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Nonlinear Excitations in Graphene and Other Carbon Nano-Polymorphs

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Nonlinear Systems, Vol. 2

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

This review summarizes recent developments in the numerical investigations of nonlinear dynamics of graphene, carbon nanotubes, and fullerenes. Discrete breathers (DBs) or, synonymously, intrinsic localized modes are discussed together with the nonlinear delocalised vibrational modes (DVM). These nonlinear excitations are expected to considerably affect physical and mechanical properties of \(sp^2\) carbon nanomaterials, for example, their thermal and electrical conductivity, defect nucleation and healing, etc. Our knowledge of the DB properties in carbon nanomaterials is insufficient for designing a setup for their reliable experimental observation, that is why numerical studies in this area are of crucial importance today. It is indicated that the results obtained by molecular dynamics method significantly depend on the interatomic potentials, making verification of these results by first-principle modelling indispensable. Finally, the associated challenges and prospects on the future study of nonlinear excitations in graphene and other carbon nanomaterials are discussed.

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References

  1. Archilla, J.F.R., Coelho, S.M.M., Auret, F.D., Dubinko, V.I., Hizhnyakov, V.: Long range annealing of defects in germanium by low energy plasma ions. Phys. D 297, 56–61 (2015)

    Article  Google Scholar 

  2. Archilla, J.F.R., Russell, F.M.: On the charge of quodons. Lett. Mater. 6, 3–8 (2016)

    Article  Google Scholar 

  3. Aubry, S.: Breathers in nonlinear lattices: existence, linear stability and quantization. Phys. D 103, 201–250 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bahadir, E.B., Sezginturk, M.K.: Applications of graphene in electrochemical sensing and biosensing. Trends Anal. Chem. 76, 1–14 (2016)

    Article  Google Scholar 

  5. Baimova, J.: Property control by elastic strain engineering: application to graphene. J. Micromech. Mol. Phys. 2, 1750001 (2016)

    Google Scholar 

  6. Baimova, J.A., Dmitriev, S.V., Zhou, K.: Discrete breather clusters in strained graphene. Europhys. Lett. 100, 36005 (2012)

    Article  ADS  Google Scholar 

  7. Baimova, J.A., Dmitriev, S.V., Zhou, K., Savin, A.V.: Unidirectional ripples in strained graphene nanoribbons with clamped edges at zero and finite temperatures. Phys. Rev. B 86, 035427 (2012)

    Article  ADS  Google Scholar 

  8. Baimova, J.A., Korznikova, E.A., Lobzenko, I.P., Dmitriev, S.V.: Discrete breathers in carbon and hydrocarbon nanostructures. Rev. Adv. Mater. Sci. 42, 68–82 (2015)

    Google Scholar 

  9. Baimova, J.A., Liu, B., Dmitriev, S.V., Zhou, K., Nazarov, A.A.: Effect of Stone-Thrower-Wales defect on structural stability of graphene at zero and finite temperatures. Europhys. Lett. 103, 46001 (2013)

    Article  ADS  Google Scholar 

  10. Baimova, Y.A., Dmitriev, S.V., Savin, A.V., Kivshar, Y.S.: Velocities of sound and the densities of phonon states in a uniformly strained flat graphene sheet. Phys. Solid State 54, 866–874 (2012)

    Google Scholar 

  11. Balandin, A.A., Ghosh, S., Bao, W., Calizo, I., Teweldebrhan, D., Miao, F., Lau, C.N.: Superior thermal conductivity of single-layer graphene. Nano Lett. 8, 902–907 (2008)

    Article  ADS  Google Scholar 

  12. Barani, E., Lobzenko, I.P., Korznikova, E.A., Soboleva, E.G., Dmitriev, S.V., Zhou, K., Marjaneh, A.M.: Transverse discrete breathers in unstrained graphene. Eur. Phys. J. B 90, 38 (2017)

    Google Scholar 

  13. Binder, P., Abraimov, D., Ustinov, A.V., Flach, S., Zolotaryuk, Y.: Observation of breathers in Josephson ladders. Phys. Rev. Lett. 84, 745–748 (2000)

    Article  ADS  Google Scholar 

  14. Bolotin, K.I., Sikes, K.J., Jiang, Z., Klima, M., Fudenberg, G., Hone, J., Kim, P., Stormer, H.L.: Ultrahigh electron mobility in suspended graphene. Solid State Commun. 146, 351–355 (2008)

    Article  ADS  Google Scholar 

  15. Brenner, D.W.: Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B 42, 9458 (1990)

    Article  ADS  Google Scholar 

  16. Burlakov, V.M., Kiselev, S.A., Rupasov, V.I.: Localized excitations of uniform anharmonic lattices. JETP Lett. 51, 544–547 (1990)

    ADS  Google Scholar 

  17. Campbell, D.K., Flach, S., Kivshar, Y.S.: Localizing energy through nonlinearity and discreteness. Phys. Today 57, 43 (2004)

    Article  ADS  Google Scholar 

  18. Chechin, G.M., Dmitriev, S.V., Lobzenko, I.P., Ryabov, D.S.: Properties of discrete breathers in graphane from ab initio simulations. Phys. Rev. B 90, 045432 (2014)

    Article  ADS  Google Scholar 

  19. Chechin, G.M., Lobzenko, I.P.: Ab initio refining of quasibreathers in graphane. Lett. Mater. 4, 226–229 (2014)

    Article  Google Scholar 

  20. Chechin, G.M., Ryabov, D.S., Shcherbinin, S.A.: Nonlinear vibrational modes in graphene: group-theoretical results. Lett. Mater. 6, 9–15 (2016)

    Article  Google Scholar 

  21. Chechin, G.M., Sakhnenko, V.P.: Interactions between normal modes in nonlinear dynamical systems with discrete symmetry. Exact results. Phys. D 117, 43–76 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  22. Chechin, G.M., Sizintsev, D.A., Usoltsev, O.A.: Properties of pi-mode vibrations in strained carbon chains. Lett. Mater. 6, 146–151 (2016)

    Article  Google Scholar 

  23. Chechin, G.M., Usoltsev, O.A., Sizintsev, D.A.: On stability of nonlinear atomic vibrations in strained carbon chains. Lett. Mater. 6, 309–316 (2016)

    Article  Google Scholar 

  24. Chetverikov, A.P., Ebeling, W., Lakhno, V.D., Shigaev, A.S., Velarde, M.G.: On the possibility that local mechanical forcing permits directionally-controlled long-range electron transfer along dna-like molecular wires with no need of an external electric field: mechanical control of electrons. Eur. Phys. J. B 89, 101 (2016)

    Article  ADS  Google Scholar 

  25. Chetverikov, A.P., Ebeling, W., Velarde, M.G.: On the temperature dependence of fast electron transport in crystal lattices. Eur. Phys. J. B 88, 202 (2015)

    Article  ADS  Google Scholar 

  26. Chetverikov, A.P., Ebeling, W., Velarde, M.G.: Long-range electron transport donor-acceptor in nonlinear lattices. Entropy 18, 92 (2016)

    Article  ADS  Google Scholar 

  27. Chetverikov, A.P., Ebeling, W., Velarde, M.G.: Soliton assisted control of source to drain electron transport along natural channels crystallographic axes in two-dimensional triangular crystal lattices. Eur. Phys. J. B 89, 196 (2016)

    Article  ADS  Google Scholar 

  28. Cuevas, J., Archilla, J.F.R., Sanchez-Rey, B., Romero, F.R.: Interaction of moving discrete breathers with vacancies. Phys. D 216, 115–120 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  29. Dmitriev, S.V.: Discrete breathers in crystals: energy localization and transport. J. Micromech. Mol. Phys. 1, 1630001 (2016)

    Article  Google Scholar 

  30. Dmitriev, S.V., Baimova, J.A., Savin, A.V., Kivshar, YuS: Ultimate strength, ripples, sound velocities, and density of phonon states of strained graphene. Comput. Mater. Sci. 53, 194–203 (2012)

    Article  Google Scholar 

  31. Dmitriev, S.V., Chetverikov, A.P., Velarde, M.G.: Discrete breathers in 2D and 3D crystals. Phys. Status Solidi B 252, 1682–1686 (2015)

    Article  ADS  Google Scholar 

  32. Dmitriev, S.V., Korznikova, E.A., Baimova, J.A., Velarde, M.G.: Discrete breathers in crystals. Phys. Usp. 59, 446–461 (2016)

    Google Scholar 

  33. Doi, Y., Nakatani, A.: Structure and stability of nonlinear vibration mode in graphene sheet. In: Procedia Engineering, Proceedings of the 11th International Conference On The Mechanical Behavior Of Materials (ICM11), vol. 10, pp. 3393–3398 (2011). Como, Italy (2011)

    Google Scholar 

  34. Doi, Y., Nakatani, A.: Numerical study on unstable perturbation of intrinsic localized modes in graphene. J. Solid. Mech. Mater. Eng. 6, 71–80 (2012)

    Article  Google Scholar 

  35. Doi, Y., Nakatani, A.: Structure and stability of discrete breather in zigzag and armchair carbon nanotubes. Lett. Mater. 6, 49–53 (2016)

    Article  Google Scholar 

  36. Dubinko, V.I., Archilla, J.F.R., Dmitriev, S.V., Hizhnyakov, V.: Rate theory of acceleration of defect annealing driven by discrete breathers. In: J.F.R. Archilla, N. Jiménez, V.J. Sánchez-Morcillo, L.M. García-Raffi (eds.) Quodons in Mica: Nonlinear Localized Travelling Excitations in Crystals, Springer Series in Materials Science, vol. 221, pp. 381–398 (2015)

    Google Scholar 

  37. Evazzade, I., Lobzenko, I.P., Korznikova, E.A., Ovidko, I.A., Roknabadi, M.R., Dmitriev, S.V.: Energy transfer in strained graphene assisted by discrete breathers excited by external ac driving. Phys. Rev. B 95, 035423 (2017)

    Article  ADS  Google Scholar 

  38. Ferrari, A.C., et al.: Science and technology roadmap for graphene, related two-dimensional crystals and hybrid systems. Nanoscale 7, 4598–4810 (2015)

    Article  ADS  Google Scholar 

  39. Flach, S., Willis, C.R.: Discrete breathers. Phys. Rep. 295, 181–264 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  40. Flach, S., Willis, C.R.: Discrete breathers in nonlinear lattices: Experimental detection in a Josephson array. Phys. Rep. 467, 1–116 (1998)

    Article  ADS  Google Scholar 

  41. Fraile, A., Koukaras, E.N., Papagelis, K., Lazarides, N., Tsironis, G.P.: Long-lived discrete breathers in free-standing graphene. Chaos Soliton Fract. 87, 262–267 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  42. Geniet, F., Leon, J.: Energy transmission in the forbidden band gap of a nonlinear chain. Phys. Rev. Lett. 89, 134102 (2002)

    Article  ADS  Google Scholar 

  43. Haas, M., Hizhnyakov, V., Shelkan, A., Klopov, M., Sievers, A.J.: Prediction of high-frequency intrinsic localized modes in Ni and Nb. Phys. Rev. B 84, 144303 (2011)

    Google Scholar 

  44. Hizhnyakov, V., Haas, M., Shelkan, A., Klopov, M.: Theory and molecular dynamics simulations of intrinsic localized modes and defect formation in solids. Phys. Scr. 89, 044003 (2014)

    Article  ADS  Google Scholar 

  45. Hizhnyakov, V., Haas, M., Shelkan, A., Klopov, M.: Standing and moving discrete breathers with frequencies above the phonon spectrum. In: J.F.R. Archilla, N. Jiménez, V.J. Sánchez-Morcillo, L.M. García-Raffi (eds.) Quodons In Mica: Nonlinear Localized Travelling Excitations In Crystals, Springer Series in Materials Science, vol. 221, pp. 229–245 (2015)

    Google Scholar 

  46. Hizhnyakov, V., Klopov, M., Shelkan, A.: Transverse intrinsic localized modes in monatomic chain and in graphene. Phys. Lett. A 380, 1075 (2016)

    Article  ADS  MATH  Google Scholar 

  47. Hizhnyakov, V., Shelkan, A., Haas, M., Klopov, M.: Discrete breathers above phonon spectrum. Lett. Mater. 6, 61–72 (2016)

    Article  Google Scholar 

  48. Iijima, S.: Helical microtubules of graphitic carbon. Nature 354, 56–58 (1991)

    Article  ADS  Google Scholar 

  49. Kevrekidis, P.G., Dmitriev, S.V., Takeno, S., Bishop, A.R., Aifantis, E.C.: Rich example of geometrically induced nonlinearity: From rotobreathers and kinks to moving localized modes and resonant energy transfer. Phys. Rev. E 70, 066627 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  50. Khadeeva, L.Z., Dmitriev, S.V.: Discrete breathers in crystals with NaCl structure. Phys. Rev. B 81, 214306 (2010)

    Article  ADS  MATH  Google Scholar 

  51. Khadeeva, L.Z., Dmitriev, S.V., Kivshar, Y.S.: Discrete breathers in deformed graphene. JETP Lett. 94, 539–543 (2011)

    Article  ADS  Google Scholar 

  52. Khomeriki, R., Lepri, S., Ruffo, S.: Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model. Phys. Rev. E 70, 066626 (2004)

    Article  ADS  Google Scholar 

  53. Kimura, M., Mitani, A., Doi, S.: Existence and stability of intrinsic localized modes in a finite FPU chain placed in three-dimensional space. Lett. Mater. 6, 22–26 (2016)

    Article  ADS  Google Scholar 

  54. Kinoshita, Y., Yamayose, Y., Doi, Y., Nakatani, A., Kitamura, T.: Selective excitations of intrinsic localized modes of atomic scales in carbon nanotubes. Phys. D 77, 024307 (2008)

    ADS  Google Scholar 

  55. Kiselev, S.A., Sievers, A.J.: Generation of intrinsic vibrational gap modes in three-dimensional ionic crystals. Phys. Rev. B 55, 5755 (1997)

    Article  ADS  Google Scholar 

  56. Kistanov, A.A., Baimova, Y.A., Dmitriev, S.V.: A molecular dynamics study of [111]-polarized gap discrete breathers in a crystal with NaCl-type structure. Tech. Phys. Lett. 38, 676 (2012)

    Article  ADS  Google Scholar 

  57. Kistanov, A.A., Dmitriev, S.V., Chetverikov, A.P., Velarde, M.G.: Head-on and head-off collisions of discrete breathers in two-dimensional anharmonic crystal lattices. Eur. Phys. J. B 87, 211 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  58. Kistanov, A.A., Dmitriev, S.V., Semenov, A.S., Dubinko, V.I., Terentev, D.A.: Interaction of propagating discrete breathers with a vacancy in a two-dimensional crystal. Tech. Phys. Lett. 40, 657 (2014)

    Article  ADS  Google Scholar 

  59. Kopidakis, G., Aubry, S.: Discrete breathers in realistic models: hydrocarbon structures. Phys. B 296, 237–250 (2001)

    Google Scholar 

  60. Korznikova, E.A., Bachurin, D.V., Fomin, SYu., Chetverikov, A.P., Dmitriev, S.V.: Instability of vibrational modes in hexagonal lattice. Eur. Phys. J. B 90, 23 (2017)

    Article  ADS  Google Scholar 

  61. Korznikova, E.A., Baimova, J.A., Dmitriev, S.V.: Effect of strain on gap discrete breathers at the edge of armchair graphene nanoribbons. Europhys. Lett. 102, 60004 (2013)

    Article  ADS  Google Scholar 

  62. Korznikova, E.A., Dmitriev, S.V.: Moving wrinklon in graphene nanoribbons. J. Phys. D Appl. Phys. 47, 345307 (2014)

    Google Scholar 

  63. Korznikova, E.A., Fomin, SYu., Soboleva, E.G., Dmitriev, S.V.: Highly symmetric discrete breather in a two-dimensional Morse crystal. JETP Lett. 103, 277–281 (2016)

    Article  ADS  Google Scholar 

  64. Korznikova, E.A., Savin, A.V., Baimova, Y.A., Dmitriev, S.V., Mulyukov, R.R.: Discrete breather on the edge of the graphene sheet with the armchair orientation. JETP Lett. 99, 222–226 (2012)

    Article  ADS  Google Scholar 

  65. Kroto, H.W., Heath, J.R., Obrien, S.C., Curl, R.F., Smalley, R.E.: C60: Buckminsterfullerene. Nature 318, 162–163 (1985)

    Article  ADS  Google Scholar 

  66. Lee, C., Wei, X., Kysar, J.W., Hone, J.: Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science 321, 385–388 (2008)

    Article  ADS  Google Scholar 

  67. Lindsay, L., Broido, D.A.: Optimized Tersoff and Brenner empirical potential parameters for lattice dynamics and phonon thermal transport in carbon nanotubes and graphene. Phys. Rev. B 81, 205441 (2010)

    Article  ADS  Google Scholar 

  68. Liu, B., Baimova, J.A., Zhou, K., Dmitriev, S.V., Wang, X., Zhu, H.: Discrete breathers in hydrogenated graphene. J. Phys. D: Appl. Phys. 46, 305302 (2013)

    Article  Google Scholar 

  69. Lobzenko, I., Dmitriev, S., Baimova, J., Dzhelauhova, G.: Numerical studies of discrete quasibreathers in graphene in the framework of density functional theory. Mater. Sci. Forum 845, 215–218 (2016)

    Article  Google Scholar 

  70. Lobzenko, I.P.: Discrete breathers properties obtained from ab-initio calculations in graphene and graphane. Lett. Mater. 6, 73–76 (2016)

    Article  Google Scholar 

  71. Lobzenko, I.P., Chechin, G.M., Bezuglova, G.S., Baimova, YuA., Korznikova, E.A., Dmitriev, S.V.: Ab initio simulation of gap discrete breathers in strained graphene. Phys. Solid State 58, 633–639 (2016)

    Google Scholar 

  72. Los, J.H., Fasolino, A.: Intrinsic long-range bond-order potential for carbon: performance in Monte Carlo simulations of graphitization. Phys. Rev. B 68, 024–107 (2003)

    Article  Google Scholar 

  73. Los, J.H., Ghiringhelli, L.M., Meijer, E.J., Fasolino, A.: Improved long-range reactive bond-order potential for carbon I. Construction. Phys. Rev. B 72, 214102 (2005)

    Article  ADS  Google Scholar 

  74. Los, J.H., Zakharchenko, K.V., Katsnelson, M.I., Fasolino, A.: Melting temperature of graphene. Phys. Rev. B 91, 045415 (2015)

    Google Scholar 

  75. Murzaev, R.T., Bachurin, D.V., Korznikova, E.A., Dmitriev, S.V.: Localized vibrational modes in diamond. Phys. Lett. A 381, 1003–1008 (2017)

    Google Scholar 

  76. Murzaev, R.T., Kistanov, A.A., Dubinko, V.I., Terentyev, D.A., Dmitriev, S.V.: Moving discrete breathers in bcc metals V, Fe and W. Comput. Mater. Sci. 98, 88 (2015)

    Article  Google Scholar 

  77. Novoselov, K.S., Fal’ko, V.I., Colombo, L., Gellert, P.R., Schwab, M.G., Kim, K.: A roadmap for graphene. Nature 490, 192–200 (2012)

    Google Scholar 

  78. Podlivaev, A.I., Katin, K.P.: On the dependence of the lifetime of an atomic cluster on the intensity of its heat exchange with the environment. JETP Lett. 92, 52–56 (2010)

    Article  ADS  Google Scholar 

  79. Podlivaev, A.I., Katin, K.P., Lobanov, D.A., Openov, L.A.: Specific features of the stone-wales transformation in the C20 and C36 fullerenes. Phys. Solid State 53, 215–220 (2011)

    Google Scholar 

  80. Raccichini, R., Varzi, A., Passerini, S., Scrosati, B.: The role of graphene for electrochemical energy storage. Nat. Mater. 14, 271–279 (2015)

    Article  ADS  Google Scholar 

  81. Reigada, R., Sarmiento, A., Lindenberg, K.: Energy relaxation in nonlinear one-dimensional lattices. Phys. Rev. E 64, 066608 (2001)

    Article  ADS  Google Scholar 

  82. Sato, M., Mukaide, T., Nakaguchi, T., Sievers, A.: Inductive intrinsic localized modes in a one-dimensional nonlinear electric transmission line. Phys. Rev. B 94, 012223 (2016)

    Article  ADS  Google Scholar 

  83. Sato, M., Sievers, A.: Experimental and numerical exploration of intrinsic localized modes in an atomic lattice. J. Biol. Phys. 35, 57–72 (2009)

    Article  Google Scholar 

  84. Savin, A.V., Kivshar, Yu.S.: Nonlinear breatherlike localized modes in C60 nanocrystals. Phys. Rev. B 85, 125427 (2012)

    Google Scholar 

  85. Savin, A.V., Kivshar, Yu.S: Localized defect modes in graphene. Europhys. Lett. 82, 66002 (2008)

    Google Scholar 

  86. Savin, A.V., Kivshar, Yu.S.: Discrete breathers in carbon nanotubes. Phys. Rev. B 88, 125417 (2013)

    Google Scholar 

  87. Savin, A.V., Kivshar, Yu.S., Hu, B.: Suppression of thermal conductivity in graphene nanoribbons with rough edges. Phys. Rev. B 82, 195422 (2010)

    Google Scholar 

  88. Savin, A.V., Korznikova, E.A., Dmitriev, S.V.: Low frequency vibrations of carbon nanoscrolls. Lett. Mater. 6, 77–81 (2016)

    Article  Google Scholar 

  89. Savin, A.V., Manevitch, L.I.: Discrete breathers in a polyethylene chain. Phys. Rev. B 67, 144302 (2003)

    Article  ADS  Google Scholar 

  90. Shimada, T., Shirasaki, D., Kinoshita, Y., Doi, Y., Nakatani, A., Kitamura, T.: Influence of nonlinear atomic interaction on excitation of intrinsic localized modes in carbon nanotubes. Phys. D 239, 407–413 (2010)

    Article  MATH  Google Scholar 

  91. Shimada, T., Shirasaki, D., Kitamura, T.: Stone-Wales transformations triggered by intrinsic localized modes in carbon nanotubes. Phys. Rev. B 81, 035401 (2010)

    Google Scholar 

  92. Sievers, A.J., Page, J.B.: Unusual anharmonic local mode systems. In: Horton, G.K., Maradudin, A.A. (eds.) Dynamical Properties of Solids, vol. 7, pp. 137–255. North Holland, Amsterdam (1995)

    Google Scholar 

  93. Stuart, S.J., Tutein, A.B., Harrison, J.A.: A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 112, 6472–6486 (2000)

    Article  ADS  Google Scholar 

  94. Terentyev, D.A., Dubinko, A.V., Dubinko, V.I., Dmitriev, S.V., Zhurkin, E.E., Sorokin, M.V.: Interaction of discrete breathers with primary lattice defects in bcc Fe. Model. Simul. Mater. Sci. Eng. 23, 085007 (2015)

    Article  ADS  Google Scholar 

  95. Velarde, M.G., Chetverikov, A.P., Ebeling, W., Dmitriev, S.V., Lakhno, V.D.: From solitons to discrete breathers. Eur. Phys. J. B 89, 233 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  96. Voulgarakis, N.K., Hadjisavvas, G., Kelires, P.C., Tsironis, G.P.: Computational investigation of intrinsic localization in crystalline Si. Phys. Rev. B 69, 113201 (2004)

    Article  ADS  Google Scholar 

  97. Xiong, D., Zhang, J.: Discrete breathers: possible effects on heat transport. Lett. Mater. 6, 27–30 (2016)

    Article  Google Scholar 

  98. Yamayose, Y., Kinoshita, Y., Doi, Y., Nakatani, A., Kitamura, T.: Excitation of intrinsic localized modes in a graphene sheet. Europhys. Lett. 80, 40008 (2007)

    Article  ADS  Google Scholar 

  99. Zakharchenko, K.V., Fasolino, A., Los, J.H., Katsnelson, M.I.: Melting of graphene: from two to one dimension. J. Phys. Condens. Mat. 23, 202202 (2011)

    Article  ADS  Google Scholar 

  100. Zhu, Y., Murali, S., Cai, W., Li, X., Suk, J.W., Potts, J.R., Ruoff, R.S.: Graphene and graphene oxide: synthesis, properties, and applications. Adv. Mater. 22, 3906–3924 (2010)

    Article  Google Scholar 

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Acknowledgements

S.V.D. would like to thank financial support from the Russian Science Foundation, grant no. 14-13-00982. E.A.K., and A.P.Ch. would like to thank financial support from the Russian Science Foundation, grant no. 16-12-10175.

J.A.B. acknowledges financial support from the Scholarship of the President of the Russian Federation for young scientists and PhD students SP-4037.2015.1.

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Authors and Affiliations

  1. Institute for Metals Superplasticity Problems of RAS, 39 Khalturin St., 450001, Ufa, Russia

    Sergey V. Dmitriev, Julia A. Baimova & Elena A. Korznikova

  2. National Research Tomsk State University, 36 Lenin Ave, 634050, Tomsk, Russia

    Sergey V. Dmitriev

  3. M.N. Mikheev Institute of Metal Physics of the Ural Branch of RAS, 18 S. Kovalevskoy, 620990, Ekaterinburg, Russia

    Julia A. Baimova

  4. Saratov State University, 83 Astrakhanskaya St., 410012, Saratov, Russia

    Alexander P. Chetverikov

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  1. Departamento de Fisica Aplicada I, ETSI Informática, Universidad de Sevilla, Sevilla, Spain

    Juan F. R. Archilla

  2. Departamento de Fisica Aplicada I, ETSI Informática, Universidad de Sevilla, Sevilla, Spain

    Faustino Palmero

  3. Departamento de Física de la Materia Condensada, Universidad de Sevilla, Sevilla, Spain

    M. Carmen Lemos

  4. Departamento de Fisica Aplicada I, EPS, Universidad de Sevilla, Sevilla, Spain

    Bernardo Sánchez-Rey

  5. Departamento de Física Atómica, Molecular y Nuclear, Universidad de Sevilla, Sevilla, Spain

    Jesús Casado-Pascual

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Dmitriev, S.V., Baimova, J.A., Korznikova, E.A., Chetverikov, A.P. (2018). Nonlinear Excitations in Graphene and Other Carbon Nano-Polymorphs. In: Archilla, J., Palmero, F., Lemos, M., Sánchez-Rey, B., Casado-Pascual, J. (eds) Nonlinear Systems, Vol. 2. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-72218-4_7

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