摘要
由于具有丰富的电学性质、奇异的量子特性以及广阔的应用前景,石墨烯、石墨烯衍生物以及类石墨烯层状化合物成为近年来的热点研究体系,并取得许多重要的研究成果。本学位论文采用第一性原理计算方法对石墨烯的物性及其性能调控开展了一系列较深入的理论研究,包括如下六章。
第一章简要介绍密度泛函理论。在简要介绍Hohenberg-Kohn定理、Kohn-Sham方案以及几种应用广泛的交换关联泛函之后,简述了密度泛函理论的数值计算流程,最后介绍了几个基于密度泛函理论的计算软件。
第二章简要介绍了石墨烯,包括石墨烯的物性、实验制备和合成的主要方法以及一些重要的研究进展。本章最后简述了本学位论文的研究动机。
第三章,紧密配合扫描隧道显微术(STM)实验测量,我们对石墨烯在Ru(0001)表面的局域电子结构进行了第一性原理计算。研究发现由于晶格失配,单层石墨烯在Ru(0001)表面表现出摩尔纹周期性高低起伏结构,可以用来作为分子组装模板。理论计算出来的局域功函数数值与实验观测值吻合,其空间分布特征取决于体系周期分布的表面电偶极矩。
第四章,我们的STM实验研究表明在CoPc分子与Ru(0001)表面之间插入单层石墨烯可以设计出一种单分子整流器件。为了解释STM实验的观测结果,我们采用第一性原理方法对比研究了CoPc分子吸附在Ru(0001)表面和石墨烯覆盖的Ru(0001)表面的吸附性质。理论研究发现由于分子与衬底之间的相互作用,在这两种不同表面吸附的CoPc分子磁性都被淬灭。CoPc分子主要通过Co原子的3dz2轨道与石墨烯覆盖的R(0001)表面耦合,STM实验中测量到的隧道电流来自-0.35eV处3dz2轨道的贡献。基于Tersoff-Hamann模型,理论计算出来的伏安曲线特征与实验一致。
第五章基于第一性原理计算,我们尝试通过载流子掺杂和应力等方式来调控单原子缺陷型石墨烯的磁性。理论研究表明,一定浓度的空穴掺杂能明显增强单缺陷石墨烯的铁磁性,而电子掺杂则使体系的磁性明显降低。对单缺陷石墨烯而言,随着施加拉伸应力的增加,体系的磁矩和铁磁耦合都显著增强。对氢吸附的单缺陷石墨烯体系,我们发现其磁性和磁稳定化能都随电子掺杂和空穴掺杂浓度的增加而呈减弱趋势。基于我们计算和分析所得到的能带结构和态密度,我们认为,计算的这些缺陷性石墨烯磁性调控机理都与费米能级附近的局域的sp2态和准局域的pz态紧密相关。这些理论研究结果为调控石墨烯磁性提供了一些有借鉴意义的理论依据。
第六章,最近实验上成功地合成出类石墨烯结构化合物-锗烷,它具有较好的热稳定性和光吸收性能。采用杂化密度泛函理论方法,我们研究了应力对锗烷物性的调控。研究表明,应力能明显改变体系的能带结构和禁带宽度,压缩锗烷能使其由直接带隙半导体转为间接带隙半导体,而拉伸应力作用下,锗烷可以由直接带隙半导体转变为金属。与此同时,我们发现应力也能有效调制其光吸收性质。
Due to their amazing electronic structures, novel quantum properties, and wide po-tential applications, Recently, graphene and graphene-like systems have attracted much research attention. Here, we try to explore and manipulate the electronic properties of graphene by performing extensive first-principles calculations. This dissertation for Ph. D includes the following chapters.
In Chapter1, we concisely review the basic ideas of density functional theory (DFT), several commonly used exchange-correlation functionals, and the flowchart of DFT calculations. At the end of this Chapter, several DFT-based packages used in this dissertation are briefly introduced.
In Chapter2, we briefly introduce graphene including its amazing electronic prop-erties and the latest progresses. The motivations of this dissertation are shortly presented at the end of this chapter.
In Chapter3, we explore the periodically modulated electronic properties of the epitaxial monolayer graphene (MG) on Ru(0001). Based on scanning tunneling mi-croscopy/spectroscopy (STM/STS) and first-principles calculations, we investigate the geometric and electronic properties of MG on Ru(0001) surface. Our theoretical results reveal that the periodic geometrical corrugation of MG originates from the strong chemi-cal bonding in combination with lattice mismatch between graphene and Ru(0001). The predicted values of local work function are close to the experimental results, and their spatial distribution are strong related to the presence of the periodic surface dipole mo-ment. These observations suggest that MG/Ru(0001) can be used as an ideal template for periodic nanostructures with various applications.
In Chapter4, we demonstrate that the tunable molecule-substrate interaction offer-s' possibility to realize a single cobalt phthalocyanine (CoPc) rectifier. When a MG is intercalated between CoPc and Ru(0001) substrate, CoPc molecule show a prominent rectifying effect. First-principles calculations clearly show that CoPc molecule couples with MG/Ru(0001) substrate mainly through the dz2orbital of Co atom, and the tun-neling between CoPc molecule and Ru(0001) substrate is mainly intermediated by the Co-dz2orbital. The resonant tunneling through this orbital at-0.35eV gives rise to the abrupt current enhancement and hence the rectifying effect. The simulated Ⅰ-Ⅴ curves using Tersoff-Hamann approximation reproduce the main feature of experimental mea-surements.
In Chapter5, we focus on tuning the magnetism of defective graphene including graphene with single atomic vacancy (GSV) and hydrogen-absorbed GSV (H-GSV) by performing extensive spin-polarized DFT calculations. Our theoretical results show that carrier (hole and electron) doping can effectively tune the magnetic properties of GSV. The hole and electron doping effect on magnetic coupling is distinct different. The hole doping can obviously enhance the magnetic coupling of the GSV system, the magnetic coupling is depressed for the cases with electron doping. At the same time, we find the applied tensile strain on GSV can significantly enhance its magnetism. As for H-GSV systems, the electron and hole doping can effectively reduce the magnetic moments and couplings. Through analysing the calculated electronic structures, we find that the magnetism tunable mechanism is strong related to the localized sp2and quasi-localized pz-derived states around the Fermi level. These theoretical findings provide practical ways and useful insights to tune the magnetism of defective graphene.
In Chapter6, the electronic properties ofhydrogenated Ge sheets (GeH) under me-chanical strains are explored by using DFT calculations with HES06hybrid functionals. We find that the energy gap of GeH can be effectively tuned by the applied strain. With increasing of compression strain, the semiconducting GeH sheet with direct band gap will change to the semiconductor with indirect band gap. While the GeH with direct band gap can be tuned to be metallic by increasing of tensile strain to be about10.0%. In addition, the optical absorption properties of GeH sheet can be modulated by the applied strain.
引文
[1]M. Planck, Verhandl. Dtsch. phys. Ges.2 (1900) 202
[2]M. Planck, Verhandl. Dtsch. phys. Ges.2 (1900) 237
[3]A. Einstein, Ann. Phys.17 (1905) 132
[4]Thomas Kuhn, The Structure of Scientific Revolutions (3rd ed,). University of Chicago Press.1996.
[5]曾谨言,量子力学.科学出版社,北京,2000.
[6]大卫·C.卡西第,海森伯传.商务印书馆,北京,2003.
[7]沃尔特·穆尔,薛定谔传.中国对外翻译出版公司,北京,2001.
[8]赫尔奇·克劳,狄拉克：科学和人生.湖南科学技术出版社,2009.
[9]詹姆斯·格雷克,费曼传.高等教育出版社,2004.
[10]R. McWeeny, Methods of Molecular Quantum Mechanics. Academic Press, London,1989.
[11]A. Szabo, N. S. Ostlund. Modern Quantum Chemistry. Dover Publications, Inc., Mineola, New York,1996
[12]R. G. Parr, W. T. Yang. Density-functional theory of atoms and molecules. Oxford University Press, New York, 1989
[13]D. R. Hartree. Proc. Cam. Phil. Soc.24 (1928) 89
[14]V. Fock, Phys. Rev. B,75 (2007) 012401
[15]徐光宪、黎乐民、王德民,量子化学(中册).科学出版社,北京,1985.
[16]唐敖庆、杨忠志、李前树,量子化学.科学出版社,北京,1982.
[17]谢希德、陆栋.固体能带理论.复旦大学出版社,上海,1998
[18]J. B. Foresman, M. Head-Gordon, J. A. Pople, M. J. Frisch, J. Chem. Phys.108 (1998) 8218
[19]C. M(?)ller, M. S. Plesset, Phys. Rev.46 (1934) 618
[20]李震宇,中国科学技术大学博士学位论文2004
[21]武晓君,中国科学技术大学博士学位论文2005
[22]向红军,中国科学技术大学博士学位论文2006
[23]胡振芃,中国科学技术大学博士学位论文2008
[24]阚二军,中国科学技术大学博士学位论文2008
[25]孙莲,中国科学技术大学博士学位论文2008
[26]胡双林,中国科学技术大学博士学位论文2009
[27]冯卫,中国科学技术大学博士学位论文2012
[28]E. P. Wigner, F. Seitz, Phys. Rev.43 (1933) 804
[29]R. M. Martin, Electromic structure. Cambridge university press,2005.
[30]P. Hohenberg, W. Kohn, Phys. Rev.136 (1964) B864
[31]W. Kohn, L. J. Sham, Phys. Rev.140 (1965) A1133
[32]J. P. Perdew, K. Burke, Int. J. Quant. Chem.57 (1996) 767
[33]J. P. Perdew, M. Ernzerhof, K. Burke, J. Chem. Phys.105 (1996) 9982
[34]M. Ernzerhof, J. P. Perdew, K. Burke, Int. J. Quantum Chem.64 (1997) 285
[35]M. Ernzerhof, G. E. Scuseria, J. Chem. Phys.110 (1999) 5029
[36]C. Adamo, V. Barone, J. Chem. Phys.110 (1999) 6158
[37]J. Heyd, G. E. Scuseria, M. Ernzerhof, J. Chem. Phys.118 (2003) 8207
[38]J. Heyd, G. E. Scuseria, M. Ernzerhof, J. Chem. Phys.124 (2006) 219906
[39]J. Hafner, J. Comput. Chem.29 (2008) 2044
[40]G. Kresse and J. Furthmuler, Phys. Rev. B 54 (1996) 11169
[41]G. Kresse and J. Furthmuler, Comput. Mat Sci.6 (1996) 15
[42]P. E. Blohl, Phys. Rev. B 50 (1994) 17953
[43]G. Kresse, J. Joubert, Phys. Rev. B 59 (1999) 1758
[44]B. Delley,J. Chem. Phys.113 (2000) 7756
[45]B. Delley,J. Chem. Phys.92 (1990) 508
[46]S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. J. Probert, K. Refson, M. C. Payne, Z. Kristallogr. 220,567 (2005).
[47]M. D. Segall, P. J. D. Lindan, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clark, M. C. Payne.J. Phys. Condens. Matter 14,2717 (2002).
[48]H. W. Kroto, J. R. Heath, S. C. O'Brein, R. F. Curl, R. E. Smally, Nat.318 (1985) 162
[49]D. Dubois, K. M. Kadish, S. Flanagan, R. E. Haufler, L. P. F. Chbante, L. J. Wilson, JACS,113 (1991) 4364
[50]Z. Xu, T. Nakane, H. Shinohara, JACS,118 (1996) 11309
[51]T. Suzuki, Y. Maruyama, T. Kato, K. Kikuchi, Y. Nakao, Y. Achiba, K. Kobayashi, S. Nagase. Angew. Chem. Int. Ed.34 (1995) 1094
[52]H. Kato, A. Taninaka, T. Sugai, H. Shinohara, JACS,125 (2003) 7782
[53]S. Iijima, Nat.354 (1991) 56
[54]S. Iijima, T. Ichihashi, Nat.363 (1993) 603
[55]D. S. Bethune, C. H. Kiang, M. S. de Vries, G. Gorman, R. Savoy, J. Vazquez, R. Beyers. Nat.363 (1993) 605
[56]K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, A. A. Firsov, Science 306 (2004) 666
[57]D. S. L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler, T. Chakraborty, Adv. Phys.59 (2010) 261.
[58]O. V. Yazyev, Rep. Prog. Phys.73 (2010) 056501.
[59]A. V. Krasheninnikov, K. Nordlund, J. Appl. Phys.107 (2010) 071301.
[60]J. H. Chen, L. Li, W. G. Cullen, E. D. Williams, M. S. Fuhrer, Nat. Phys.7 (2011) 535.
[61]A. Ney, P. Papakonstantinou, A. Kumar, N. G. Shang, N. H. Peng, Appl. Phys. Lett.99 (2011) 102504.
[62]R. R. Nair, M. Sepioni, I-Ling Tsai, O. Lehtinen, J. Keinonen, A. V. Krasheninnikov, T. Thomson, A. K. Geim, I. V. Grigorieva, Nat. Phys.8 (2012) 199.
[63]A. K. Geim, K. S. Novoselov, Nature mater.6 (2007) 183
[64]A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, A. K. Geim, Rev. Mod. Phys.81 (2009) 109
[65]W. Li, M. Zhao, X. Zhao, Y. Xiab, Y. Mu, Phys. Chem. Chem. Phys.12 (2010) 13699
[66]P. Esquinazi, D. Spemann, R. Hohne, A. Setzer, K.-H. Han, T. Butz, Phys. Rev. Lett.91 (2003) 227201
[67]P. O. Lehtinen, A. S. Foster, Y. C. Ma, A. V. Krasheninnikov, R. M. Nieminen, Phys. Rev. Lett.93 (2004) 187202
[68]O. V. Yazyev, L. Helm, Phys. Rev. B 75 (2007) 125408.
[69]K. Nakada, M. Fujita, G. Dresselhaus, M. S. Dresselhaus, Phys Rev B 54 (1996) 17954
[70]Y.-W. Son, M. L. Cohen, S. G. Louie, Nat.444 (2006) 347
[71]E.-j. Kan, Z. Y. Li, J. L. Yang, J. G. Hou, J. Am. Chem. Soc.130 (2008) 4224
[72]S. L. Hu, J. Zhao, Jin, Y. D. Jin, J. L. Yang, H. Petek, J. G. Hou, Nano Lett.10 (2010) 4830
[73]J. O. Sofo, A. S. Chaudhari, G. D. Barber, Phys. Rev. B 75 (2007) 153401
[74]D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim, K. S. Novoselov, Science 323 (2009) 610
[75]J. Zhou, Q. Wang, Q. Sun, X. S. Chen, Y. Kawazoe, P. Jena, Nano Lett.9 (2009) 3867
[76]M. Jaiswal, C. H. Yi Xuan Lim, Q. Bao, C. T. Toh, K. P. Loh, B. Ozyilmaz, ACS Nano 5 (2011) 888
[77]K. Takeda, K. Shiraishi, Phys. Rev. B 50 (1994) 14916
[78]S. Cahangirov, M. Topsakai, E. Akturk, H. Sahin, S. Ciraci, Phys. Rev. Lett.102 (2009) 236804
[79]B. Aufray, A. Kara, S. Vizzini, H. Oughaddou, C. Leandri, B. Ealet, G. Le Lay, App. Phys. Lett.96(2010) 183102
[80]B. Lalmi, H. Oughaddou, H. Enriquez, A. Kara, S. Vizzini, B. Ealet, B. Aufray, Appl. Phys. Lett.97 (2010) 223109
[81]E. Bianco, S. Butler, S. Jiang, O. D. Restrepo, W. Windl, J. E. Goldberger, DOI:10.1021/nn4009406
[82]M. Xu, T. Liang, M. Shi, H. Chen, Chem. Rev.113 (2013) 3766
[83]X. S. Li, W. W. Cai, J. H. An, S. Kim, J. Nah, D. X. Yang, R. Piner, A. Velamakanni, I. Jung, E. Tutuc, S. K. Banerjee, L. Colombo, R. S. Ruoff, Science 324 (2009) 1312
[84]K. S Kim, Y. Zhao, H. Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. Ahn, P. Kim, J. Y. Choi, B. H. Hong, Nature 457 (2009) 706
[85]E. Sutter, P. Albrecht, P. Sutter, Appl. Phys. Lett.95 (2009) 133109
[86]Z. Klusek, W. Kozlowski, Z. Waqar, S. Datta, J. S. Burnell-Gray, I. V. Makarenko, N. R. Gall, E. V. Rutkov, A. Y. Tontegode, A. N. Titkov, Appl. Surf. Sci.252 (2005) 1221
[87]A. L. V. de Parga, F. Calleja, B. Borca, M. C. G. Passeggi, J. J. Hinarejos, F. Guinea, R. Miranda, Phys. Rev. Lett.100 (2008) 056807
[88]Kwon, S. Y.; Ciobanu, C. V.; Petrova, V.; Shenoy, V. B.; Bareno, J.; Gambin, V.; Petrov, I.; Kodambaka, S. Nano Lett.9 (2009) 3985
[89]B. Wang, M. Caffio, C. Bromley, H. Fruchtl, R.I. Schaub, ACS Nano 4 (2010) 5773
[90]C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, W. A. de Heer, Science 312 (2006) 1191
[91]Y. Pan, H. G. Zhang, D. X. Shi, J. T. Sun, S. X. Du, F. Liu, H. J. Gao, Adv. Mater.21 (2009) 2777
[92]Y. Cui, Q. Fu, X. H. Bao, Phys. Chem. Chem. Phys.12 (2010) 5053
[93]H. Zhang, Q. Fu, Y. Cui, D. L. Tan, X. H. Bao, J. Phys. Chem. C 113 (2009) 8296
[94]S. Marchini, S. Gunther, J. Wintterlin, Phys. Rev. B 76 (2007) 075429
[95]D. Martoccia, P. R. Willmott, T. Brugger, M. Bjorck, S. Gunther, C. M. Schleputz, A. Cervellino, S. A. Pauli, B. D. Patterson, S. Marchini, J. Wintterlin, W. Moritz, T. Greber, Phys. Rev. Lett.101 (2008) 126102
[96]D. Martoccia, M. Bjorck, C. M. Schleputz, T. Brugger, S. A. Pauli, B. D. Patterson, T. Greber, P. R. Willmott, New J. Phys.12 (2010) 043028
[97]Moritz, W.; Wang, B.; Bocquet, M. L.; Brugger, T.; Greber, T.; Wintterlin, J.; Gunther, S. Phys. Rev. Lett.104 (2010) 136102
[98]A. B. Preobrajenski, M. L. Ng, A. S. Vinogradov, N. Martensson, Phys. Rev. B 78 (2008) 073401
[99]B. Wang, M. L. Bocquet, S. Marchini, S. Gunther, J. Wintterlin, Phys. Chem. Chem. Phys.10 (2008) 3530
[100]D. E. Jiang, M. H. Du, S. Dai, J. Chem. Phys.130 (2009) 074705
[101]T. Brugger, S. Gunther, B. Wang, J. H. Dil, M. L. Bocquet, J. Osterwalder, J. Wintterlin, T. Greber, Phys. Rev. B 79 (2009) 045407
[102]L. M. Kong, C. Bjelkevig, S. Gaddam, M. Zhou, Y. H. Lee, G. H. Han, H. K. Jeong, N. Wu, Z. Z. Zhang, J. Xiao, P. A. Dowben, J. A. Kelber, J. Phys. Chem. C 114 (2010) 21618
[103]J. H. Mao, H. G. Zhang, Y. H. Jiang, Y. Pan, M. Gao, W. D. Xiao, H. J. Gao, J. Am. Chem. Soc.131 (2009) 14136
[104]K. Donner, P. Jakob, J. Chem. Phys.131 (2009) 164701
[105]Z. H. Zhou, F. Gao, D. W. Goodman, Surf. Sci.604 (2010) L31
[106]M. Vladimirova, M. Stengel, A. De Vita, A. Baldereschi, M. Bohringer, K. Morgenstern, R. Berndt, W. D. Schneider, Europhys. Lett.56 (2001) 254
[107]W. D. Xiao, P. Ruffieux, K. Ait-Mansour, O. Groning, K. Palotas, W. A. Hofer, P. Groning, R. Fasel, J. Phys. Chem. B 110(2006)21394
[108]J. V. Barth, Annu. Rev. Phys. Chem.58 (2007) 375
[109]P. Ruffieux, K. Ait-Mansour, A. Bendounan, R. Fasel,L. Patthey, P. Groning, O. Groning, Phys. Rev. Lett.102 (2009)086807
[110]K. Appl. Wandelt, Surf. Sci.111(1997) 1
[111]H. Dil, J. Lobo-Checa, R. Laskowski,; P. Blaha, S. Berner,; J. Osterwalder, T. Greber, Science 319 (2008) 1824
[112]J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett.77(1996) 3865
[113]B. Wang, S. Gunther, J. Wintterlin, M. L. Bocquet, New J. Phys.12 (2010) 043041
[114]T. Jung, Y. W. Mo, F. J. Himpsel, Phys. Rev. Lett.74 (1995) 1641
[115]M. Pivetta, F. Patthey, M. Stengel, A. Baldereschi, and W.-D. Schneider, Phys. Rev. B 72 (2005) 115404
[116]C. L. Lin, S. M. Lu, W. B. Su, H. T. Shih, B. F. Wu, Y. D. Yao, C. S. Chang, T. T. Tsong, Phys. Rev. Lett.99 (2007)216103
[117]B. Borca, S. Barja, M. Garnica, D. Sanchez-Portal, V. M. Silkin, E. V. Chulkov, C. F. Hermanns, J. J. Hinarejos, A. L. Vazquez de Parga, A. Arnau, P. M. Echenique, R. Miranda, Phys. Rev. Lett.105 (2010) 036804
[118]F. J.Himpsel, K. Christmann, P. Heimann, D. E. Eastman, P. J. Feibelman, Surf. Sci. Lett.115 (1982) 159
[119]R. Smoluchowski, Phys. Rev.60 (1941) 661
[120]G. Binnig, H. Rohrer, C. Gerber, E. Weibel, Appl. Phys. Lett.40 (1982) 178
[121]G. Binnig, N. Garcia, H. Rohrer, Phys. Rev. B 30 (1984) 4816
[122]L. Vitali, G. Levita, R. Ohmann, A. Comisso, A. De Vita, K. Kern, Nature Mater.9 (2010) 320
[123]E. Wigner, J. Bardeen, Phys. Rev.48 (1935) 84
[124]S. J. Altenburg, J. Kroger, B. Wang, M.-L. Bocquet, N. Lorente, R. Berndt, Phys. Rev. Lett.105 (2010) 236101
[125]W. Mizutani, T. Ishida, N. Choi, T. Uchihashi, H. Tokumoto, Appl. Phys. Lett.72 (2001) S181
[126]R. Schuster, J. V. Barth, J. Wintterlin, R. J. Behm, G. Ertl, Ultramicroscopy 42-44 (1992) 533-540
[127]H. B. Michaelson, J. Appl. Phys.48 (1977) 4729
[128]G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, P. J. Kelly, Phys. Rev. Lett.101 (2008) 026803
[129]J. T. Sun,;S. X. Du,; W. D. Xiao,; H. Hu,; Y. Y. Zhang,; G. Li,; H. J. Gao, Chin. Phys. B 18 (2009) 3008
[130]A. Aviram and M. A. Ratner, Chem. Phys. Lett.29 (1974) 277
[131]J. Zhao, C. Zeng, X. Cheng, K. D. Wang, G. W. Wang, J. L. Yang, J. G. Hou, and Q. S. Zhu, Phys. Rev. Lett. 95 (2005) 045502
[132]M. Elbing, R. Ochs, M. Koentopp, M. Fischer, Carsten von Hanisch, F. Weigend, F. Evers, H. B. Weber and M. Mayor, Proc. Natl. Acad. Sci. USA 102 (2005) 8815
[133]B. Wang, Y. S. Zhou, X. L. Ding, K. D. Wang, X. P. Wang, J. L. Yang, and J. G. Hou, J. Phys. Chem. B 110 (2006) 24505
[134]J. Hihath, C. Bruot, H. Nakamura, Y. Asai, I. Diez-Perez, Y. Lee, L. P. Yu, and N. J. Tao, ACS Nano 5 (2011) 8331
[135]N. A. Zimbovskaya and M. R. Pederson, Phys. Rep.509 (2011) 1
[136]W. Feng, S. L. Lei, Q. X. Li, and A. D. Zhao, J. Phys. Chem. C 115 (2011) 24858
[137]A. D. Zhao, Q. X. Li, L. Chen, H. J. Xiang, W. H. Wang, S. Pan, B. Wang, X. D. Xiao, J. L. Yang, J. G. Hou, and Q. S. Zhu, Science 309 (2005) 1542
[138]Y. F. Wang, X. Ge, C. Manzano, J. Kroger, R. Berndt, W. A. Hofer, H. Tang, and J. Cerda, J. Am. Chem. Soc. 131 (2010) 10400
[139]S. K. Hamalainen, M. Stepanova, R. Drost, P. Liljeroth, J. Lahtinen, and J. Sainio, J. Phys. Chem. C 116 (2012) 20433
[140]S.-H. Chang, S. Kuck, J. Brede, L. Lichtenstein, G. Hoffmann, and R. Wiesendanger, Phys. Rev. B 78 (2008) 233409
[141]A. F. Takacs, F. Witt, S. Schmaus, T. Balashov, M. Bowen, E. Beaurepaire, and W. Wulfhekel, Phys. Rev. B 78(2008)233404
[142]R. Cuadrado, J. I. Cerda, Y. F. Wang, G. Xin, R. Berndt, and H. Tang, J. Chem. Phys.133 (2010) 154701
[143]B. W. Heinrich, C. Iacovita, T. Brumme, D.-J. Choi, Laurent Limot, Mircea V. Rastei, Werner A. Hofer, Jens Kortus, Jean-Pierre Bucher, J. Phys. Chem. Lett.1 (2010) 1517
[144]H. T. Zhou, J. H. Mao, G. Li, Y. L. Wangl X. L. Feng, S. X. Du, K. Mullen, and H.-J. Gao, Appl. Phys. Lett. 99(2011)153101
[145]H. G. Zhang, J. T. Sun, T. Low, L. Z. Zhang, Y. Pan, Q. Liu, J. H. Mao, H. T. Zhou, H. M. Guo, S. X. Du, F. Guinea, and H.-J. Gao, Phys. Rev. B 84 (2011) 245436
[146]W. D. Dou, S. P. Huang, R. Q. Zhang, and C. S. Lee, J. Chem. Phys.134 (2011) 094705
[147]J. Tersoff and D. R. Hamann, Phys. Rev. B 31 (1985) 805
[148]L. Chen, Z. P. Hu, A. D. Zhao, B. Wang, Y. Luo, J. L. Yang, and J. G. Hou, Phys. Rev. Lett.99 (2007) 146803
[149]O. V. Yazyev, Phys. Rev. Lett.101 (2008) 037203.
[150]L. Pisani, B. Montanari, N. M. Harrison, New J. Phys.10 (2008) 033002.
[151]D. C. Yu, E. M. Lupton, M. Liu, W. Liu, F. Liu, Nano Res.1 (2008) 56.
[152]F. Banhart, J. Kotakoski, A. V. Krasheninnikov, ACS Nano 5 (2011) 26.
[153]H. H. Xia, W. F. Li, Y. Song, X. M. Yang, X. D. Liu, M. W. Zhao, Y. Y. Xia, C. Song, T. W. Wang, D. Z. Zhu, J. L. Gong, Z. Y. Zhu, Adv. Mater.20 (2008) 4679.
[154]J. Cervenka and C. F. J. Flipse, Phys. Rev. B 79 (2009) 195429.
[155]I. C. Gerber, A. V. Krasheninnikov, A. S. Foster, R. M. Nieminen, New J. Phys.12 (2010) 113021.
[156]T. Makarova, F. Palacio (ed), Carbon-based magnetism:An overview of metal free carbon-based compounds and materials, Elsevier, Amsterdam,2006.
[157]Y. Zhang, S. Talapatra, S. Kar, R. Vajtai, S. K. Nayak, P. M. Ajayan, Phys. Rev. Lett.99 (2007) 107201.
[158]D. W. Boukhvalov, M. I. Katsnelson, Nano Lett.8 (2008) 4373.
[159]A. Reserbat-Plantey, P. Gava, N. Bendiab, A. M. Saitta, EPL 96 (2011) 57001.
[160]R. Faccio, L. Fernandez-Werner, H. Pardo, C. Goyenola, O. N. Ventura, A. W. Mombru, J. Phys. Chem. C 114 (2010) 18961.
[161]X. Q. Dai, J. H. Zhao, M. H. Xie, Y. N. Tang, Y. H. Li, B. Zhao, Eur. Phys. J. B 80 (2011) 343.
[162]E. J. G. Santos, D. Sanchez-Portal, A. Ayuela, Phys. Rev. B 81 (2010) 125433.
[163]L. Kou, C. Tang, W. L. Guo, C. F. Chen, ACS Nano 5 (2011) 1012.
[164]E. J. G. Santos, S. Riikonen, D. Sanchez-Portal, A. Ayuela, J. Phys. Chem. C 116 (2012) 7602.
[165]M. Bokdam, P. A. Khomyakov, G. Brocks, Z. C. Zhong, P. J. Kelly, Nano Lett.11 (2011) 4631.
[166]H. S. S. R. Matte, K. S. Subrahmanyam, C. N. R. Rao, J. Phys. Chem. C 113 (2009) 9982.
[167]O. Leenaerts, B. Partoens, F. M. Peeters, Phys. Rev. B 77 (2008) 125416.
[168]J. Berashevich, T. Chakraborty, Phys. Rev. B 80 (2009) 033404.
[169]H. Lee, S. Yang, J. Choi, Y. Park, S. Kim, J. Phys. Chem. C 115 (2011) 18736.
[170]R. Jalilian, L. A Jauregui, G. Lopez, J. F. Tian, C. Roecker, M. M. Yazdanpanah, R. W. Cohn, I. Jovanovic, Y. P. Chen, Nanotechnology 22 (2011) 295705.
[171]E. R. Margine, V. H. Crespi, Phys. Rev. Lett.96 (2006) 196803.
[172]P. Lou, J. Y. Lee, J. Phys. Chem. C.114 (2010) 10947.
[173]S. S. Alexandre, A. D. Lucio, A. H. C. Neto, R. W. Nunes, Nano Lett.12 (2012) 5097.
[174]A. A. El-Barbary, R. H. Telling, C. P. Ewels, M. I. Heggie, P. R. Briddon, Phys. Rev. B 68 (2008) 144107.
[175]H. Amara, S. Latil, V. Meunier, Ph. Lambin, J.-C. Charlier, Phys. Rev. B 76 (2007) 115423.
[176]P. A. Thrower, R. M. Mayer, Phys. Stat. Sol. A 47 (1978) 11.
[177]G. Henkelman, A. Arnaldsson, H. Jonsson, Comput. Mater. Sci.36 (2006) 354.
[178]E. Sanville, S. D. Kenny, R. Smith, G. Henkelman, J. Comp. Chem.28 (2007) 899.
[179]W. Tang, E. Sanville, G. Henkelman, J. Phys.:Condens. Matter 21 (2009) 084204.
[180]T. M. G. Mohiuddin, A. Lombardo, R. R. Nair, A. Bonetti, G. Savini, R. Jalil, N. Bonini, D. M. Basko, C. Galiotis, Phys. Rev. B 79 (2009) 205433
[181]Vitor M. Pereira, A. H. Castro Neto, Phys. Rev. Lett.103 (2009) 046801
[182]F. Guinea, M. I. Katsnelson and A. K. Geim, Nat. Phys.6 (2010) 30
[183]S. J. Woo, Young-Woo Son, Phys. Rev. B 87 (2013) 075419
[184]C. Rice, R. J. Young, R. Zan, U. Bangert,D. Wolverson, T. Georgiou, R. Jalil, K. S. Novoselov, Phys. Rev. B 87(2013)081307(R)
[185]H. H. Pu, S. H. Rhim, C. J. Hirschmugl, M. Gajdardziska-Josifovska, M. Weinert, J. H. Chen, Phys. Rev. B 87(2013)085417
[186]S. Horzum, H. Sahin, S. Cahangirov, P. Cudazzo, A. Rubio, T. Serin, F. M. Peeters, Phys. Rev. B 87 (2013) 125415
[187]Stefan Schumacher, Daniel F. FOrster, Malte Rosner, Tim O. Wehling, Thomas Michely, Phys. Rev. Lett.110 (2013)086111
[188]L. T. Singh, S. Bhattacharyya, Abhishek K. Singh, K. K. Nanda, Phys. Rev. Lett.110 (2013) 095504
[189]Priya Johari, Vivek Shenoy, ACS nano 6 (2012) 5449
[190]Y. Zhou, Zhiguo Wang, Ping Yang, Xiaotao Zu, Li Yang, Xin Sun, Fei Gao, ACS nano 6 (2012) 9727
[191]Y. Ma, Y. Dai, M. Guo, C. Niu, L. Yu, B. Huang, Nanoscale 3 (2011) 2301
[192]Y. Ma, Y. Dai, M. Guo, C. Niu, Z. Zhang B. Huang, Phys. Chem. Chem. Phys.14 (2012) 3651
[193]Y. Ma, Y. Dai, W. Wei and B. Huang, J. Mater. Chem. C 1 (2013) 941
[194]S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta, H. R. Gutierrez, T. F. Heinz, S. S. Hong, J. Huang, A. F. Ismach, Ezekiel Johnston-Halperin, M. Kuno, V. V. Plashnitsa, R. D. Robinson, R. S. Ruoff, S. Salahuddin, J. Shan, L. Shi, M. G. Spencer, M. Terrenes, W. Windl, J. E. Goldberger, ACS Nano 7 (2013) 2898
[195]Gunther Vogg. Martion S. Brandt, Martin Stutzmann, Adv. Mater.12 (2000) 1278
[196]Zoltan Hajnal, Gunther Vogg, Lex J.-P. Meyer, Bernadett Szfics, Martin S. Brandt, Thomas Frauenheim, Phys. Rev. B 64 (2001) 033311
[197]G. Seifert, T. Kohler, Z.n Hajnal, T. Frauenheim, Solid state communications 119 (2001) 653
[198]L. Stille, C. J. Tabert, E. J. Nicol, Phys. Rev. B 86 (2012) 195405
[199]O. Pulci, P. Gori, M. Marsili, V. Garbuio, R. Del Sole, F. Bechstedt, EPL,98 (2012) 37004
[200]C. Liu, W. Feng, Y. Yao, Phys. Rev. Lett 107 (2011) 076802
[201]G. Liu, S. Wu, C. Y. Ouyang, B. Xu, EPL 99 (2012) 17010