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Using the classical molecular dynamics simulations, we have investigated the thermally-excited ripples of the multilayer graphenes at different temperatures, and compared them with those of the single- and doublelayer graphene. It is found that: 1) the ripples in multilayer graphene are intrinsic with a characteristic size of about 100 at room tempe- rature, increasing with increase of temperature; at the same time, the ripples height also increases with the temperature; 2) the ripples intralayer height-height correlation functions for the multilayer graphene follow a power-law behavior, Gh(q) q-; the scaling exponent decreases as temperature increases. Moreover, the scaling exponents are different for different types of multilayer graphene even at the same temperature. All these phenomena result from the anharmonic effects which are induced by the temperature and the interlayer interactions.
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Keywords:
- multilayer graphene /
- molecular dynamics /
- stacking /
- ripple
[1] Morozov S V, Novoselov K S, Katsnelson M I, Schedin F, Ponomarenko L A, Jiang D, Geim A K 2006 Phys. Rev. Lett. 97 016801
[2] Geim A K, Novoselov K S 2007 Nat. Mater. 6 183
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[8] [9] Mermin N D, Wagner H 1966 Phys. Rev. Lett. 17 1133
[10] Mermin N D 1968 Phys. Rev. 176 250
[11] [12] [13] Zinke-Allmang M, Feldman L C, Grabow M H 1992 Surf. Sci. Rep. 16 377
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[15] [16] Landau L D 1937 Phys. Z. Sowjetunion 11 26
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[20] Meyer J C, Geim A K, Katsnelson M I, Novoselov K S, Booth T J, Roth S 2007 Nature 446 60
[21] [22] Fasolino A, Los J H, Katsnelson M I 2007 Nat. Mater. 6 858
[23] [24] [25] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[26] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
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[30] [31] Carlsson J M 2007 Nat. Mater. 6 801
[32] Katsnelson M I, Geim A K 2008 Phil. Trans. R. Soc. A 366 195
[33] [34] Zakharchenko K V, Katsnelson M I, Fasolino A 2009 Phys. Rev. Lett. 102 046808
[35] [36] Liu Z, Suenaga K, Harris P J F, Iijima S 2009 Phys. Rev. Lett. 102 015501
[37] [38] Lu C L, Chang C P, Lin M F 2007 Eur. Phys. J. B 60 161
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[42] de Andres P L, Ramrez R, Vergs J A 2008 Phys. Rev. B 77 045403
[43] [44] [45] Wang T, Guo Q, Liu Y, Sheng K 2012 Chin. Phys. B 21 067301
[46] Meyer J C, Geim A K, Katsnelson M I, Novoselov K S, Obergfell D, Roth S, Girit C, Zettl A 2007 Solid State Commun. 143 101
[47] [48] Chang X, Ge Y, Dong J M 2010 Eur. Phys. J. B 78 103
[49] [50] [51] Norimatsu W, Kusunoki M 2010 Phys. Rev. B 81 161410(R)
[52] Mak K F, Lui C H, Shan J, Heinz T F 2009 Phys. Rev. Lett. 102 256405
[53] [54] [55] Zhu G B, Zhang P 2013 Chin. Phys. B 22 017303
[56] [57] Liu D C, Nocedal J 1989 Mathematical Programming B 45 503
[58] Han T W, He P F 2010 Acta Phys. Sin. 59 3408 (in Chinese) [韩同伟, 贺鹏飞 2010 物理学报 59 3408]
[59] [60] Wang W D, Hao Y, Ji X, Yi C L, Niu X Y 2012 Acta Phys. Sin. 61 200207 (in Chinese) [王卫东, 郝跃, 纪翔, 易成龙, 牛翔宇 2012 物理学报 61 200207]
[61] [62] [63] Hoover W G 1985 Phys. Rev. A 31 1695
[64] [65] Tersoff J 1988 Phys. Rev. B 37 6991
[66] [67] Lennard-Jones J E 1924 Proceedings of the Royal Society (Vol. 106) pp463-469
[68] [69] [70] Popov V N, Henrard L 2002 Phys. Rev. B 65 235415
[71] [72] Lu J P, Yang W 1994 Phys. Rev. B 49 11421
[73] [74] Los J H, Katsnelson M I, Yazyev O V, Zakharchenko K V, Fasolino1 A 2009 Phys. Rev. B 80 121405
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[1] Morozov S V, Novoselov K S, Katsnelson M I, Schedin F, Ponomarenko L A, Jiang D, Geim A K 2006 Phys. Rev. Lett. 97 016801
[2] Geim A K, Novoselov K S 2007 Nat. Mater. 6 183
[3] [4] [5] Nelson D R, Peliti L 1987 J. Phys. 48 1085
[6] [7] Doussal P Le, Radzihovsky L 1992 Phys. Rev. Lett. 69 1209
[8] [9] Mermin N D, Wagner H 1966 Phys. Rev. Lett. 17 1133
[10] Mermin N D 1968 Phys. Rev. 176 250
[11] [12] [13] Zinke-Allmang M, Feldman L C, Grabow M H 1992 Surf. Sci. Rep. 16 377
[14] Peierls R E 1934 Helv. Phys. Acta 7 81
[15] [16] Landau L D 1937 Phys. Z. Sowjetunion 11 26
[17] [18] [19] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[20] Meyer J C, Geim A K, Katsnelson M I, Novoselov K S, Booth T J, Roth S 2007 Nature 446 60
[21] [22] Fasolino A, Los J H, Katsnelson M I 2007 Nat. Mater. 6 858
[23] [24] [25] Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V, Firsov A A 2005 Nature 438 197
[26] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
[27] [28] [29] Schedin F, Geim A K, Morozov S V, Hill E W, Blake P, Katsnelson M I, Novoselov K S 2007 Nat. Mater. 6 652
[30] [31] Carlsson J M 2007 Nat. Mater. 6 801
[32] Katsnelson M I, Geim A K 2008 Phil. Trans. R. Soc. A 366 195
[33] [34] Zakharchenko K V, Katsnelson M I, Fasolino A 2009 Phys. Rev. Lett. 102 046808
[35] [36] Liu Z, Suenaga K, Harris P J F, Iijima S 2009 Phys. Rev. Lett. 102 015501
[37] [38] Lu C L, Chang C P, Lin M F 2007 Eur. Phys. J. B 60 161
[39] [40] [41] Ho J H, Lu C L, Hwang C C, Chang C P, Lin M F 2006 Phys. Rev. B 74 085406
[42] de Andres P L, Ramrez R, Vergs J A 2008 Phys. Rev. B 77 045403
[43] [44] [45] Wang T, Guo Q, Liu Y, Sheng K 2012 Chin. Phys. B 21 067301
[46] Meyer J C, Geim A K, Katsnelson M I, Novoselov K S, Obergfell D, Roth S, Girit C, Zettl A 2007 Solid State Commun. 143 101
[47] [48] Chang X, Ge Y, Dong J M 2010 Eur. Phys. J. B 78 103
[49] [50] [51] Norimatsu W, Kusunoki M 2010 Phys. Rev. B 81 161410(R)
[52] Mak K F, Lui C H, Shan J, Heinz T F 2009 Phys. Rev. Lett. 102 256405
[53] [54] [55] Zhu G B, Zhang P 2013 Chin. Phys. B 22 017303
[56] [57] Liu D C, Nocedal J 1989 Mathematical Programming B 45 503
[58] Han T W, He P F 2010 Acta Phys. Sin. 59 3408 (in Chinese) [韩同伟, 贺鹏飞 2010 物理学报 59 3408]
[59] [60] Wang W D, Hao Y, Ji X, Yi C L, Niu X Y 2012 Acta Phys. Sin. 61 200207 (in Chinese) [王卫东, 郝跃, 纪翔, 易成龙, 牛翔宇 2012 物理学报 61 200207]
[61] [62] [63] Hoover W G 1985 Phys. Rev. A 31 1695
[64] [65] Tersoff J 1988 Phys. Rev. B 37 6991
[66] [67] Lennard-Jones J E 1924 Proceedings of the Royal Society (Vol. 106) pp463-469
[68] [69] [70] Popov V N, Henrard L 2002 Phys. Rev. B 65 235415
[71] [72] Lu J P, Yang W 1994 Phys. Rev. B 49 11421
[73] [74] Los J H, Katsnelson M I, Yazyev O V, Zakharchenko K V, Fasolino1 A 2009 Phys. Rev. B 80 121405
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