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利用基于密度泛函理论的第一性原理方法，系统研究了变形、电场及共同作用对石墨烯电学特性影响的电子机理.研究表明，本征石墨烯的能隙及态密度值在费米能级处均为0，呈现出半金属特性；在一定的变形量下对石墨烯施加剪切、拉伸、扭转及弯曲变形作用，发现剪切和扭转变形对打开石墨烯能隙的作用明显；对本征石墨烯施加不同方向的电场，可知电场方向对打开石墨烯能隙的作用效果最强.这是因为该电场方向下石墨烯C–C原子间的布居数正值较大，成键键能较高，而负值数值较小，反键键能较低；线性增加电场强度，石墨烯的能隙呈线性增长势；变形及电场共同作用下，外加电场提高了变形对打开石墨烯能隙的作用效果，但不及两种外场叠加的作用效果.Based on the first-principles method of density functional theory, a systematic research is conducted on the electron mechanism of the effect of deformation, electric field action and combined action on the electrical properties of graphene. The research results show that the energy gap and density of states of graphene are both 0 at the Fermi level, indicating semi-metallic character, which implies that the calculation model and the parameter setting are reasonable in this paper. After some deformation actions, such as shear, stretch, torsion and bending deformation on the graphene, it is found that shear and torsion exert an obvious effect on opening the energy gap of graphene, but the effects of tensile and bending deformation on the energy gap of graphene are negligible. Therefore, shear deformation and torsion deformation are a preferred alternative to controlling the energy gap of graphene. By adding the electric field to the graphene in different directions, it is found that the , and direction electric fields which are parallel to the plane of graphene exert a strong effect on opening the energy gap of graphene, but the effect of direction electric field which is perpendicular to the plane of graphene is weak. Especially, the direction electric field has the strongest effect on opening the energy gap of the graphene because the positive value of the population of graphene C–C atoms in the direction is relatively large and bond energy is high while the negative value is small and the antibond energy is low. In order to investigate the influence of electric field strength on energy gap of graphene, the electric field strength is increased linearly from 0.1 eV/Å/e to 0.5 eV/Å/e. It can be observed that the energy gap of graphene increases in turn, and shows a linear growth. Under the action of 0.1 eV/Å/e electric field strength, shear deformation, stretch deformation, torsion deformation and bending deformation take place on the grapheme. It is found that under the combined action of deformation and electric field, the electric field improves the effect of deformation on the energy gap, but the effect is not so good asunder the superposition of two fields.
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Keywords:
- graphene /
- deformation /
- electric field /
- energy gap
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[1] Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva V, Firsov A A 2004 Science 306 666
[2] Novoselov K S, Jiang D, Schedin F, Booth T J, Khotkevich W, Morozov S V, Geim A K 2005 Proc. Natl. Acad. Sci. USA 102 10451
[3] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
[4] Ney A, Papakonstantinou P, Kumar A, Shang N G, Peng N 2011 Appl. Phys. Lett. 99 102504
[5] Nair R R, Sepioni M, Tsai I L, Lehtinen O, Keinonen J, Krasheninnikov A V, Thomson T, Geim A K, Grigorieva I V 2012 Nat. Phys. 8 199
[6] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 109
[7] He J, Chen K Q, Fan Z Q, Tang L M, Hu W P T 2010 Appl. Phys. Lett. 97 193305
[8] Sun L F, Fang C, Liang T X 2013 Chin. Phys. Lett. 30 047201
[9] Zhou S, Liu G, Fan D 2017 Phys. B: Condens. Matter 506 156
[10] Prezzi D, Varsano D, Ruini A, Marini A, Molinari E 2008 Phys. Rev. B 77 041404
[11] Liao W H 2010 Ph. D. Dissertation (Hunan: Hunan Normal University) (in Chinese) [廖文虎 2010 博士学位论文 (湖南: 湖南师范大学)]
[12] Wei Y, Tong G P 2009 Acta Phys. Sin. 58 1931 (in Chinese) [韦勇, 童国平 2009 物理学报 58 1931]
[13] Gui G, Li J, Zhong J X 2008 Phys. Rev. B 78 075435
[14] Yu J, Zhang X X, Ji J S, Huang D, Xi W 2015 Chin. J. Nonferrous Met. 25 3452
[15] Park J S, Choi H J 2015 Phys. Rev. B: Condens. Matter Mat. Phys. 92 045402
[16] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[17] Vanderbilt D 1990 Phys. Rev. B: Condens. Matter 41 7892
[18] Monkhorst H J, Pack J D 1976 Phys. Rev. B 135 188
[19] Shanno D F 1970 Math. Comput. 24 647
[20] 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]
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