Please wait a minute...
Chin. Phys. B, 2019, Vol. 28(9): 096101    DOI: 10.1088/1674-1056/ab38a5
CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES Prev   Next  

Van der Waals interlayer potential of graphitic structures: From Lennard-Jones to Kolmogorov-Crespy and Lebedeva models

Zbigniew Koziol1, Grzegorz Gawlik2, Jacek Jagielski1,2
1 National Center for Nuclear Research, Materials Research Laboratory, ul. Andrzeja So?tana 7, 05-400 Otwock-wierk, Poland;
2 Institute of Electronic Materials Technology, ul. Wólczyńska 133, 01-919 Warszawa, Poland
Abstract  

The experimental knowledge on interlayer potential of graphitic materials is summarized and compared with the computational results based on phenomenological models. Besides Lennard-Jones approximation, the Mie potential is discussed, as well as the Kolmogorov-Crespy model and equation of Lebedeva et al. An agreement is found between a set of reported physical properties of graphite (layer binding energies, compressibility along c-axis in a broad pressure range, Raman frequencies for bulk shear and breathing modes under pressure), when a proper choice of model parameters is taken. It is argued that anisotropic potentials, Kolmogorov-Crespy and Lebedeva, are preferable for modeling, as they provide a better, self-consistent description. A method of fast numerical modeling, convenient for the accurate estimation of the discussed physical properties, is proposed. It may be useful in studies of other van der Waals homo/heterostructures as well.

Keywords:  graphene      van der Waals structures      interlayer potential  
Received:  06 June 2019      Revised:  16 July 2019      Accepted manuscript online: 
PACS:  61.46.-w (Structure of nanoscale materials)  
  73.20.At (Surface states, band structure, electron density of states)  
  73.22.-f (Electronic structure of nanoscale materials and related systems)  
  61.48.De (Structure of carbon nanotubes, boron nanotubes, and other related systems)  
Corresponding Authors:  Zbigniew Kozioł     E-mail:  zbigniew.koziol@ncbj.gov.pl

Cite this article: 

Zbigniew Koziol, Grzegorz Gawlik, Jacek Jagielski Van der Waals interlayer potential of graphitic structures: From Lennard-Jones to Kolmogorov-Crespy and Lebedeva models 2019 Chin. Phys. B 28 096101

[40] Jiang L, Huang Y, Jiang H, Ravichandran G, Hwang H G and Liu B 2006 J. Mech. Phys. Solids 54 2436
[1] Geim A K and Grigorieva I V 2013 Nature 499 419
[41] He X, Kitipornchai S and Liew K 2005 J. Mech. Phys. Solids 53 303
[2] Le N B, Huan T D and Woods L M 2016 ACS Appl. Mater. Interfaces 9 6286
[42] Kitipornchai S, He X Q and Liew K M 2005 Phys. Rev. B 72 075443
[3] Wijk M M V, Schuring A, Katsnelson M I and Fasolino A 2015 2D Materials 2 34010
[43] Tan H, Jiang L, Huang Y, Liu B and Hwang K 2007 Compos. Sci. Technol. 67 2941
[4] Wijk M M V, Schuring A, Katsnelson M I and Fasolino A 2014 Phys. Rev. Lett. 113 135504
[44] Mie G 1903 Ann. Phys. 316 657
[5] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E and Jarillo-Herrero P 2018 Nature 43 556
[45] Avendano C, Lafitte T, Galindo A, Adjiman C S, Jackson G and Muller E 2011 J. Phys. Chem. B 115 11154
[6] Bistritzer R and MacDonald A H 2011 Proc. Nat. Acad. Sci. 108 12233
[46] Kolmogorov A N and Crespi V H 2000 Phys. Rev. Lett. 85 4727
[7] Tarnopolsky G, Kruchkov A J Vishwanath A 2019 Phys. Rev. Lett 122 106405
[47] Kolmogorov A N and Crespi V H 2005 Phys. Rev. B 71 235415
[8] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E and Jarillo-Herrero P 2018 Nature 556 43
[48] Naik M H, Maity I, Maiti P K, and Jain M 2019 J. Phys. Chem. C 123 9770
[9] Peng H, Schröter N B M, Yin J, Wang H, Chung T F, Yang H, Ekahana S, Liu Z, Jiang J, Yang L, Zhang T, Ni H H, Barinov A, Chen Y P, Liu Z, Peng H and Chen Y 2017 Adv. Mater. 1606741
[49] Wijk M M V, Schuring A, Katsnelson M I and Fasolino A 2014 Phys. Rev. Lett. 113 135504
[10] Argentero G, Mittelberger A, Monazam M R A, Cao Y, Pennycook T J, Mangler C, Kramberger C, Kotakoski J, Geim A K and Meyer A J C 2017 Nano Lett. 17 1409
[50] Schuring A 2014 Master Thesis (Radbound University Niimegen)
[11] Lin S, Lu Y, Xu J, Feng S and Li J 2017 Nano Energy 40 122
[51] Ng T W, Lau C Y, Bernados-Chamagne E, Liu J Z, Sheridan J and Tan N 2012 Nanoscale Res. Lett. 7 185
[12] Skoblin G, Sun J and Yurgens A 2018 Appl. Phys. Lett. 112 063501
[52] Guerra R, Tartaglino U, Vanossi A and Tosatti E 2010 Nat. Mater. 9 634
[13] Wei X, Yan F G, Shen C, Lv Q S and Wang K Y 2017 Chin. Phys. B 26 038504
[53] Lebedeva I V, Knizhnik A A, Popov A M, Lozovik Y E and Potapkin B V 2012 Physica E 44 949
[14] Congpu M, Jianyong X and Zhongyuan L 2017 J. Mater. Res. 32 4115
[54] Lebedeva I V, Knizhnik A A, Popov A M, Lozovik Y E and Potapkin B V 2011 Phys. Rev. B 84 245437
[15] Celebonovic V, Pesic J, Gajic R, Vasic B and Matkovic A 2019 J. Appl. Phys. 125 154301
[55] Jiang J 2014 J. Appl. Phys. 116 164313
[16] Wang J G, Mu X J, Sun M T and Mu T J 2019 Appl. Mater. Today 6 1
[56] Baskin V and Meyer L 1955 Phys. Rev. B 100 544
[17] Houssa M, Dimoulas A and Molle A 2015 J. Phys.:Condens. Matter 27 253002
[57] Kiang C H, Endo M, Ajayan P M, Dresselhaus G and Dresselhaus M S 1998 Phys. Rev. Lett. 81 1869
[18] Kvashnin D G and Chernozatonskii L A 2017 JETP Lett. 105 250
[58] Trucano P and Chen R 1975 Nature 258 136
[19] Luo M, Shen Y H and Yin T L 2017 JETP Lett. 105 255
[59] Plimpton S 1995 J. Comp. Phys. 7 1
[20] Bellus M Z, Li M, Lane S D, Ceballos F, Cui Q, Zeng X C and Zhao H 2017 Nanoscale Horiz. 2 31
[60] Gao W and Huang R 2011 J. Phys. D 44 452001
[21] Yan F, Zhao L, Patané A, Hu P A, Wei X, Luo W, Zhang D, Lv Q, Feng Q, Shen C, Chang K, Eaves L and Wang K 2017 Nanotechnology 28 27LT01
[61] Wang Y, Panzik J E, Kiefer B and Lee K K M 2012 Sci. Rep. 2 520
[22] Luo M, Yin H H and Chu J H 2017 JETP Lett. 6 672
[62] Lynch R W and Drickamer H G 1966 J. Chem. Phys. 44 181
[23] Sanchez O L, Ovchinnikov D, Misra S, Allain A and Kis A 2016 Nano Lett. 16 5792
[63] Zhao Y X and Spain I L 1989 Phys. Rev. B 40 993
[24] Gurram M, Omar S and Wees B J V 2017 Nat. Commun. 8 248
[64] Hanfland M, Beister H and Syassen K 1989 Phys. Rev. B 39 12598
[25] Shim J, Jo S, Kim M, Song Y J, Kim J and Park J 2017 ACS Nano 11 6319
[65] Clark S, Jeon K, Chen J and Yoo C 2013 Solid State Commun. 4 15
[26] Li W, Wang X and Dai X 2017 Solid State Commun. 254 37
[66] Lee J, Lee S, Ahn J, Kim S, Wilson J I B and John P 2008 J. Chem. Phys. 129 234709
[27] Michel K H, Çakir D, Sevik C and Peeters F M 2017 Phys. Rev. B 95 125415
[67] Dahn J R, Fong R and Spoon M J 1990 Phys. Rev. B 42 6424
[28] Kawai S, Foster A S, Björkman T, Nowakowska S, Björk J, Canova F F, Gade L H, Jung T A and Meyer E 2016 Nat. Commun. 7 11559
[68] Norimatsu W and Kusunoki M 2010 Phys. Rev. B 81 161410
[29] Rozhkov A, Sboychakov A, Rakhmanov A and Nori F 2016 Phys. Rep. 648 1
[69] Charlier J, Gonze X and Michenaud J 1991 Phys. Rev. B 43 4579
[30] Girifalco L A and Hodak M 2002 Phys. Rev. B 65 125404
[70] Yoshizawa K, Kato T and Yamabe T 1996 J. Chem. Phys. 105 2099
[31] Charlier J, Gonze X and Michenaud J 1994 Europhys. Lett. 28 403
[71] Charlier J C, Gonze X and Michenaud J P 1994 Carbon 32 289
[32] Trickey S B, Müller-Plathe F, Diercksen G H F and Boettger J C 1992 Phys. Rev. B 45 4460
[72] Gao W and Tkatchenko A 2015 Phys. Rev. Lett. 114 096101
[33] Rydberg H, Dion M, Jacobson N, Schröder E, Hyldgaard P, Simak S I, Langreth D C and Lundqvist B I 2003 Phys. Rev. Lett. 91 126402
[73] Tao W, Qing G, Yan L and Kuang S 2012 Chin. Phys. B 21 067301
[34] DiVincenzo D P, Mele E J and Holzwarth N A W 1983 Phys. Rev. B 27 2458
[74] Lipson H and Stokes A 1942 Proc. Roy. Soc. A 181 101
[35] Schabel M C and Martins J L 1992 Phys. Rev. B 46 7185
[75] Dolling G and Brockhouse B N 1962 Phys. Rev. 128 1120
[36] Mostaani E, Drummond N D and Fal'ko V I 2015 Phys. Rev. Lett. 115 115501
[76] Lebedev A V, Lebedeva I V, Popov A M and Knizhnik A A 2017 Phys. Rev. B 96 085432
[37] Birowska M, Milowska K and Majewski J 2011 Acta Phys. Pol. A 120 845
[77] Shang J, Cong C, Zhang J, Xiong Q, Gurzadyan G G and Yu T 2013 J. Raman Spec. 44 70
[38] Chakarova-Kack S D, Schroder E, Lundqvistand B I and Langreth D C 2006 Phys. Rev. Lett. 96 146107
[78] Baranowski J M, Mozdzonek M, Dabrowski P, Grodecki K, Osewski P, Kozlowski W, Kopciuszynski M, Jalochowski M and Strupinski W 2013 Graphene 2 115
[39] Lu J P, Li X P and Martin R M 1992 Phys. Rev. Lett. 68 1551
[79] Lui C H and Heinz T F 2013 Phys. Rev. B 87 121404
[40] Jiang L, Huang Y, Jiang H, Ravichandran G, Hwang H G and Liu B 2006 J. Mech. Phys. Solids 54 2436
[80] Thornton S T and Marion J B 2003 Classical Dynamics of Particles and Systems (5th edn.) (Brooks Cole, Pacific Grove, CA)
[41] He X, Kitipornchai S and Liew K 2005 J. Mech. Phys. Solids 53 303
[81] Tan P H, Han W P, Zhao W J, Wu Z H, Chang K, Wang H, Wang Y F, Bonini N, Marzari N, Savini G, Lombardo A and Ferrari A C 2012 Nat. Mater. 11 294
[42] Kitipornchai S, He X Q and Liew K M 2005 Phys. Rev. B 72 075443
[82] Cong C and Yu T 2014 Nat. Commun. 5 4709
[43] Tan H, Jiang L, Huang Y, Liu B and Hwang K 2007 Compos. Sci. Technol. 67 2941
[44] Mie G 1903 Ann. Phys. 316 657
[45] Avendano C, Lafitte T, Galindo A, Adjiman C S, Jackson G and Muller E 2011 J. Phys. Chem. B 115 11154
[46] Kolmogorov A N and Crespi V H 2000 Phys. Rev. Lett. 85 4727
[47] Kolmogorov A N and Crespi V H 2005 Phys. Rev. B 71 235415
[48] Naik M H, Maity I, Maiti P K, and Jain M 2019 J. Phys. Chem. C 123 9770
[49] Wijk M M V, Schuring A, Katsnelson M I and Fasolino A 2014 Phys. Rev. Lett. 113 135504
[50] Schuring A 2014 Master Thesis (Radbound University Niimegen)
[51] Ng T W, Lau C Y, Bernados-Chamagne E, Liu J Z, Sheridan J and Tan N 2012 Nanoscale Res. Lett. 7 185
[52] Guerra R, Tartaglino U, Vanossi A and Tosatti E 2010 Nat. Mater. 9 634
[53] Lebedeva I V, Knizhnik A A, Popov A M, Lozovik Y E and Potapkin B V 2012 Physica E 44 949
[54] Lebedeva I V, Knizhnik A A, Popov A M, Lozovik Y E and Potapkin B V 2011 Phys. Rev. B 84 245437
[55] Jiang J 2014 J. Appl. Phys. 116 164313
[56] Baskin V and Meyer L 1955 Phys. Rev. B 100 544
[57] Kiang C H, Endo M, Ajayan P M, Dresselhaus G and Dresselhaus M S 1998 Phys. Rev. Lett. 81 1869
[58] Trucano P and Chen R 1975 Nature 258 136
[59] Plimpton S 1995 J. Comp. Phys. 7 1
[60] Gao W and Huang R 2011 J. Phys. D 44 452001
[61] Wang Y, Panzik J E, Kiefer B and Lee K K M 2012 Sci. Rep. 2 520
[62] Lynch R W and Drickamer H G 1966 J. Chem. Phys. 44 181
[63] Zhao Y X and Spain I L 1989 Phys. Rev. B 40 993
[64] Hanfland M, Beister H and Syassen K 1989 Phys. Rev. B 39 12598
[65] Clark S, Jeon K, Chen J and Yoo C 2013 Solid State Commun. 4 15
[66] Lee J, Lee S, Ahn J, Kim S, Wilson J I B and John P 2008 J. Chem. Phys. 129 234709
[67] Dahn J R, Fong R and Spoon M J 1990 Phys. Rev. B 42 6424
[68] Norimatsu W and Kusunoki M 2010 Phys. Rev. B 81 161410
[69] Charlier J, Gonze X and Michenaud J 1991 Phys. Rev. B 43 4579
[70] Yoshizawa K, Kato T and Yamabe T 1996 J. Chem. Phys. 105 2099
[71] Charlier J C, Gonze X and Michenaud J P 1994 Carbon 32 289
[72] Gao W and Tkatchenko A 2015 Phys. Rev. Lett. 114 096101
[73] Tao W, Qing G, Yan L and Kuang S 2012 Chin. Phys. B 21 067301
[74] Lipson H and Stokes A 1942 Proc. Roy. Soc. A 181 101
[75] Dolling G and Brockhouse B N 1962 Phys. Rev. 128 1120
[76] Lebedev A V, Lebedeva I V, Popov A M and Knizhnik A A 2017 Phys. Rev. B 96 085432
[77] Shang J, Cong C, Zhang J, Xiong Q, Gurzadyan G G and Yu T 2013 J. Raman Spec. 44 70
[78] Baranowski J M, Mozdzonek M, Dabrowski P, Grodecki K, Osewski P, Kozlowski W, Kopciuszynski M, Jalochowski M and Strupinski W 2013 Graphene 2 115
[79] Lui C H and Heinz T F 2013 Phys. Rev. B 87 121404
[80] Thornton S T and Marion J B 2003 Classical Dynamics of Particles and Systems (5th edn.) (Brooks Cole, Pacific Grove, CA)
[81] Tan P H, Han W P, Zhao W J, Wu Z H, Chang K, Wang H, Wang Y F, Bonini N, Marzari N, Savini G, Lombardo A and Ferrari A C 2012 Nat. Mater. 11 294
[82] Cong C and Yu T 2014 Nat. Commun. 5 4709
[1] Polarization Raman spectra of graphene nanoribbons
Wangwei Xu(许望伟), Shijie Sun(孙诗杰), Muzi Yang(杨慕紫), Zhenliang Hao(郝振亮), Lei Gao(高蕾), Jianchen Lu(卢建臣), Jiasen Zhu(朱嘉森), Jian Chen(陈建), and Jinming Cai(蔡金明). Chin. Phys. B, 2023, 32(4): 046803.
[2] Spin- and valley-polarized Goos-Hänchen-like shift in ferromagnetic mass graphene junction with circularly polarized light
Mei-Rong Liu(刘美荣), Zheng-Fang Liu(刘正方), Ruo-Long Zhang(张若龙), Xian-Bo Xiao(肖贤波), and Qing-Ping Wu(伍清萍). Chin. Phys. B, 2023, 32(3): 037301.
[3] Graphene metasurface-based switchable terahertz half-/quarter-wave plate with a broad bandwidth
Xiaoqing Luo(罗小青), Juan Luo(罗娟), Fangrong Hu(胡放荣), and Guangyuan Li(李光元). Chin. Phys. B, 2023, 32(2): 027801.
[4] Correlated states in alternating twisted bilayer-monolayer-monolayer graphene heterostructure
Ruirui Niu(牛锐锐), Xiangyan Han(韩香岩), Zhuangzhuang Qu(曲壮壮), Zhiyu Wang(王知雨), Zhuoxian Li(李卓贤), Qianling Liu(刘倩伶), Chunrui Han(韩春蕊), and Jianming Lu(路建明). Chin. Phys. B, 2023, 32(1): 017202.
[5] Adsorption dynamics of double-stranded DNA on a graphene oxide surface with both large unoxidized and oxidized regions
Mengjiao Wu(吴梦娇), Huishu Ma(马慧姝), Haiping Fang(方海平), Li Yang(阳丽), and Xiaoling Lei(雷晓玲). Chin. Phys. B, 2023, 32(1): 018701.
[6] Dynamically tunable multiband plasmon-induced transparency effect based on graphene nanoribbon waveguide coupled with rectangle cavities system
Zi-Hao Zhu(朱子豪), Bo-Yun Wang(王波云), Xiang Yan(闫香), Yang Liu(刘洋), Qing-Dong Zeng(曾庆栋), Tao Wang(王涛), and Hua-Qing Yu(余华清). Chin. Phys. B, 2022, 31(8): 084210.
[7] Dual-channel tunable near-infrared absorption enhancement with graphene induced by coupled modes of topological interface states
Zeng-Ping Su(苏增平), Tong-Tong Wei(魏彤彤), and Yue-Ke Wang(王跃科). Chin. Phys. B, 2022, 31(8): 087804.
[8] Recent advances of defect-induced spin and valley polarized states in graphene
Yu Zhang(张钰), Liangguang Jia(贾亮广), Yaoyao Chen(陈瑶瑶), Lin He(何林), and Yeliang Wang(王业亮). Chin. Phys. B, 2022, 31(8): 087301.
[9] Precisely controlling the twist angle of epitaxial MoS2/graphene heterostructure by AFM tip manipulation
Jiahao Yuan(袁嘉浩), Mengzhou Liao(廖梦舟), Zhiheng Huang(黄智恒), Jinpeng Tian(田金朋), Yanbang Chu(褚衍邦), Luojun Du(杜罗军), Wei Yang(杨威), Dongxia Shi(时东霞), Rong Yang(杨蓉), and Guangyu Zhang(张广宇). Chin. Phys. B, 2022, 31(8): 087302.
[10] Longitudinal conductivity in ABC-stacked trilayer graphene under irradiating of linearly polarized light
Guo-Bao Zhu(朱国宝), Hui-Min Yang(杨慧敏), and Jie Yang(杨杰). Chin. Phys. B, 2022, 31(8): 088102.
[11] Valley-dependent transport in strain engineering graphene heterojunctions
Fei Wan(万飞), X R Wang(王新茹), L H Liao(廖烈鸿), J Y Zhang(张嘉颜),M N Chen(陈梦南), G H Zhou(周光辉), Z B Siu(萧卓彬), Mansoor B. A. Jalil, and Yuan Li(李源). Chin. Phys. B, 2022, 31(7): 077302.
[12] Thermionic electron emission in the 1D edge-to-edge limit
Tongyao Zhang(张桐耀), Hanwen Wang(王汉文), Xiuxin Xia(夏秀鑫), Chengbing Qin(秦成兵), and Xiaoxi Li(李小茜). Chin. Phys. B, 2022, 31(5): 058504.
[13] Photoelectrochemical activity of ZnO:Ag/rGO photo-anodes synthesized by two-steps sol-gel method
D Ben Jemia, M Karyaoui, M A Wederni, A Bardaoui, M V Martinez-Huerta, M Amlouk, and R Chtourou. Chin. Phys. B, 2022, 31(5): 058201.
[14] TiS2-graphene heterostructures enabling polysulfide anchoring and fast electrocatalyst for lithium-sulfur batteries: A first-principles calculation
Wenyang Zhao(赵文阳), Li-Chun Xu(徐利春), Yuhong Guo(郭宇宏), Zhi Yang(杨致), Ruiping Liu(刘瑞萍), and Xiuyan Li(李秀燕). Chin. Phys. B, 2022, 31(4): 047101.
[15] Light-modulated electron retroreflection and Klein tunneling in a graphene-based n-p-n junction
Xingfei Zhou(周兴飞), Ziying Wu(吴子瀛), Yuchen Bai(白宇晨), Qicheng Wang(王起程), Zhentao Zhu(朱震涛), Wei Yan(闫巍), and Yafang Xu(许亚芳). Chin. Phys. B, 2022, 31(4): 047301.
No Suggested Reading articles found!