Issue

Vol. 12 (2020)

Opportunities and Challenges in Twisted Bilayer Graphene: A Review

https://doi.org/10.1007/s40820-020-00464-8
Amol Nimbalkar
Division of Biotechnology, Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu 42988, Republic of Korea
Hyunmin Kim
Division of Biotechnology, Daegu Gyeongbuk Institute of Science and Technology (DGIST), Daegu 42988, Republic of Korea

Corresponding Author: Hyunmin Kim

hyunmin.kim@dgist.ac.kr

Nano-Micro Letters, Vol. 12 (2020), Article Number: 126

Abstract

Two-dimensional (2D) materials exhibit enhanced physical, chemical, electronic, and optical properties when compared to those of bulk materials. Graphene demands significant attention due to its superior physical and electronic characteristics among different types of 2D materials. The bilayer graphene is fabricated by the stacking of the two monolayers of graphene. The twisted bilayer graphene (tBLG) superlattice is formed when these layers are twisted at a small angle. The presence of disorders and interlayer interactions in tBLG enhances several characteristics, including the optical and electrical properties. The studies on twisted bilayer graphene have been exciting and challenging thus far, especially after superconductivity was reported in tBLG at the magic angle. This article reviews the current progress in the fabrication techniques of twisted bilayer graphene and its twisting angle-dependent properties.


Highlights:


1 This article presents an overview of twisted bilayer graphene (tBLG) on their fabrication techniques and twisting angle-dependent properties.
2 The properties of tBLG can be controlled by controlling the twisting angle between two graphene sheets.

Keywords

Graphene Twisted bilayer graphene Magic angle Superconductivity van Hove singularities
Nimbalkar, Amol, and Hyunmin Kim. 2020. “Opportunities and Challenges in Twisted Bilayer Graphene: A Review”. Nano-Micro Letters 12 (June):126. https://doi.org/10.1007/s40820-020-00464-8.
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX
References
  1. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Electric field effect in atomically thin carbon films. Science 306(5696), 666–669 (2004). https://doi.org/10.1126/science.1102896
  2. M. Tahriri, M. Del Monico, A. Moghanian, M.T. Yaraki, R. Torres, A. Yadegari, L. Tayebi, Graphene and its derivatives: opportunities and challenges in dentistry. Mater. Sci. Eng. C 102, 171–185 (2019). https://doi.org/10.1016/j.msec.2019.04.051
  3. Z. Peng, Z. Yan, Z. Sun, J.M. Tour, Direct growth of bilayer graphene on SiO2 substrates by carbon diffusion through nickel. ACS Nano 5(10), 8241–8247 (2011). https://doi.org/10.1021/nn202923y
  4. A.I. Cocemasov, D.L. Nika, A.A. Balandin, Phonons in twisted bilayer graphene. Phys. Rev. B 88, 035428 (2013). https://doi.org/10.1103/PhysRevB.88.035428
  5. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson et al., Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005). https://doi.org/10.1038/nature04233
  6. Y.B. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005). https://doi.org/10.1038/nature04235
  7. M. Freitag, H.Y. Chiu, M. Steiner, V. Perebeinos, P. Avouris, Thermal infrared emission from biased graphene. Nat. Nanotechnol. 5, 497–501 (2010). https://doi.org/10.1038/NNANO.2010.90
  8. C. Xu, H. Li, K. Banerjee, Modeling, analysis, and design of graphene nano-ribbon interconnects. IEEE Trans. Electron Dev. 56, 8 (2009). https://doi.org/10.1109/TED.2009.2024254
  9. W. Liu, S. Kraemer, D. Sarkar, H. Li, P.M. Ajayan, K. Banerjee, Controllable and rapid synthesis of high-quality and large-areabernal stacked bilayer graphene using chemical vapor deposition. Chem. Mater. 26(2), 907–915 (2014). https://doi.org/10.1021/cm4021854
  10. S.Y. Dai, Y. Xiang, D.J. Srolovitz, Twisted bilayer graphene: moiré with a twist. Nano Lett. 16, 5923–5927 (2016). https://doi.org/10.1021/acs.nanolett.6b02870
  11. J. Hicks, M. Sprinkle, K. Shepperd, F. Wang, Symmetry breaking in commensurate graphene rotational stacking: comparison of theory and experiment. Phys. Rev. B 83, 205403 (2011). https://doi.org/10.1103/PhysRevB.83.205403
  12. E.S. Morell, P. Vargas, Charge redistribution and interlayer coupling in twisted bilayer graphene under electric fields. Phys. Rev. B 84, 195421 (2011). https://doi.org/10.1103/PhysRevB.84.195421
  13. G. Tarnopolsky, A.J. Kruchkov, A. Vishwanath, Origin of magic angles in twisted bilayer graphene. Phys. Rev. Lett. 122, 106405 (2019). https://doi.org/10.1103/PhysRevLett.122.106405
  14. M. Anđelković, L. Covaci, F.M. Peeters, DC conductivity of twisted bilayer graphene: angle-dependent transport properties and effects of disorder. Phys. Rev. Mater. 2, 034004 (2018). https://doi.org/10.1103/PhysRevMaterials.2.034004
  15. E.J. Mele, Commensuration and interlayer coherence in twisted bilayer graphene. Phys. Rev. B 81, 161405(R) (2010). https://doi.org/10.1103/PhysRevB.81.161405
  16. B.L. Huang, C.P. Chuu, M.F. Lin, Asymmetry-enriched electronic and optical properties of bilayer graphene. Sci. Rep. 9, 859 (2019). https://doi.org/10.1038/s41598-018-37058-9
  17. C.Y. Lin, J.Y. Wu, Y.H. Chiu, C.P. Chang, M.F. Lin, Stacking-dependent magnetoelectronic properties in multilayer graphene. Phys. Rev. B 90, 205434 (2014). https://doi.org/10.1103/PhysRevB.90.205434
  18. D.S. Lee, C. Riedl, T. Beringer, A.H.C. Neto, K.V. Klitzing, U. Starke, J.H. Smet, Quantum hall effect in twisted bilayer graphene. Phys. Rev. Lett. 107, 216602 (2011). https://doi.org/10.1103/PhysRevLett.107.216602
  19. C.C. Lu, Y.C. Lin, Z. Liu, C.H. Yeh, K. Suenaga, P.W. Chiu, Twisting bilayer graphene superlattices. ACS Nano 7(3), 2587–2594 (2013). https://doi.org/10.1021/nn3059828
  20. J.M.B. Lopes dos Santos, N.M.R. Peres, A.H.C. Neto, Graphene bilayer with a twist: electronic structure. Phys. Rev. Lett. 99, 256802 (2007). https://doi.org/10.1103/PhysRevLett.99.256802
  21. A.O. Sboychakov, A.L. Rakhmanov, A.V. Rozhkov, F. Nori, Electronic spectrum of twisted bilayer graphene. Phys. Rev. B 92, 075402 (2015). https://doi.org/10.1103/PhysRevB.92.075402
  22. W. Yan, W.Y. He, Z.D. Chu, M.X. Liu, L. Meng et al., Strain and curvature induced evolution of electronic band structures in twisted graphene bilayer. Nat. Commun. 4, 2159 (2013). https://doi.org/10.1038/ncomms3159
  23. J.S. Alden, A.W. Tsen, P.Y. Huang, R. Hovden, L. Brown, J.W. Park, D.A. Muller, P.L. McEuen, Strain solitons and topological defects in bilayer graphene. PNAS 110(28), 11256–11260 (2013). https://doi.org/10.1073/pnas.1309394110
  24. K. Kim, M. Yankowitz, B. Fallahazad, S. Kang, H.C.P. Movva et al., van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16(3), 1989–1995 (2016). https://doi.org/10.1021/acs.nanolett.5b05263
  25. L.J. Yin, H. Jiang, J.B. Qiao, L. He, Direct imaging of topological edge states at a bilayer graphene domain wall. Nat. Commun. 7, 11760 (2016). https://doi.org/10.1038/ncomms11760
  26. L. Huder, A. Artaud, T.L. Quang, G.T. de Laissardière, A.G.M. Jansen, G. Lapertot, C. Chapelier, V.T. Renard, Electronic spectrum of twisted graphene layers under heterostrain. Phys. Rev. Lett. 120, 156405 (2018). https://doi.org/10.1103/PhysRevLett.120.156405
  27. J.B. Qiao, L.J. Yin, L. He, Twisted graphene bilayer around the first magic angle engineered by heterostrain. Phys. Rev. B 98, 235402 (2018). https://doi.org/10.1103/PhysRevB.98.235402
  28. L. Liao, H. Wang, H. Peng, J.B. Yin, A.L. Koh, Y.L. Chen, Q. Xie, H.L. Peng, Z.F. Liu, van Hove singularity enhanced photochemical reactivity of twisted bilayer graphene. Nano Lett. 15(8), 5585–5589 (2015). https://doi.org/10.1021/acs.nanolett.5b02240
  29. C.R. Woods, L. Britnell, A. Eckmann, R.S. Ma, J.C. Lu, H.M. Guo et al., Commensurate-incommensurate transition in graphene on hexagonal boron nitride. Nat. Phys. 10, 451–456 (2014). https://doi.org/10.1038/NPHYS2954
  30. Q. Ye, J. Wang, Z.B. Liu, Z.C. Deng, X.T. Kong et al., Polarization-dependent optical absorption of graphene under total internal reflection. Appl. Phys. Lett. 102, 021912 (2013). https://doi.org/10.1063/1.4776694
  31. R.W. Havener, Y.F. Liang, L. Brown, L. Yang, J. Park, Van Hove singularities and excitonic effects in the optical conductivity of twisted bilayer graphene. Nano Lett. 14, 3353–3357 (2014). https://doi.org/10.1021/nl500823k
  32. M.D. Corato, C. Cocchi, D. Prezzi, M.J. Caldas, E. Molinari, A. Ruini, Optical properties of bilayer graphene nanoflakes. J. Phys. Chem. C 118(40), 23219–23225 (2014). https://doi.org/10.1021/jp504222m
  33. S.K. Jain, V. Juričić, G.T. Barkema, Structure of twisted and buckled bilayer graphene. 2D Mater. 4, 015018 (2017). https://doi.org/10.1088/2053-1583/4/1/015018
  34. S. Shallcross, S. Sharma, O.A. Pankratov, Quantum interference at the twist boundary in graphene. Phys. Rev. Lett. 101, 056803 (2008). https://doi.org/10.1103/PhysRevLett.101.056803
  35. R. de Gail, M.O. Goerbig, F. Guinea, G. Montambaux, A.H.C. Neto, Topologically protected zero modes in twisted bilayer graphene. Phys. Rev. B 84, 045436 (2011). https://doi.org/10.1103/PhysRevB.84.045436
  36. R. Bistritzer, A.H. MacDonald, Moiré butterflies in twisted bilayer graphene. Phys. Rev. B 84, 035440 (2011). https://doi.org/10.1103/PhysRevB.84.035440
  37. G.T. de Laissardie`re, D. Mayou, L. Magaud, Localization of dirac electrons in rotated graphene bilayers. Nano Lett. 10, 804–808 (2010). https://doi.org/10.1021/nl902948m
  38. L. Meng, W. Yan, L.J. Yin, Z.D. Chu, Y.F. Zhang, L. Feng, R. Dou, J. Nie, Tuning the interlayer coupling of the twisted bilayer graphene by molecular adsorption. J. Phys. Chem. C 118, 6462–6466 (2014). https://doi.org/10.1021/jp4109915
  39. W. Yan, M.X. Liu, R.F. Dou, L. Meng, L. Feng et al., Angle-dependent van Hove Singularities in a slightly twisted graphene bilayer. Phys. Rev. Lett. 109, 126801 (2012). https://doi.org/10.1103/PhysRevLett.109.126801
  40. V.H. Nguyen, P. Dollfus, Strain-induced modulation of Dirac cones and van Hove singularities in twisted graphene bilayer. 2D Mater. 2, 035005 (2015). https://doi.org/10.1088/2053-1583/2/3/035005
  41. J.D.S.Y. Taniguchi, A. Yacoby, P. Jarillo-Herrero, Quantum hall effect, screening, and layer-polarized insulating states in twisted bilayer graphene. Phys. Rev. Lett. 108, 076601 (2012). https://doi.org/10.1103/PhysRevLett.108.076601
  42. M. Zarenia, I. Yudhistira, S. Adam, G. Vignale, Enhanced hydrodynamic transport in near magic angle twisted bilayer graphene. Phys. Rev. B 101, 045421 (2020). https://doi.org/10.1103/PhysRevB.101.045421
  43. Y. Cao, V. Fatemi, A. Demir, S. Fang, S.L. Tomarken et al., Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018). https://doi.org/10.1038/nature26154
  44. B. Lian, Z.J. Wang, B.A. Bernevig, Twisted bilayer graphene: a phonon-driven superconductor. Phys. Rev. Lett. 122, 257002 (2019). https://doi.org/10.1103/PhysRevLett.122.257002
  45. N.F.Q. Yuan, L. Fu, Model for the metal-insulator transition in graphene superlattices and beyond. Phys. Rev. B 98, 045103 (2018). https://doi.org/10.1103/PhysRevB.98.045103
  46. H.C. Po, L.J. Zou, A. Vishwanath, T. Senthil, Origin of Mott insulating behavior and superconductivity in twisted bilayer graphene. Phys. Rev. X 8, 031089 (2018). https://doi.org/10.1103/PhysRevX.8.031089
  47. C. Xu, L. Balents, Topological superconductivity in twisted multilayer graphene. Phys. Rev. Lett. 121, 087001 (2018). https://doi.org/10.1103/PhysRevLett.121.087001
  48. B. Roy, V. Juričić, Unconventional superconductivity in nearly flat bands in twisted bilayer graphene. Phys. Rev. B 99, 121407(R) (2019). https://doi.org/10.1103/PhysRevB.99.121407
  49. G.E. Volovik, Graphite, graphene and the flat band superconductivity. JETP Lett. 107, 516 (2018). https://doi.org/10.1134/S0021364018080052
  50. B. Padhi, C. Setty, P.W. Phillips, Doped twisted bilayer graphene near magic angles: proximity to Wigner crystallization, not Mott insulation. Nano Lett. 18, 6175 (2018). https://doi.org/10.1021/acs.nanolett.8b02033
  51. J.F. Dodaro, S.A. Kivelson, Y. Schattner, X.Q. Sun, C. Wang, Phases of a phenomenological model of twisted bilayer graphene. Phys. Rev. B 98, 075154 (2018). https://doi.org/10.1103/PhysRevB.98.075154
  52. G. Baskaran, Theory of emergent Josephson lattice in neutral twisted bilayer graphene (moiŕe is different). arXiv:1804.00627
  53. F.C. Wu, A.H. MacDonald, I. Martin, Theory of phonon-mediated superconductivity in twisted bilayer graphene. Phys. Rev. Lett. 121, 257001 (2018). https://doi.org/10.1103/PhysRevLett.121.257001
  54. H. Isobe, N.F.Q. Yuan, L. Fu, Unconventional superconductivity and density waves in twisted bilayer graphene. Phys. Rev. X 8, 041041 (2018). https://doi.org/10.1103/PhysRevX.8.041041
  55. T.Y. Huang, L.F. Zhang, T.X. Ma, Antiferromagnetically ordered mott insulator and d + id superconductivity in twisted bilayer graphene: a quantum monte carlo study. Sci. Bull. 64, 310 (2019). https://doi.org/10.1016/j.scib.2019.01.026
  56. Y.Z. You, A. Vishwanath, Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene. NPJ Quantum Mater. 4, 16 (2019). https://doi.org/10.1038/s41535-019-0153-4
  57. X.C. Wu, K.A. Pawlak, C.M. Jian, C.K. Xu, Emergent superconductivity in the weak Mott insulator phase of bilayer graphene Moiŕe superlattice. arXiv:1805.06906
  58. Y.H. Zhang, D. Mao, Y. Cao, P.J. Herrero, T. Senthil, Nearly flat chern bands in moiré superlattices. Phys. Rev. B 99, 075127 (2019). https://doi.org/10.1103/PhysRevB.99.075127
  59. J. Kang, O. Vafek, Maximally localized Wannier states, and a low-energy model for twisted bilayer graphene narrow bands. Phys. Rev. X 8, 031088 (2018). https://doi.org/10.1103/PhysRevX.8.031088
  60. M. Koshino, N.F.Q. Yuan, T. Koretsune, M. Ochi, K. Kuroki, L. Fu, Maximally localized Wannier orbitals and the extended Hubbard model for twisted bilayer graphene. Phys. Rev. X 8, 031087 (2018). https://doi.org/10.1103/PhysRevX.8.031087
  61. D.M. Kennes, J. Lischner, C. Karrasch, Strong correlations and d + id superconductivity in twisted bilayer graphene. Phys. Rev. B 98, 241407(R) (2018). https://doi.org/10.1103/PhysRevB.98.241407
  62. L. Zhang, Lowest-energy moire band formed by Dirac zero modes in twisted bilayer graphene. Sci. Bull. 64, 495 (2019). https://doi.org/10.1016/j.scib.2019.03.010
  63. J.M. Pizarro, M.J. Calderón, E. Bascones, The nature of correlations in the insulating states of twisted bilayer graphene. J. Phys. Commun. 3, 035024 (2019). https://doi.org/10.1088/2399-6528/ab0fa9
  64. F. Guineaa, N.R. Walet, Electrostatic effects, band distortions, and superconductivity in twisted graphene bilayers. Proc. Natl. Acad. Sci. U. S. A. 115, 13174 (2018). https://doi.org/10.1073/pnas.1810947115
  65. L.J. Zou, H.C. Po, A. Vishwanath, T. Senthil, Band structure of twisted bilayer graphene: emergent symmetries, commensurate approximants, and Wannier obstructions. Phys. Rev. B 98, 085435 (2018). https://doi.org/10.1103/PhysRevB.98.085435
  66. M.P. Lima, J.E. Padilha, R.B. Pontes, A. Fazzio, A.J.R. Silva, Stacking-dependent transport properties in few-layers graphene. Solid State Commun. 250, 70–74 (2017). https://doi.org/10.1016/j.ssc.2016.11.012
  67. C.X. Cong, T. Yu, Enhanced ultra-low-frequency interlayer shear modes in folded graphene layers. Nat. Commun. 5, 4709 (2014). https://doi.org/10.1038/ncomms5709
  68. K.N. Kudin, B. Ozbas, H.C. Schniepp, R.K. Prud’homme, I.A. Aksay, R. Car, Raman spectra of graphite oxide and functionalized graphene sheets. Nano Lett. 8(1), 36–41 (2008). https://doi.org/10.1021/nl071822y
  69. K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, A.K. Geim, Two-dimensional atomic crystals. PNAS 102(30), 10451–10453 (2005). https://doi.org/10.1073/pnas.0502848102
  70. S. Stankovich, D.A. Dikin, R.D. Piner, K.A. Kohlhaas, A. Kleinhammes et al., Synthesis of graphene-based nanosheets via chemical reduction of exfoliated graphite oxide. Carbon 45, 1558–1565 (2007). https://doi.org/10.1016/j.carbon.2007.02.034
  71. C. Virojanadara, M. Syväjarvi, R. Yakimova, L.I. Johansson, A.A. Zakharov, T. Balasubramanian, Homogeneous large-area graphene layer growth on 6H-SiC(0001). Phys. Rev. B 78, 245403 (2008). https://doi.org/10.1103/PhysRevB.78.245403
  72. C. Berger, Z.M. Song, X.B. Li, X.S. Wu, N. Brown et al., Electronic confinement and coherence in patterned epitaxial graphene. Science 312(5777), 1191–1196 (2006). https://doi.org/10.1126/science.1125925
  73. X. Li, W.W. Cai, J. An, S. Kim, J. Nah et al., Large-area synthesis of high-quality and uniform graphene films on copper foils. Science 324(5932), 1312–1314 (2009). https://doi.org/10.1126/science.1171245
  74. Y.C. Chen, W.H. Lin, W.S. Tseng, C.C. Chen, G.R. Rossman, C.D. Chen, Y.S. Wu, N.C. Yeh, Direct growth of mm-size twisted bilayer graphene by plasma-enhanced chemical vapor deposition. Carbon 156, 212–224 (2020). https://doi.org/10.1016/j.carbon.2019.09.052
  75. J.T. Robinson, S.W. Schmucker, C.B. Diaconescu, J.P. Long, J.C. Culbertson, T. Ohta, A.L. Friedman, T.E. Beechem, Electronic hybridization of large-area stacked graphene films. ACS Nano 7(1), 637–644 (2013). https://doi.org/10.1021/nn304834p
  76. K.S. Kim, Y. Zhao, H. Jang, S.Y. Lee, J.M. Kim et al., Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 457, 706–710 (2009). https://doi.org/10.1038/nature07719
  77. A. Reina, X.T. Jia, J. Ho, D. Nezich, H. Son et al., Large area, few-layer graphene films on arbitrary substrates by chemical vapor deposition. Nano Lett. 9(1), 30–35 (2009). https://doi.org/10.1021/nl801827v
  78. S. Bae, H. Kim, Y. Lee, X.F. Xu, J.S. Park et al., Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nat. Nanotechnol. 5, 574–578 (2010). https://doi.org/10.1038/NNANO.2010.132
  79. K. Kim, A. DaSilva, S.Q. Huang, B. Fallahazad, S. Larentis et al., Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. PNAS 114(13), 3364–3369 (2017). https://doi.org/10.1073/pnas.1620140114
  80. L. Wang, I. Meric, P.Y. Huang, Q. Gao, Y. Gao et al., One dimensional electrical contact to a two-dimensional material. Science 342(6158), 614–617 (2013). https://doi.org/10.1126/science.1244358
  81. X.D. Chen, W. Xin, W.S. Jiang, Z.B. Liu, Y.S. Chen, J.G. Tian, High-precision twist-controlled bilayer and trilayer graphene. Adv. Mater. 28, 2563–2570 (2016). https://doi.org/10.1002/adma.201505129
  82. B. Wang, M. Huang, N.Y. Kim, B.V. Cunning, Y. Huang et al., Controlled folding of single crystal graphene. Nano Lett. 17, 1467–1473 (2017). https://doi.org/10.1021/acs.nanolett.6b04459
  83. L. Ju, Z.W. Shi, N. Nair, Y. Lv, C.H. Jin et al., Topological valley transport at bilayer graphene domain walls. Nature 520, 650–655 (2015). https://doi.org/10.1038/nature14364
  84. A. Thomson, S. Chatterjee, S. Sachdev, M.S. Scheurer, Triangular antiferromagnetism on the honeycomb lattice of twisted bilayer graphene. Phys. Rev. B 98, 075109 (2018). https://doi.org/10.1103/PhysRevB.98.075109
  85. T. Ohta, A. Bostwick, T. Seyller, K. Horn, E. Rotenberg, Controlling the electronic structure of bilayer graphene. Science 313(5789), 951–954 (2006). https://doi.org/10.1126/science.1130681
  86. J.B. Yin, H. Wang, H. Peng, Z.J. Tan, L. Liao et al., Selectively enhanced photocurrent generation in twisted bilayer graphene with van Hove singularity. Nat. Commun. 7, 10699 (2016). https://doi.org/10.1038/ncomms10699
  87. S. Shallcross, S. Sharma, O. Pankratov, Emergent momentum scale, localization, and van Hove singularities in the graphene twist bilayer. Phys. Rev. B 87, 245403 (2013). https://doi.org/10.1103/PhysRevB.87.245403
  88. S. Shallcross, S. Sharma, E. Kandelaki, O.A. Pankratov, Electronic structure of turbostratic graphene. Phys. Rev. B 81, 1 (2010). https://doi.org/10.1103/PhysRevB.81.165105
  89. W. Landgraf, S. Shallcross, K. Türschmann, D. Weckbecker, O. Pankratov, Electronic structure of twisted graphene flakes. Phys. Rev. B 87, 075433 (2013). https://doi.org/10.1103/PhysRevB.87.075433
  90. T. Ohta, J.T. Robinson, P.J. Feibelman, A. Bostwick, E. Rotenberg, T.E. Beechem, Evidence for interlayer coupling and moiré periodic potentials in twisted bilayer graphene. Phys. Rev. Lett. 109, 186807 (2012). https://doi.org/10.1103/PhysRevLett.109.186807
  91. W. Yan, L. Meng, M.X. Liu, J.B. Qiao, Z.D. Chu et al., Angle-dependent van Hove singularities and their breakdown in twisted graphene bilayers. Phys. Rev. B 90, 115402 (2014). https://doi.org/10.1103/PhysRevB.90.115402
  92. A. Luican, G.H. Li, A. Reina, J. Kong, R.R. Nair, K.S. Novoselov, A.K. Geim, E.Y. Andrei, Single-layer behavior and its breakdown in twisted graphene layers. Phys. Rev. Lett. 106, 126802 (2011). https://doi.org/10.1103/PhysRevLett.106.126802
  93. S. Coh, L.Z. Tan, S.G. Louie, M.L. Cohen, Theory of the Raman spectrum of rotated double-layer graphene. Phys. Rev. B 88, 165431 (2013). https://doi.org/10.1103/PhysRevB.88.165431
  94. K. Sato, R. Saito, C.X. Cong, T. Yu, M.S. Dresselhaus, Zone folding effect in Raman G-band intensity of twisted bilayer graphene. Phys. Rev. B 86, 125414 (2012). https://doi.org/10.1103/PhysRevB.86.125414
  95. P. Poncharal, A. Ayari, T. Michel, J.L. Sauvajol, Raman spectra of misoriented bilayer graphene. Phys. Rev. B 78, 113407 (2008). https://doi.org/10.1103/PhysRevB.78.113407
  96. Z.H. Ni, Y.Y. Wang, T. Yu, Y.M. You, Z.X. Shen, Reduction of fermi velocity in folded graphene observed by resonance Raman spectroscopy. Phys. Rev. B 77, 235403 (2008). https://doi.org/10.1103/PhysRevB.77.235403
  97. Y.Y. Wang, Z.H. Ni, L. Liu, Y.H. Liu, C.X. Cong et al., Stacking-dependent optical conductivity of bilayer graphene. ACS Nano 4(7), 4074–4080 (2010). https://doi.org/10.1021/nn1004974
  98. I. Brihuega, P. Mallet, H. González-Herrero, G. Trambly de Laissardière, M.M. Ugeda et al., Unraveling the intrinsic and robust nature of van Hove singularities in twisted bilayer graphene by scanning tunneling microscopy and theoretical analysis. Phys. Rev. Lett. 109, 196802 (2012). https://doi.org/10.1103/PhysRevLett.109.196802
  99. F. Symalla, S. Shallcross, I. Beljakov, K. Fink, W. Wenzel, V. Meded, Band-gap engineering with a twist: formation of intercalant superlattices in twisted graphene bilayers. Phys. Rev. B 91, 205412 (2015). https://doi.org/10.1103/PhysRevB.91.205412
  100. D. Wong, Y. Wang, J. Jung, S. Pezzini, A.M. DaSilva et al., Crommie, local spectroscopy of moiré-induced electronic structure in gate-tunable twisted bilayer graphene. Phys. Rev. B 92, 155409 (2015). https://doi.org/10.1103/PhysRevB.92.155409
  101. J.B. Wu, M.L. Lin, X. Cong, H.N. Liua, P.H. Tan, Raman spectroscopy of graphene-based materials and its applications in related devices. Chem. Soc. Rev. 47, 1822 (2018). https://doi.org/10.1039/c6cs00915h
  102. H. Nishi, Y. Matsushita, A. Oshiyama, Band-unfolding approach to moiré-induced band-gap opening and Fermi level velocity reduction in twisted bilayer graphene. Phys. Rev. B 95, 085420 (2017). https://doi.org/10.1103/PhysRevB.95.085420
  103. K. Uchida, S. Furuya, J.I. Iwata, A. Oshiyama, Atomic corrugation and electron localization due to moiré patterns in twisted bilayer graphenes. Phys. Rev. B 90, 155451 (2014). https://doi.org/10.1103/PhysRevB.90.155451
  104. A. Ferrari, D. Basko, Raman spectroscopy as a versatile tool for studying the properties of graphene. Nat. Nano 8, 235–246 (2013). https://doi.org/10.1038/NNANO.2013.46
  105. L.M. Malard, M.A. Pimenta, G. Dresselhaus, M.S. Dresselhaus, Raman spectroscopy in graphene. Phys. Rep. 473, 51–87 (2009). https://doi.org/10.1016/j.physrep.2009.02.003
  106. L.M. Malard, J. Nilsson, D.C. Elias, J.C. Brant, F. Plentz, E.S. Alves, A.H. Castro Neto, M.A. Pimenta, Probing the electronic structure of bilayer graphene by Raman scattering. Phys. Rev. B 76, 201401(R) (2007). https://doi.org/10.1103/PhysRevB.76.201401
  107. A.C. Ferrari, J.C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri et al., Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97, 187401 (2006). https://doi.org/10.1103/PhysRevLett.97.187401
  108. R. Saito, A. Jorio, A.G. Souza Filho, G. Dresselhaus, M.S. Dresselhaus, M.A. Pimenta, Probing phonon dispersion relations of graphite by double resonance Raman scattering. Phys. Rev. Lett. 88, 027401 (2001). https://doi.org/10.1103/PhysRevLett.88.027401
  109. C. Thomsen, S. Reich, Double resonant Raman scattering in graphite. Phys. Rev. Lett. 85(24), 5214–5217 (2000). https://doi.org/10.1103/PhysRevLett.85.5214
  110. V. Carozo, C.M. Almeida, E.H.M. Ferreira, L.G. Cancado, C.A. Achete, A. Jorio, Raman signature of graphene superlattices. Nano Lett. 11, 4527–4534 (2011). https://doi.org/10.1021/nl201370m
  111. J.B. Wu, X. Zhang, M. Ijäs, W.P. Han, X.F. Qiao et al., Resonant Raman spectroscopy of twisted multilayer graphene. Nat. Commun. 5, 5309 (2014). https://doi.org/10.1038/ncomms6309
  112. J. Campos-Delgado, L.G. Cançado, C.A. Achete, A. Jorio, J.P. Raskin, Raman scattering study of the phonon dispersion in twisted bilayer graphene. Nano Res. 6, 269–274 (2013). https://doi.org/10.1007/s12274-013-0304-z
  113. J.B. Wu, H. Wang, X.L. Li, H.L. Peng, P.H. Tan, Raman spectroscopic characterization of stacking configuration and interlayer coupling of twisted multilayer graphene grown by chemical vapor deposition. Carbon 110, 225–231 (2016). https://doi.org/10.1016/j.carbon.2016.09.006
  114. C.H. Lui, L.M. Malard, S. Kim, G. Lantz, F.E. Laverge, R. Saito, T.F. Heinz, Observation of layer-breathing mode vibrations in few-layer graphene through combination Raman scattering. Nano Lett. 12, 5539–5544 (2012). https://doi.org/10.1021/nl302450s
  115. R. He, T.F. Chung, C. Delaney, C. Keiser, L.A. Jauregui et al., Observation of low energy Raman modes in twisted bilayer graphene. Nano Lett. 13, 3594–3601 (2013). https://doi.org/10.1021/nl4013387
  116. A.K. Gupta, Y.J. Tang, V.H. Crespi, P.C. Eklund, Nondispersive Raman D band activated by well-ordered interlayer interactions in rotationally stacked bilayer graphene. Phys. Rev. B 82, 241406(R) (2010). https://doi.org/10.1103/PhysRevB.82.241406
  117. A. Jorio, M. Kasperczyk, N. Clark, E. Neu, P. Maletinsky, A. Vijayaraghavan, L. Novotny, Optical-phonon resonances with saddle-point excitons in twisted-bilayer graphene. Nano Lett. 14, 5687–5692 (2014). https://doi.org/10.1021/nl502412g
  118. R.W. Havener, H. Zhuang, L. Brown, R.G. Hennig, J. Park, Angle-resolved Raman imaging of interlayer rotations and interactions in twisted bilayer graphene. Nano Lett. 12, 3162–3167 (2012). https://doi.org/10.1021/nl301137k
  119. J. Hass, F. Varchon, J.E. Millán-Otoya, M. Sprinkle, N. Sharma et al., Why multilayer graphene on 4H-SiC(0001) behaves like a single sheet of graphene. Phys. Rev. Lett. 100, 125504 (2008). https://doi.org/10.1103/PhysRevLett.100.125504
  120. R. Bistritzer, A.H. MacDonald, Moiré bands in twisted double-layer graphene. PNAS 108(30), 12233–12237 (2011). https://doi.org/10.1073/pnas.1108174108
  121. J.M.B. Lopes dos Santos, N.M.R. Peres, A.H. Castro Neto, Continuum model of the twisted graphene bilayer. Phys. Rev. B 86, 155449 (2012). https://doi.org/10.1103/PhysRevB.86.155449
  122. M. Koshino, Stacking-dependent optical absorption in multilayer graphene. N. J. Phys. 15, 015010 (2013). https://doi.org/10.1088/1367-2630/15/1/015010
  123. Z.Q. Li, E.A. Henriksen, Z. Jiang, Z. Hao, M.C. Martin, P. Kim, H.L. Stormer, D.N. Basov, Band structure asymmetry of bilayer graphene revealed by infrared spectroscopy. Phys. Rev. Lett. 102, 037403 (2009). https://doi.org/10.1103/PhysRevLett.102.037403
  124. K.F. Mak, M.Y. Sfeir, J.A. Misewich, T.F. Heinz, The evolution of electronic structure in few-layer graphene revealed by optical spectroscopy. PNAS 107(34), 14999–15004 (2010). https://doi.org/10.1073/pnas.1004595107
  125. Y.B. Zhang, T.T. Tang, C. Girit, Z. Hao, M.C. Martin et al., Direct observation of a widely tunable bandgap in bilayer graphene. Nature 459, 820–823 (2009). https://doi.org/10.1038/nature08105
  126. H.A. Le, V.N. Do, Electronic structure and optical properties of twisted bilayer graphene calculated via time evolution of states in real space. Phys. Rev. B 97, 125136 (2018). https://doi.org/10.1103/PhysRevB.97.125136
  127. K. Yu, N.V. Luan, T. Kim, J. Jeon, J. Kim, P. Moon, Y.H. Lee, E.J. Choi, Gate tunable optical absorption and band structure of twisted bilayer graphene. Phys. Rev. B 99, 241405(R) (2019). https://doi.org/10.1103/PhysRevB.99.241405
  128. C.J. Tabert, E.J. Nicol, Optical conductivity of twisted bilayer graphene. Phys. Rev. B 87, 121402(R) (2013). https://doi.org/10.1103/PhysRevB.87.121402
  129. P. Moon, M. Koshino, Optical absorption in twisted bilayer graphene. Phys. Rev. B 87, 205404 (2013). https://doi.org/10.1103/PhysRevB.87.205404
  130. H. Patel, L. Huang, C.J. Kim, J. Park, M.W. Graham, Stacking angle-tunable photoluminescence from interlayer exciton states in twisted bilayer graphene. Nat. Commun. 10, 1445 (2019). https://doi.org/10.1038/s41467-019-09097-x
  131. F. Xia, T. Mueller, R.G. Mojarad, M. Freitag, Y.M. Lin, J. Tsang, V. Perebeinos, P. Avouris, Photocurrent imaging and efficient photon detection in a graphene transistor. Nano Lett. 9(3), 1039–1044 (2009). https://doi.org/10.1021/nl8033812
  132. T. Mueller, F. Xia, M. Freitag, J. Tsang, P. Avouris, Role of contacts in graphene transistors: a scanning photocurrent study. Phys. Rev. B 79, 245430 (2009). https://doi.org/10.1103/PhysRevB.79.245430
  133. U. Mogera, R. Dhanya, R. Pujar, C. Narayana, G.U. Kulkarni, Highly decoupled graphene multilayers: turbostraticity at its best. J. Phys. Chem. Lett. 6, 4437–4443 (2015). https://doi.org/10.1021/acs.jpclett.5b02145
  134. U. Mogera, S. Walia, B. Bannur, M. Gedda, G.U. Kulkarni, Intrinsic nature of graphene revealed in temperature-dependent transport of twisted multilayer graphene. J. Phys. Chem. C 121, 13938–13943 (2017). https://doi.org/10.1021/acs.jpcc.7b04068
  135. Z.W. Yu, A. Song, L.Z. Sun, Y. Li, L. Gao et al., Understanding interlayer contact conductance in twisted bilayer graphene. Small (2019). https://doi.org/10.1002/smll.201902844
  136. L. Brown, R. Hovden, P. Huang, M. Wojcik, D.A. Muller, J. Park, Twinning and twisting of tri- and bilayer graphene. Nano Lett. 12, 1609–1615 (2012). https://doi.org/10.1021/nl204547v
  137. H. Polshyn, M. Yankowitz, S.W. Chen, Y.X. Zhang, K. Watanabe, T. Taniguchi, C.R. Dean, A.F. Young, Large linear-in-temperature resistivity in twisted bilayer graphene. Nat. Phys. 15, 1011–1016 (2019). https://doi.org/10.1038/s41567-019-0596-3
  138. L.J. Yin, J.B. Qiao, W.X. Wang, W.J. Zuo, W. Yan et al., Landau quantization and Fermi velocity renormalization in twisted graphene bilayers. Phys. Rev. B 92, 201408(R) (2015). https://doi.org/10.1103/PhysRevB.92.201408
  139. J. Wang, X. Mu, L. Wang, M. Sun, Properties and applications of new superlattice: twisted bilayer graphene. Mater. Today Phys. 9, 100099 (2019). https://doi.org/10.1016/j.mtphys.2019.100099
  140. B. Deng, B.B. Wang, N. Li, R. Li, Y. Wang et al., Interlayer decoupling in 30° twisted bilayer graphene quasicrystal. ACS Nano 14, 1656–1664 (2020). https://doi.org/10.1021/acsnano.9b07091
  141. Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, P.J. Herrero, Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018). https://doi.org/10.1038/nature26160
  142. Y. Cao, J.Y. Luo, V. Fatemi, S. Fang, J.D. Sanchez-Yamagishi et al., Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117, 116804 (2016). https://doi.org/10.1126/science.aav1910
  143. M. Yankowitz, S.W. Chen, H. Polshyn, Y.X. Zhang, K. Watanabe et al., Tuning superconductivity in twisted bilayer graphene. Science 363(6431), 1059–1064 (2019). https://doi.org/10.1073/pnas.1108174108
  144. E. Codecido, Q.Y. Wang, R. Koester, S. Che, H.D. Tian, Correlated insulating and superconducting states in twisted bilayer graphene below the magic. Sci. Adv. 5(9), eaaw9770 (2019). https://doi.org/10.1126/sciadv.aaw9770
  145. F. Hu, S.R. Das, Y. Luan, T.F. Chung, Y.P. Chen, Z. Fei, Real-space imaging of the tailored plasmons in twisted bilayer graphene. Phys. Rev. Lett. 119, 247402 (2017). https://doi.org/10.1103/PhysRevLett.119.247402
  146. Y. Cao, D. Chowdhury, D.R. Legrain, O.R. Bigorda, K. Watanabe et al., Strange metal in magic-angle graphene with near Planckian dissipation. Phys. Rev. Lett. 124, 076801 (2020). https://doi.org/10.1103/PhysRevLett.124.076801
  147. L.A. Ponomarenko, R.V. Gorbachev, G.L. Yu, D.C. Elias, R. Jalil et al., Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013). https://doi.org/10.1038/nature12187
  148. C.R. Dean, L. Wang, P. Maher, C. Forsythe, F. Ghahari et al., Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013). https://doi.org/10.1038/nature12186
Read More
Author biographies are not available.
Download this PDF file
PDF
Statistic
Read Counter : 6110 Download : 4621