多层石墨烯的表面起伏的分子动力学模拟

常旭

doi:10.7498/aps.63.086102

摘要

运用经典分子动力学方法，研究了呈现不同堆积方式的多层石墨烯在不同温度下的表面起伏，并且和单层、双层石墨烯做对比. 计算发现：室温下，多层石墨烯中存在着横向特征尺寸约为100 的起伏，该尺寸会随着温度的升高而增大；同时，起伏的高度也随着温度的升高而增大. 这些石墨烯的层内起伏高度关联函数都遵从幂指数标度行为 Gh（q） q-，对于同一种石墨烯，温度越高幂指数越小；而在同一温度下，不同堆积方式的石墨烯的幂指数也不同. 所有这些特征都来源于温度以及层间耦合作用引起的非谐效应.

关键词:

Abstract

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.

Keywords:

作者及机构信息

常旭

1.
商丘师范学院物理与电气信息学院, 商丘 476000

基金项目: 国家自然科学基金（批准号：11247289，11204169）、河南省教育厅科学技术研究重点项目（批准号：12B140012，13B140191）、商丘师范学院青年科研基金（批准号：2011QN13）和商丘师范学院教改项目（批准号：2012jgxm25）资助的课题.

Authors and contacts

Chang Xu

1.
School of Physics and Electrical Information, Shangqiu Normal University, Shangqiu 476000, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11247289, 11204169), the Key Program of Science and Technology Research of the Education Department of Henan Province, China (Grant Nos. 12B140012, 13B140191), the Science Research Foundation for Young Scientists of Shangqiu Normal University, China (Grant No. 2011QN13), and the Education Reform Project of Shangqiu Normal University, China (Grant No. 2012jgxm25).

参考文献

[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

施引文献

[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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