AFM tipencounters the BN structure it cants causing a repositioning of the reflected laser spot in the four-quadrant photodetector.The resulting voltage difference is proportional to the tip cant angle (referred to here as the tip deflection) and serves as ameasure of the torque force acting at the end of the tip. b , Tip deflection versus time in a translational push of the upper BNstructure. Different regimes of the measurement are identifiable: (i) as the tip drags along the surface, tip-substrate frictionresults in a steady state tip deflection (ii) when the tip encounters the BN structure it initially resists translation and the tipdeflection increases. We refer to this as the static friction regime (iii) Once the BN is in motion the tip deflection relaxes slightlyproviding a measure of the dynamic friction at the BN-graphene interface. c , tip deflection versus absolute angle measuredduring a continuous rotation of the BN. Two peaks are observed, spaced 60 degrees apart. in the position of the 2D and G peaks with relative an-gle (see supplementary information), a full discussion ofwhich is beyond the scope of this report.Mechanical resistance while pushing the BN impartsa torque to the AFM tip, causing it to cant away froma vertical position and produce a voltage difference inthe AFM’s photodetector. This can be used to identifyvariations in frictional forces (Fig. 2a.) When sliding thetop BN layer with the AFM tip, in a translational motionfar from alignment, we identify three regimes (see Fig.2b): i) sliding friction between the tip and the substratebefore the tip encounters the BN; ii) static friction whenthe tip encounters the BN but it resists translation; andiii) dynamic friction once the BN begins to move.Figure 2c shows a plot of the change in the tip de-flection under continuous rotation (dynamic friction),where the background due to piezoelectric drift andresidual friction has been subtracted. Two prominentpeaks appear, separated by 60 degrees. This closely re-sembles previous measurement of friction between twographitic structures in which a transition from superlu-bricity (where the structures are in an incommensurate position and the atomic shear forces are negligible) to adissipative state was observed at commensurate angles ofthe 3-fold symmetric hexagonal lattices[30–32]. However,since there is a lattice mismatch between graphene andBN there is not true lattice commensurability at any an-gle and therefore the increase of the friction should havea different origin. Recent numerical simulations suggestthat contributions of the Moir´e superlattice to the fric-tional force cannot be neglected and are expected to bemaximal for aligned layers [33], which could explain ourexperimental result. A more detailed study of the in-terlayer frictional forces will be necessary to fully under-stand this behavior. While this is beyond the presentscope, we note that this new device structure allow us tostudy mechanical properties, such as frictional force, inatomically flat materials without rugosity contributions.These results also highlight the possibility to use the fric-tion response as an in situ method to monitor and controllayer alignment in heterostructures.Our device design allows us to measure electron trans-port in the active layer (in this case graphene) whilechanging the relative orientation of the over-layer. Fig- -8 -4 0 4 80.00.51.01.52.02.5 θ =0+/-0.2 θ =1.6+/-0.2 R P ( k Ω ) V g - V CNP (V) AC B D E
10 12 140.00.51.01.52040
300 K1.7 K R S a t ( k Ω ) λ (nm) -1.0 -0.5 0.0 0.5 1.045678 ExperimentTheory V CN P - V S a t ( V ) θ (degrees) E k Δ CNP Δ Sat
E k F -3 -2 -1 0 1 2 3203040 ∆ CNP ∆ Sat ∆ ( m e V ) θ (degrees) FIG. 3.
Electronic transport properties. a , Four-terminal resistance as a function of the gate voltage for different alignmentsof the graphene/BN structure, acquired at room temperature. b , Position of the satellite peak in gate voltage as a functionof the relative angle. The 0.2 degrees error bar in the angle reports the precision achieved with the AFM imaging in tappingmode. c , Linear dependence of the maximum value of the four-terminal resistance at the satellite peak at 300 K (red) and 1.7K (blue) as a function of the Moir´e length. d Energy gap, measured by thermal activation, for the satellite peak (circles) andthe charge neutrality point (diamonds) as a function of the relative angle. Open symbols represent a repeated measurement ata given angle after moving through other angles and thermally cycling. e , Schematic band structure for native graphene and f for a graphene-hBN heterostructure with a small twist angle. ure 3a shows a plot of the four-terminal resistance ofthe graphene layer as a function of back gate voltage V g for different values of θ at room temperature. Near θ = 0, additional satellite resistance peaks appear sym-metrically in density around the charge neutrality point(CNP). This is consistent with the emergence of satel-lite Dirac points induced by scattering from the Moir´esuperlattice potential [18, 20–22].As θ increases away from zero, the satellite peaks di-minish in intensity and moves further from the CNP tohigher gate values. To analyze this behavior more quan-titatively, Figure 3b plots the satellite peak position in V g versus θ determined from the AFM imaging. The mea-sured position shows excellent agreement with the valuesof carrier density at which the full filling of the minibandoccurs, n = 8 / √ λ , where the carrier density and gatevoltage are related by n = C g ( V g − V CNP ) and λ is givenby expression (S1) [18, 20–22]. The error bars in Fig. 3b,approximately ± . θ can be determined from the AFM topographic images. Determining θ from the gate voltage position ofthe satellite peak at low temperature provides a more ac-curate measurement with uncertainty less than < ± . λ for a single device reveals an apparently linear variationin the magnitude of the satellite peak resistance (Fig.3c). Interestingly, the resistance of the CNP does notchange linearly with θ in this range (see supplementaryinformation). The origin of this linear dependence isnot known at present. The striking observation howeverhighlights an example of a physical phenomenon previ-ously obscured[18, 20–22] by sample-to-sample variationsbut which becomes clear when able to measure the effectof varying rotation in single sample.We measured the energy gap versus angle at both thecentral and satellite Dirac points by thermal activation.The gap magnitudes, shown in Fig. 3d, are in good agree- ABC -2 0 2203040 F W H M D ( c m - ) -2 0 20204060 ∆ T i p de f l e c t i on ( m V ) -2 0 20.40.81.2 R P ( k Ω ) θ (degrees) FIG. 4.
Compilation of the angle control technique.a
Four-terminal resistance as a function of the relative anglemeasured at a carrier density of -1.9x10 cm − . b , Tip de-flection in friction measured simultaneously as the electronictransport. c , FWHM of the 2D peak of the Raman spectrumas a function of the angle. All measurements were performedin the same device. ment with electronic transport measurements in encapsu-lated [34] and non-encapsulated devices [19, 20], opticalmeasurements made in epitaxial BN/graphene structures[35], and theoretical calculations [36]. As shown in Fig-ure 3d, the energy gap of the satellite peak decreasessmoothly away from θ = 0. In contrast, the energy gapat the CNP displays a more complex behavior near θ = 0and only decreases significantly for | θ | > i.e, after thermally cycling and rotatingthrough different angles and back). The difference inbehavior of the two energy gaps, impossible to observein study utilizing multiple samples at fixed angles [34],reflects their different physical origins and highlights theimportance of our new technique in the fully understand-ing the band structure modifications resulting from vari-ations in angular alignment, Fig. 3e-f. The persistanceof an energy gap at the CNP in encapsulated devicesfor angles beyond the angle at which a commensurate-incommensurate transition was previously identified [19]suggests that this energy gap is not related solely to thepresence of a commensurate state.Fig. 4 shows a direct comparison of the optical, me-chanical and electrical response versus angle measured inthe same device. The four probe resistance (Fig. 4a),the maximum tip deflection signal (friction, Fig. 4b)and the maximum FWHM of the Raman 2D peak (Fig.4c) coincides exactly, confirming the relationship betweenthese properties. The four-probe resistance (Fig. 4a) andfriction response (Fig. 4b) were acquired simultaneouslyat a fixed carrier density of 1.9x10 cm − (correspond-ing to the dashed line in Fig. S2) while continuouslyrotating the BN layer. We note that at this relativelylarge carrier density the bulk resistance is modulated bymore than an order of magnitude over less than 2 degreesof rotation (at cryogenic temperatures this increases isof more than two orders of magnitude, see supplemen-tary information). Our demonstration that rotatableheterostructures with dynamically tunable device char-acteristics can be realized provides a new opportunity indevice engineering. While here we have investigated BNencapsulated graphene as a model tunable system, thistechnique is readily extended to generic heterostructuresfabricated from 2D materials where in addition to bandstructure tunability, emergent phases such as supercon-ductivity and magnetism may be controllably varied withrotation. ∗ R. R.-P. and Ch.Z. contributed equally to this work;R.R.-P. Present address: Centre de Nanosciences etde Nanotechnologies (C2N), CNRS, Univ Paris Sud,Universit´e Paris-Saclay, 91120 Palaiseau, France; [email protected][1] S. Carr, D. Massatt, S. Fang, P. Cazeaux, M. Luskin,and E. Kaxiras, Phys. Rev. B , 075420 (2017).[2] L. Britnell, R. V. Gorbachev, A. K. Geim, L. A. Pono-marenko, A. Mishchenko, M. T. Greenaway, T. M.Fromhold, K. S. Novoselov, and L. Eaves, Nat. Com-mun. , 1794 (2013).[3] A. Mishchenko, J. S. Tu, Y. Cao, R. V. Gorbachev, J. R.Wallbank, M. T. Greenaway, V. E. Morozov, S. V. Mo-rozov, M. J. Zhu, S. L. Wong, F. Withers, C. R. Woods,Y.-J. Kim, K. Watanabe, T. Taniguchi, E. E. Vdovin, O. Makarovsky, T. M. Fromhold, V. I. Fal’ko, A. K.Geim, L. Eaves, and K. S. Novoselov, Nat. Nanotech-nol. , 808 (2014).[4] M. T. Greenaway, E. E. Vdovin, A. Mishchenko,O. Makarovsky, A. Patan`e, J. R. Wallbank, Y. Cao, A. V.Kretinin, M. J. Zhu, S. V. Morozov, V. I. Fal’ko, K. S.Novoselov, A. K. Geim, T. M. Fromhold, and L. Eaves,Nat. Phys. , 1057 (2015).[5] B. Fallahazad, K. Lee, S. Kang, J. Xue, S. Larentis,C. Corbet, K. Kim, H. C. P. Movva, T. Taniguchi,K. Watanabe, L. F. Register, S. K. Banerjee, and E. Tu-tuc, Nano Lett. , 428 (2015).[6] T. Chari, R. Ribeiro-Palau, C. R. Dean, and K. Shepard,Nano Lett. , 4477 (2016).[7] E. Koren, I. Leven, E. L¨ortscher, A. Knoll, O. Hod, andU. Duerig, Nat. Nanotechnol. , 752 (2016).[8] J. R. Wallbank, D. Ghazaryan, A. Misra, Y. Cao, J. S.Tu, B. A. Piot, M. Potemski, S. Pezzini, S. Wiedmann,U. Zeitler, T. L. M. Lane, S. V. Morozov, M. T. Green-away, L. Eaves, A. K. Geim, V. I. Fal’ko, K. S. Novoselov,and A. Mishchenko, Science , 575 (2016).[9] L. A. Gonzalez-Arraga, J. L. Lado, F. Guinea, andP. San-Jose, Phys. Rev. Lett. , 107201 (2017).[10] Y. Cao, J. Y. Luo, V. Fatemi, S. Fang, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, andP. Jarillo-Herrero, Phys. Rev. Lett. , 116804 (2016).[11] J. D. Sanchez-Yamagishi, J. Y. Luo, A. F. Young,B. M. Hunt, K. Watanabe, T. Taniguchi, R. C. Ashoori,and P. Jarillo-Herrero, Nature Nanotechnology , 118(2016).[12] L. Ju, Z. Shi, N. Nair, Y. Lv, C. Jin, J. Velasco Jr,C. Ojeda-Aristizabal, H. A. Bechtel, M. C. Martin,A. Zettl, J. Analytis, and F. Wang, Nature , 650(2015).[13] C.-J. Kim, A. S´anchez-Castillo, Z. Ziegler, Y. Ogawa,C. Noguez, and J. Park, Nature Nanotechnology ,520 (2016).[14] Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi,E. Kaxiras, and P. Jarillo-Herrero, Nature , 43 (2018).[15] H. Yu, Y. Wang, Q. Tong, X. Xu, and W. Yao, Phys.Rev. Lett. , 187002 (2015).[16] P. Rivera, K. L. Seyler, H. Yu, J. R. Schaibley, J. Yan,D. G. Mandrus, W. Yao, and X. Xu, Science , 688(2016).[17] P. Rivera, J. R. Schaibley, A. M. Jones, J. S. Ross, S. Wu,G. Aivazian, P. Klement, K. Seyler, G. Clark, N. J.Ghimire, J. Yan, D. G. Mandrus, W. Yao, and X. Xu,Nat. Commun. , 6242 (2015).[18] M. Yankowitz, J. Xue, D. Cormode, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, P. Jarillo-Herrero, P. Jacquod, and B. J. LeRoy, Nature Physics , 382 (2012).[19] C. R. Woods, L. Britnell, A. Eckmann, R. S. Ma, J. C.Lu, H. M. Guo, X. Lin, G. L. Yu, Y. Cao, R. V. Gor-bachev, A. V. Kretinin, J. Park, L. A. Ponomarenko,M. I. Katsnelson, Y. N. Gornostyrev, K. Watanabe,T. Taniguchi, C. Casiraghi, H.-J. Gao, A. K. Geim, andK. S. Novoselov, Nature Physics , 451 (2014).[20] B. Hunt, J. D. Sanchez-Yamagishi, A. F. Young,M. Yankowitz, B. J. LeRoy, K. Watanabe, T. Taniguchi,P. Moon, M. Koshino, P. Jarillo-Herrero, and R. C.Ashoori, Science , 1427 (2013).[21] L. A. Ponomarenko, R. V. Gorbachev, G. L. Yu, D. C.Elias, R. Jalil, A. A. Patel, A. Mishchenko, A. S. Mayorov, C. R. Woods, J. R. Wallbank, M. Mucha-Kruczynski, B. A. Piot, M. Potemski, I. V. Grigorieva,K. S. Novoselov, F. Guinea, V. I. Fal’ko, and A. K. Geim,Nature , 594 (2013).[22] C. R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari,Y. Gao, J. Katoch, M. Ishigami, P. Moon, M. Koshino,T. Taniguchi, K. Watanabe, K. L. Shepard, J. Hone, andP. Kim, Nature , 598 (2013).[23] K. Kim, M. Yankowitz, B. Fallahazad, S. Kang,H. C. P. Movva, S. Huang, S. Larentis, C. M. Corbet,T. Taniguchi, K. Watanabe, S. K. Banerjee, B. J. LeRoy,and E. Tutuc, Nano Letters , 1989 (2016).[24] D. Wang, G. Chen, C. Li, M. Cheng, W. Yang, S. Wu,G. Xie, J. Zhang, J. Zhao, X. Lu, P. Chen, G. Wang,J. Meng, J. Tang, R. Yang, C. He, D. Liu, D. Shi,K. Watanabe, T. Taniguchi, J. Feng, Y. Zhang, andG. Zhang, Phys. Rev. Lett. , 126101 (2016).[25] 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,T. Taniguchi, A. K. Geim, A. Mishchenko, and K. S.Novoselov, Nature Communications , 10800 (2016).[26] L. Wang, I. Meric, P. Y. Huang, Q. Gao, Y. Gao, H. Tran,T. Taniguchi, K. Watanabe, L. M. Campos, D. A. Muller,J. Guo, P. Kim, J. Hone, K. L. Shepard, and C. R. Dean,Science , 614 (2013).[27] C. R. Dean, A. F. Young, I. Meric, C. Lee, L. Wang,S. Sorgenfrei, K. Watanabe, T. Taniguchi, P. Kim, K. L.Shepard, and J. Hone, Nature Nanotechnology , 722(2010).[28] A. Eckmann, J. Park, H. Yang, D. Elias, A. S. May-orov, G. Yu, R. Jalil, K. S. Novoselov, R. V. Gorbachev,M. Lazzeri, A. K. Geim, and C. Casiraghi, Nano Letters , 5242 (2013).[29] C. Neumann, S. Reichardt, P. Venezuela, M. Dr¨ogeler,L. Banszerus, M. Schmitz, K. Watanabe, T. Taniguchi,F. Mauri, B. Beschoten, S. Rotkin, and C. Stampfer,Nat Commun , 9429 (2015).[30] M. Dienwiebel, G. S. Verhoeven, N. Pradeep, J. W. M.Frenken, J. A. Heimberg, and H. W. Zandbergen, Phys.Rev. Lett. , 126101 (2004).[31] Z. Liu, J. Yang, F. Grey, J. Z. Liu, Y. Liu, Y. Wang,Y. Yang, Y. Cheng, and Q. Zheng, Phys. Rev. Lett. , 205503 (2012).[32] A. E. Filippov, M. Dienwiebel, J. W. M. Frenken,J. Klafter, and M. Urbakh, Phys. Rev. Lett. , 046102(2008).[33] E. Koren and U. Duerig, Phys. Rev. B , 045401 (2016).[34] L. Wang, Y. Gao, B. Wen, Z. Han, T. Taniguchi,K. Watanabe, M. Koshino, J. Hone, and C. R. Dean,Science , 1231 (2015).[35] Z.-G. Chen, Z. Shi, W. Yang, X. Lu, Y. Lai, H. Yan,F. Wang, G. Zhang, and Z. Li, Nature Communications , 4461 (2014).[36] J. C. W. Song, A. V. Shytov, and L. S. Levitov, Phys.Rev. Lett. , 266801 (2013).[37] D. J. Lockwood, M. W. C. Dharma-wardana, J. M.Baribeau, and D. C. Houghton, Phys. Rev. B , 2243(1987).[38] A. K. Sood, J. Men´endez, M. Cardona, and K. Ploog,Phys. Rev. Lett. , 2111 (1985). ACKNOWLEDGEMENTS
We acknowledge discussions with Matthew Yankowitzand Andres Botello-Mendez as well as Juan Huerta,Shaowen Chen and Martin Gustafsson for technical sup-port. This research was supported by the NSF MRSECprogramme through Columbia in the Center for Preci-sion Assembly of Superstratic and Superatomic Solids(DMR-1420634). C.R.D. acknowledges partial supportby the National Science Foundation (DMR-1462383).
AUTHOR CONTRIBUTIONS
R.R.-P. and C.R.D. designed the experiment. Ch.Z.and R.R.-P. fabricated the samples, performed the ex-periments, analyzed the data and wrote the paper. T.T.and K.W. grew the crystals of hexagonal boron nitride.J.H. and C.R.D. advised on experiments, data analysisand writing the paper.
SUPPLEMENTARY INFORMATIONRAMAN SPECTRUM OF ALIGNEDSTRUCTURES
The inset in Fig. S7a shows a plot of the FWHMof the 2D peak versus calculated Moir´e wavelegth. Aremarkably linear dependence, described by the linear fitFWHM = 2 . λ − .
77, is observed. The slope of this linear fit is identical, within experimental uncertainty, toprevious observations [28]. Previous theoretical studies ofthe modification of the Raman spectra by a superlatticepotential associated this changes with the folding of thephonon structure due to the Moir´e pattern[37, 38], whichcould also be the case in graphene.
ANGLE AND MOIR´E LENGTH RELATION
The angle between layers, θ , and the Moir´e length, λ are related by λ = (1 + δ ) a (cid:112) δ )(1 − cos ( θ )) + δ (S1)where δ = 0 .
017 is the lattice mismatch, a is the latticeconstant of graphene [18]. As explained in the main textthe energy of this satellite peaks is given by: E = ± hv F √ λ (S2)As previously reported in [18] we found that the satel-lite peak is weaker for the conduction band (positiveV g ) than the one of the valence band (negative V g ).This asymmetry in strength has been associated withthe breaking of the electron-hole symmetry induced bya modulated hopping between different graphene sub-lattices. Initial layers stackPurple: SiO2 substrateBlue: h-BN; Gray: graphene E-beam lithography+ O2 etching Dry transfer E-beam lithography + metal deposition a b c d µ m2 µ m FIG. S1.
Fabrication process . a , Initial graphene/BN stack deposited on a Si/SiO substrate b , etching of the grapheneflake to give a Hall bar shape. c , Dry transfer of a pre-shaped BN structure. d , electrical connection with Cr/Pd/Au topsurface contacts.
32 33 34 35 362698270027022704 P o s i t i on D ( c m - ) θ A (degrees) Misaligned a bc
32 34 3615881590159215941596 P o s i t i on G ( c m - ) θ A (degrees) d -60 -40 -20 0 20 40 600.00.51.01.52.0 R P ( k Ω ) V g - V CNP (V) - θ + θ F W H M ( c m - ) λ (nm) misaligned FIG. S2.
Raman spectrum . a , FWHM of the 2D peak as a function of the Moir´e length, notice that the slope of the curveis the same reported in [28], see main text. Position of the 2D c and G d peaks as a function of the absolute angle. d , Roomtemperature measurement of the four-terminal resistance as a function of gate voltage for each Raman spectrum of this figureand of figure 1 of the main text. e , Maximum of the resistance at the satellite peak as a function of the Moir´e wavelength andenergy calculated using n = 8 / √ λ and E = hv F / √ λ , where the capacitive coupling of C g /e = 6 . × V − m − wasobtained experimentally from Hall measurements. a b c -60 -40 -20 0 20 40 600.00.51.01.52.0 R P ( k Ω ) V g - V CNP (V)
11 12 13 140.60.81.01.21.4 -0.24 -0.22 -0.20 -0.19 E (eV) R m a x - s a t ( k Ω ) λ (nm) -1.0 -0.5 0.0 0.5 1.0304050 AFM angleTheory V CN P - V s a t ( V ) θ (degrees) FIG. S3.
Satellite peaks . a , four probes resistance as a function of the back gate for different angles. Dashed lines representsthe carrier density used when measuring simultaneaously resistance and friction in Figure 4 of main text. b position of thesatellite peak in gate voltage as a function of the angle measured witht he AFM (where the minumum has been reported aszero. Solid line represents numerical fit using eqs S1 and S2. d Resistance of the satellite peak as a functon of the Moir´e length.
CNPSAT - electronsSAT - Holes R m a x ( k Ω ) λ (nm) T =1.7 K b
11 12 13 140.51.01.5
SAT - HolesCNP R m a x ( k Ω ) λ (nm) T =300 K a -6 -4 -2 0 2 4 6 80.1110 R P ( k Ω ) V bg - V CNP (V) T =1.6 K c FIG. S4.
Linear resistance dependence . Value of the four probe resistance at the charge neutrality point and satellitepeaks at 300 K a and 1.6 K b for a second sample. The linear fits for the second sample can be described by R max − h(300K) =275 . λ − R max − e(1 . = 81 . λ −
711 and R max − h(1 . = 10040 λ − . ∆ CN P ( m e V ) λ (nm) - θ + θ
10 11 12 13 1412162024 + θ - θ ∆ s a t ( m e V ) λ (nm) a b c T (K) G SA T ( m S ) T -1 (K -1 ) FIG. S5.
Energy gaps . a , Arhenious plot for satellite peak at three different angles. Energy gap of the CNP b and satellitepeak c as a function of the Moir´e length for the measurements reported in the main text. a b c FIG. S6.
Magneto transport . Longitudinal conductivity as a function of back gate voltage and magnetic field for 0 degrees( λ = 14 . ± . a , -0.47 degrees b and 0.83 degrees c . Moir´e length is calculated from the fits to Landau level crossing ofHofstadter spectrum and Hofstadter oscillations [20].FIG. S7. Rotation of monolayer graphene . Left , Graphene on BN as fabricated.
Rigth same graphene/BN stack afterrotation of one monolayer. Dashed lines are guides to the eye with the shape and orientation of the left image. Scale bar 3 µµ