Tuning the Interlayer Coupling of the Twisted Bilayer Graphene by

Feb 28, 2014 - Low-energy Van Hove singularities (VHSs) and superlattice Dirac cones, induced by the interlayer coupling and graphene-on-graphene moir...
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Tuning the Interlayer Coupling of the Twisted Bilayer Graphene by Molecular Adsorption Lan Meng,† Wei Yan,† Longjing Yin,† Zhao-Dong Chu,† Yanfeng Zhang,‡ Lei Feng,† Ruifen Dou,*,† and Jiacai Nie† †

Department of Physics, Beijing Normal University, Beijing 100875, People’s Republic of China College of Engineering, Peking University, Beijing 100871, People’s Republic of China

‡

ABSTRACT: We describe a facile method to modulate the local interlayer coupling by adsorption of single-molecule magnets (SMMs) onto twisted bilayer graphene and report the characterization of its electronic band structure using scanning tunneling microscopy and spectroscopy. Low-energy Van Hove singularities (VHSs) and superlattice Dirac cones, induced by the interlayer coupling and graphene-on-graphene moiré, respectively, are observed in the tunneling spectra. Our experiments demonstrate that the energy difference of the two VHSs, which reflects the magnitude of interlayer coupling, can be tuned by the local coverage density of molecular adsorption.

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INTRODUCTION The experimental studies of graphene started with the pioneering work of Novoselov et al. in 2004.1 Since that time, there has been a continuously growing interest in both the fundamental physics and applications of this system.2−7 Several years later, unabated new phenomena are still being uncovered in this active field.4,7−9 Compared with single-layer graphene, bilayer graphene displays even more intriguing properties10−19 including a nematic phase transition20 and low-energy Van Hove singularities (VHSs).21−26 The interlayer electron hopping of bilayer graphene markedly affects its band structure and electronic properties.13,14,16,21−29 Accordingly, controlling the interlayer coupling is becoming one of the central issue in the physics of bilayer graphene systems. Recently, Li et al. demonstrated that a rotation between stacked graphene layers can influence the interlayer hopping and lead to the appearance of two low-energy VHSs flanking the Dirac point.21 This result not only opens intriguing prospects for VHS engineering of electronic phases but also reveals exciting opportunities for inducing and exploring new phases with desirable properties in graphene.24−26 In a previous article,24 we demonstrated that the magnitude of the interlayer coupling can be enhanced by adsorption of single-molecule magnets (SMMs), [Mn 1 2 O 1 2 (CH 3 COO) 1 6 (H 2 O) 4 ]· 2CH3COOH·H2O (Mn12-ac), onto twisted bilayer graphene.30 The adsorption of Mn12-ac induces local curvature variation of graphene, which is expected to shorten the distance between bilayer graphene and enhance the interlayer electron hopping locally. Two low-energy VHSs, induced by the enhanced interlayer coupling, were observed as two pronounced peaks in the tunneling spectra. Our experiments also indicated that the periodic AB stacked atoms (the A atom of layer 1 and the B © 2014 American Chemical Society

atom of layer 2 that have the same horizontal positions) of twisted graphene bilayer with a finite interlayer hopping enhances the intervalley scattering from one Dirac cone to the other.24 Bringing the potential of inducing and exploring correlated electronic phases in graphene bilayer to reality requires a facile method to precisely control the interlayer coupling and therefore tune the electronic structure and properties of the twisted graphene bilayer. In this article, we show that it is possible to tune the interlayer coupling through the local coverage density of Mn12-ac on the twisted bilayer graphene. Using scanning tunneling microscopy and spectroscopy (STM and STS), we found that the adsorption of Mn12-ac markedly enhances the interlayer coupling and alters the electronic band structure of the bilayer graphene. Our experiments demonstrate that the energy difference between the two VHSs, which reflects the magnitude of interlayer coupling, can be tuned by the local coverage density of Mn12-ac. Additionally, possible evidence for superlattice Dirac cones,31−33 induced by the graphene-on-graphene moiré of the twisted graphene bilayer, was observed in the tunneling spectra.

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EXPERIMENTAL DETAILS Epitaxial graphene bilayer was grown in ultrahigh vacuum by thermal Si sublimation on a hydrogen-etched n-doped 6HSiC(0001̅) substrate with a doping density of 1016 cm−3, which was purchased from TanKeBlue Semiconductor Co. Ltd. (Beijing, China). The details of the synthesis were reported Received: November 8, 2013 Revised: February 27, 2014 Published: February 28, 2014 6462

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in our previous articles.24,30 The as-grown sample was charectarized by micro-Raman spectroscopy, STM, and STS measurements. The thickness of the sample was mainly bilayer. Our experiments demonstrated that bilayer graphene with a twist angle of ∼4.5° (moiré pattern period of about 3.1 nm) behaves as single-layer graphene. The interlayer coupling strength is so weak that the electronic band structure is identical to that of single-layer graphene.30 Later, we demonstrated that the adsorption of Mn12-ac onto twisted bilayer graphene enhances the interlayer coupling and strengthens the intervalley scattering.24 In this work, we carefully studied the electronic band structure of twisted bilayer graphene as a function of the local coverage density of Mn12-ac. The Mn12-ac powders were diluted in isopropanol solution with the help of supersonic cleaner. Two drops of the isopropanol solution with the diluted Mn12-ac powders were dripped on the epitaxial graphene. The sample was dried in a stream of dry nitrogen and transferred into an ultrahigh-vacuum chamber for STM and STS studies. Next, the sample was transferred out of the STM chamber to increase the coverage density of Mn12-ac, and the newly obtained sample was further studied by STM and STS measurements. The STM system was an ultrahigh-vacuum four-probe scanning probe microscopy (SPM) instrument from UNISOKU. All STM and STS measurements were performed at liquid-nitrogen temperature, and the images were taken in constant-current scanning mode. The STM tips were obtained by chemical etching from a wire of Pt(80%)Ir(20%) alloys. Lateral dimensions observed in the STM images were calibrated using a standard graphene lattice. The STS spectrum, that is, the dI/dV−V curve, was measured with a standard lockin technique using a 957 Hz alternating-current modulation of the bias voltage.

angle of the bilayer graphene. The Mn12-ac molecules are randomly dispersed on the surface of graphene. The height of most Mn12-ac molecules was measured to be about 2.8 nm, which is slightly larger than the size of a single Mn12-ac molecule (∼2.0 nm).24 This fact can be attributed to the influence of the protuberances of the moiré pattern and/or local curvature variation of graphene induced by the adsorption of Mn12-ac molecules. The nominal coverage density of the Mn12-ac molecules in Figure 1a was estimated to be 1.32 × 10−3 nm−2. This value was estimated from the total number of Mn12ac molecules, approximately 64, in an area of 4.86 × 104 nm2, and the obtained coverage density should be taken as only a very rough estimate because the Mn12-ac molecules were not uniformly distributed. To study the effects of Mn12-ac molecules on the electronic band structures of the twisted graphene bilayer, STS measurements were performed. The tunnelling spectrum gives direct access to the local density of states (LDOS) of the surface at the position of the STM tip. Figure 1c shows four typical dI/ dV−V curves obtained on the surface of the epitaxial bilayer graphene around the Mn12-ac molecules. The curves from I to IV are STS spectra recorded at the positions labeled in Figure 1a. The obtained results indicate that the twisted bilayer graphene no longer shows single-layer behavior.24,30 Instead, the spectra develop two sharp peaks flanking the Dirac points with an energy separation of ∼0.50 eV. The intensity of the peaks varies at different positions; however, the energy difference of the two peaks is almost constant, irrespective of the positions. The two sharp peaks in the spectra were attributed to the low-energy VHSs of the twisted graphene bilayer induced by interlayer coupling. The positions of the two VHSs flanking the Dirac points are not symmetrical about zero bias. This might arise from the slight departure between the Fermi level and the Dirac point ED (pointed out by the red arrow in the dI/dV−V curves). For twisted graphene bilayer, the Dirac points of the two layers no longer coincide, and there is a shift between the corresponding Dirac points (K and Kθ for the first layer and the sublayer, respectively) in momentum space by an amount of ΔK = 2K sin(θ/2), where θ is the twist angle and K = 4π/3a with a ≈ 0.246 nm the lattice constant of the hexagonal lattice (the schematic Dirac cones of twisted graphene bilayer are shown in Figure 2a). The displaced Dirac cones cross, and in the presence of interlayer hopping, two intersections of the saddle points (VHSs) are unavoidable along the two cones.21−26 In the four-band model, four peaks including two low-energy VHSs can be obtained in the density of states (DOS) of the twisted bilayer graphene, as shown in Figure 2b. The energy difference of the two low-energy VHSs, ΔEvhs, decreases with increasing interlayer hopping, whereas the opposite is the case for the energy difference between the two peaks in positive (or negative) bias (the two peaks include one of the VHSs and its nearest peak).21 In addition to the two VHSs, the tunneling curves in Figure 1c show a dip in the LDOS (marked by an arrow) placed at about −0.87 eV away from the graphene Dirac point. This dip is attributed to the superlattice Dirac cones induced by a weak periodic potential of the moiré pattern.31−33 Very recently, Yankowitz et al. demonstrated the emergence of superlattice Dirac cones induced by the moiré pattern between graphene and hexagonal boron nitride (BN).31 Even though the interlayer coupling is significantly different between the insulator graphene/BN system and the graphene/

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RESULTS Figure 1a shows an STM image of the epitaxial twisted graphene bilayer modified with a low coverage density of Mn12ac molecules. A clear moiré pattern with a period of 3.1 nm as pristine twisted graphene bilayer can be seen in Figure 1b, which indicates that the chemisorption did not alter the twist

Figure 1. (a) Typical STM image (Vsample = 314 mV and I = 0.28 nA) of Mn12-ac molecule adsorption on the surface of bilayer graphene, with a nominal coverage density of Mn12-ac molecules of ∼1.32 × 10−3 nm−2. The bright green dots are Mn12-ac molecules with a height of about 2−3 nm. (b) (b) Enlarged STM topography of the bilayer graphene (Vsample = 314 mV and I = 0.28 nA) with a clear moiré pattern. The period of the moiré pattern is about 3.1 nm. (c) Typical dI/dV−V curves obtained on the surface of the epitaxial bilayer graphene around the Mn12-ac molecules. The curves from I to IV were measured at the positions labeled in the STM image. The red arrow near zero bias of the spectra points to the Dirac point ED of twist bilayer graphene. The dip at about −0.8 V of the spectra is attributed to the superlattice Dirac points ESD. Two peaks flanking the Dirac points, marked by green dotted lines, are attributed to the low-energy VHSs induced by interlayer coupling. 6463

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Figure 2. (a) Schematic Dirac cones of twisted graphene bilayer. The separation of the Dirac cones, ΔK, in the two layers is attributed to the rotation between the graphene layers. (b) Left panel: Electronic band structure of twisted bilayer graphene with a finite interlayer coupling calculated with the four-band model. Middle panel: Cut of the electronic band structure along K and K′ in the low-energy spectrum near the Dirac points. Right panel: Peaks of the density of states at the energy that ΔEk shows singularities.

graphene system, the moiré pattern acts as a weak periodic potential that can generally generate superlattice Dirac points at energies of ESD ≈ ±ℏνF|G|/2 (where ℏ is the reduced Planck constant, νF is the Fermi velocity of graphene, and G is the reciprocal superlattice vectors of the moiré pattern). Thus, in our case, the presence of these dips in the DOS at approximately −0.87 eV in graphene/SiC still can be attributed to superlattice Dirac points, which are generally of asymmetric strength. Experimentally, the dip in the valence band is much deeper than that in the conduction band, and the dip in the conduction band is usually not visible.31 Considering the period of the graphene-on-graphene moiré to be ∼3.1 nm, ESD (±ℏνF| G|/2) of the twisted graphene bilayer is estimated to be about ±0.85 eV, which agrees well with the experimental result. We will show more experimental evidence and analysis that support our understanding subsequently. Figure 3a,c shows two typical STM images of a sample with a higher coverage density of Mn12-ac molecules. The moiré pattern of the twisted bilayer graphene with the period of 3.1 nm can still be observed clearly. The nominal coverage density of Mn12-ac in panels a and c of Figure 3 is estimated to be 2.0 × 10−3 and 3.0 × 10−3 nm−2, respectively. Figure 3b,d shows the corresponding dI/dV−V curves obtained on the surface of the epitaxial bilayer graphene around the Mn12-ac molecules. Three characteristics can be easily observed from the tunneling curves: (I) The energy difference of the two low-energy VHSs, ΔEvhs, decreases with increasing coverage density of Mn12-ac molecules. (II) The superlattice Dirac points are observed at approximately −0.86 eV, irrespective of the coverage density of adsorption. (III) More peaks appear between the VHSs and the superlattice Dirac points ESD, and the energy difference between the VHS and the nearest peak ΔE increases with increasing coverage density of Mn12-ac molecules. Recently, it was predicted that strong interlayer coupling of twisted graphene could lead to many saddle points and/or maxima, minima, and flat bands in the electronic band structure.27−29 These moiré bands also result in many singularities in the DOS, which might be the origin of the other peaks observed in the tunneling spectra. Our experimental results and analysis are summarized in Figure 4. Figure 4a shows the ΔEvhs and ESD values of the twisted bilayer graphene as functions of the coverage density of Mn12-ac molecules. With increasing coverage density of adsorption, the magnitude of ΔEvhs decreases from about 0.50 to 0.23 eV. For twisted graphene bilayer with a small interlayer coupling, the energy difference of the VHSs can be

Figure 3. (a,c) Two typical STM images at a higher coverage density of Mn12-ac molecules adsorption on the surface of the bilayer graphene (for panel a, Vsample = 302 mV and I = 0.39 nA; for panel c, Vsample = 393 mV and I = 0.42 nA). The bright green dots are Mn12-ac molecules. The nominal coverage of the Mn12-ac molecules was estimated to be (a) 2.0 × 10−3 and (c) 3.0 × 10−3 nm−2. (b,d) Typical dI/dV−V curves obtained around the Mn12-ac molecules on the surface of the epitaxial bilayer graphene. The curves from I to IV were measured at the positions labeled in the STM images at left. All spectra show two peaks flanking the Dirac points with energy separations of ΔEvhs ≈ (b) 0.36 and (d) 0.23 eV. The superlattice Dirac points are still observed at approximately −0.8 eV, irrespective of the coverage density of adsorption. Other peaks appear between the Van Hove singularities and the superlattice Dirac points ESD. The energy difference between the Van Hove singularity and the nearest peak is denoted as δE.

roughly estimated as ΔEvhs = ℏνFΔK − 2t⊥.21 Here, νF is the Fermi velocity of twisted bilayer graphene, and t⊥ is the interlayer hopping parameter. This expression indicates that the value of ΔEvhs depends strongly on both the twist angle and the interlayer coupling. Very recently, several groups reported the twist-angle-dependent VHSs in twisted bilayer graphene.21,25,26 In this work, the twist angle was constant (θ ≈ 4.5°). Therefore, the observed decrease in the magnitude of ΔEvhs is attributed to an increase in interlayer coupling, which is induced by the chemisorptions of Mn12-ac molecules. This 6464

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Research Funds for the Central Universities, and the Ministry of Science and Technology of China (Grants 2012CB933002 and 2011CB921903).

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(1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Electric Field Effect in Atomically Thin Carbon Films. Science 2004, 306, 666−669. (2) Geim, A. K.; Novoselov, K. S. The rise of graphene. Nat. Mater. 2007, 6, 183−191. (3) Castro Neto, A. H.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 2009, 81, 109−162. (4) Das Sarma, S.; Adam, S.; Hwang, E. H.; Rossi, E. Electronic transport in two-dimensional graphene. Rev. Mod. Phys. 2011, 83, 407−470. (5) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Katsnelson, M. I.; Grigorieva, I. V.; Dubonos, S. V.; Firsov, A. A. Twodimensional gas of massless Dirac fermions in graphene. Nature 2005, 438, 197−200. (6) Zhang, Y. B.; Tan, Y. W.; Stormer, H. L.; Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 2005, 438, 201−204. (7) Goerbig, M. O. Electronic properties of graphene in a strong magnetic field. Rev. Mod. Phys. 2011, 83, 1193−1243. (8) Levy, N.; Burke, S. A.; Meaker, K. L.; Panlasigui, M.; Zettl, A.; Guinea, F.; Castro Neto, A. H.; Crommie, M. F. Strain-Induced Pseudo-Magnetic Fields Greater Than 300 Tesla in Graphene Nanobubbles. Science 2010, 329, 544−547. (9) Yan, H.; Sun, Y.; He, L.; Nie, J. C.; Chan, M. H. W. Observation of Landau-level-like quantization at 77 K along a strained-induced graphene ridge. Phys. Rev. B 2012, 85, 035422−03525. (10) McCann, E.; Fal’ko, V. I. Landau-Level Degeneracy and Quantum Hall Effect in a Graphite Bilayer. Phys. Rev. Lett. 2006, 96, 086805−086808. (11) Novoselov, K. S.; McCann, E.; Morozov, S. V.; Fal’ko, V. I.; Katsnelson, M. I.; Zeitler, U.; Jiang, D.; Schedin, F.; Geim, A. K. Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene. Nat. Phys. 2006, 2, 177−180. (12) Rutter, G. M.; Jung, S.; Klimov, N. N.; Newell, D. B.; Zhitenev, N. B.; Stroscio, J. A. Microscopic polarization in bilayer graphene. Nat. Phys. 2011, 7, 649−655. (13) Li, Z. Q.; Henriksen, E. A.; Jiang, Z.; Hao, Z.; Martin, M. C.; Kim, P.; Stormer, H. L.; Basov, D. N. Band Structure Asymmetry of Bilayer Graphene Revealed by Infrared Spectroscopy. Phys. Rev. Lett. 2009, 102, 037403−037406. (14) Lopes dos Santos, J. M. B.; Peres, N. M. R.; Castro Neto, A. H. Graphene Bilayer with a Twist: Electronic Structure. Phys. Rev. Lett. 2007, 99, 256802−256805. (15) Kim, S.; Lee, K.; Tutuc, E. Spin-Polarized to Valley-Polarized Transition in Graphene Bilayers at ν = 0 in High Magnetic Fields. Phys. Rev. Lett. 2011, 107, 016803−016806. (16) Killi, M.; Wu, S.; Paramekanti, A. Band Structures of Bilayer Graphene Superlattices. Phys. Rev. Lett. 2011, 107, 086801−086804. (17) Nandkishore, R.; Levitov, L. Polar Kerr Effect and Time Reversal Symmetry Breaking in Bilayer Graphene. Phys. Rev. Lett. 2011, 107, 097402−097405. (18) Gu, N.; Rudner, M.; Levitov, L. Chirality-Assisted Electronic Cloaking of Confined States in Bilayer Graphene. Phys. Rev. Lett. 2011, 107, 156603−156606. (19) Lee, D. S.; Riedl, C.; Beringer, T.; Castro Neto, A. H.; von Klitzing, K.; Strake, U.; Smet, H. J. Quantum Hall Effect in Twisted Bilayer Graphene. Phys. Rev. Lett. 2011, 107, 216602−216605. (20) Mayorov, A. S.; Elias, D. C.; Mucha-Kruczynski, M.; Gorbachev, R. V.; Tudorovskiy, T.; Zhukov, A.; Morozov, S. V.; Katsnelson, M. I.; Fal’ko, V. I.; Geim, A. K.; Novoselov, K. S. Interaction-Driven Spectrum Reconstruction in Bilayer Graphene. Science 2011, 333, 860−863.

Figure 4. (a) ΔEvhs (left y axis) and positions of the superlattice Dirac cone (right y axis) of the twist bilayer graphene as a function of the coverage density of Mn12-ac molecules. The error bars in energy represent the minimum and maximum observed energies of ΔEvhs and ESD − ED. The error bars along the x axis represent the uncertainty in coverage density. (b) Theoretical energy separation of ΔEvhs as a function of interlayer coupling calculated by the tight-binding model (solid curve). Experimental ΔEvhs values are also plotted to estimated the interlayer coupling parameter.

means that the magnitude of interlayer coupling can be tuned by the local coverage density of Mn12-ac. The curve in Figure 4b shows the theoretical ΔEvhs value as a function of the interlayer coupling calculated by the tight-binding model. The expression ΔEvhs = ℏνFΔK − 2t⊥ is valid only for very weak interlayer coupling. The interlayer hopping parameter is estimated as 0.27, 0.42, and 0.82 eV for nominal coverage densities of Mn12-ac molecules of 1.32 × 10−3, 2.0 × 10−3, and 3.0 × 10−3 nm−2, respectively. With increasing interlayer coupling, the magnitude of δE also increases from 0.25 eV, as shown in Figure 3b, to about 0.31 eV, as shown in Figure 3d. On the basis of the above results, it can be concluded that the chemisorption of Mn12-ac molecules enhances the coupling between graphene bilayer, which might originate from the modulation of the distance between the sheets of the bilayer. Further experiments should be carried out to explore the exact origin of the enhanced interlayer coupling induced by the chemisorption. The reported superlattice Dirac cones induced by the graphene-on-graphene moiré pattern also represent a very interesting topic. Further experiments to study the twisting-angle dependence of ESD could provide an unmistakable signature of the emergence of superlattice Dirac cones induced by a graphene-on-graphene moiré. In summary, we report a facile method for modulating interlayer coupling through the absorption of SMMs onto twisted bilayer graphene. The separation of the two VHSs flanking the Dirac point decreases with increasing interlayer hopping (the nominal coverage density of adsorption). Meanwhile, evidence for superlattice Dirac cones induced by the graphene-on-graphene moiré of the twisted graphene bilayer was observed in the tunneling spectra. The results reported herein open opportunities for bringing the potential of inducing and exploring correlated electronic phases in graphene bilayer to reality.

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: + 86-10-58802947-807. Fax: + 86-10-5880-0141. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Grants 10804010, 10974019, 11004010, 51172029, 91121012, and 11311120461), the Fundamental 6465

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(21) Li, G. H.; Luican, A.; Lopes dos Santos, J. M. B.; Castro Neto, A. H.; Reina, A.; Kong, J.; Andrei, E. Y. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 2010, 6, 109−113. (22) Luican, A.; Li, G. H.; Reina, A.; Kong, J.; Nair, R. R.; Novoselov, K. S.; Geim, A. K.; Andrei, E. Y. Single-Layer Behavior and Its Breakdown in Twisted Graphene Layers. Phys. Rev. Lett. 2011, 106, 126802−126805. (23) Hicks, J.; Sprinkle, M.; Shepperd, K.; Wang, F.; Tejeda, A.; Taleb- Ibrahimi, A.; Bertran, F.; Le Fevre, P.; de Heer, W. A.; Berger, C.; Conrad, E. H. Symmetry breaking in commensurate graphene rotational stacking: Comparison of theory and experiment. Phys. Rev. B 2011, 83, 205403−20510. (24) Meng, L.; Chu, Z.-D.; Zhang, Y. F.; Yang, J. Y.; Dou, R. F.; Nie, J. C.; He, L. Enhanced intervalley scattering of twisted bilayer graphene by periodic AB stacked atoms. Phys. Rev. B 2012, 85, 235453−235457. (25) Yan, W.; Liu, M. X.; Dou, R. F.; Meng, L.; Feng, L.; Chu, Z.-D.; Zhang, Y. F.; Liu, Z. F.; Nie, J.-C.; He, L. Angle-Dependent van Hove Singularities in a Slightly Twisted Graphene Bilayer. Phys. Rev. Lett. 2012, 109, 126801−126804. (26) Kim, K.; Coh, S.; Tan, L. Z.; Regan, W.; Yuk, J. M.; Chatterjee, E.; Crommie, M. F.; Cohen, M. L.; Louie, S. G.; Zettl, A. Raman spectroscopy study of rotated double-layer graphene: Misorientationangle dependence of electronic structure. Phys. Rev. Lett. 2012, 108, 246103−246106. (27) Bistritzer, R.; MacDonald, A. H. Moiré bands in twisted doublelayer graphene. Proc. Natl. Acad. Sci. U.S.A. 2011, 08, 12233−12237. (28) Tan, L. Z.; Park, C.-H.; Louie, S. G. New Dirac Fermions in Periodically Modulated Bilayer Graphene. Nano Lett. 2011, 11, 2596− 2600. (29) de Gail, R.; Goerbig, M. O.; Guinea, F.; Montambaux, G.; Castro Neto, A. H. Topologically protected zero modes in twisted bilayer graphene. Phys. Rev. B 2011, 84, 045436−045440. (30) Meng, L.; Zhang, Y. F.; Yan, W.; Feng, L.; He, L.; Dou, R. F.; Nie, J. C. Single-layer behavior and slow carrier density dynamic of twisted graphene bilayer. Appl. Phys. Lett. 2012, 100, 091601−091604. (31) Yankowitz, M.; Xue, J.; Cormode, D.; Sanchez-Yamagishi, J. D.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P.; Jacquod, P.; LeRoy, B. J. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 2012, 8, 382−386. (32) Park, C.-H.; Yang, L.; Son, Y.-W.; Cohen, M. L.; Louie, S. G. New Generation of Massless Dirac Fermions in Graphene under External Periodic Potentials. Phys. Rev. Lett. 2008, 101, 126804− 126807. (33) Park, C.-H.; Yang, L.; Son, Y.-W.; Cohen, M. L.; Louie, S. G. Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials. Nat. Phys. 2008, 4, 213−217.

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