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The geometry, spin multiplicity, magnetic moment, electronic density of states and the spin density of single-layer trigonal graphene quantum dots with zigzag edges have been systematically investigated using density functional theory with the generalized gradient approximation under different sizes. The calculated results such as lattice constants are in good agreement with experimental data and indicate that the system behaves like metal, while the electrons with up spins occupy the Fermi energy. The influence of quantum size effect is remarkable in the system of small size. It is also found that the sp2 hybridization and nonbonding electrons play an important part in the single-layer trigonal graphene quantum dots, just like in graphene. The spin multiplicity and magnetic moment of the system increase with the increase of the system size. Based on our calculation, the total magnetic moment of the system mainly comes from the nonbonding electrons on the 2p orbital of the zigzag boundary. Our calculation may be helpful in designing devices based on trigonal graphene quantum dots.
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Keywords:
- graphene /
- quantum dot /
- electronic structure /
- magnetism
[1] 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
[2] 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
[3] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
[4] Tan C L, Tan Z B, Ma L, Chen J, Yang F, Qu F M, Liu G T, Yang H F, Yang C L, Lü L 2009 Acta Phys. Sin. 58 5726 (in Chinese) [谭长玲、 谭振兵、 马 丽、 陈 军、 杨 帆、 屈凡明、 刘广同、 杨海方、 杨昌黎、 吕 力 2009 物理学报 58 5726]
[5] Hu H X, Zhang Z H, Liu X H, Qiu M, Ding K H 2009 Acta Phys. Sin. 58 7165 (in Chinese) [胡海鑫、 张振华、 刘新海、 邱 明、 丁开和 2009 物理学报 58 7165]
[6] Tombros N, Jozsa C, Popinciuc M, Jonkman H T, Wees B J 2007 Nature 448 571
[7] Ouyang F P, Xu Hui, Wei Chen 2008 Acta Phys. Sin. 57 1073 (in Chinese) [欧阳方平、 徐 慧、 魏 辰 2008 物理学报 57 1073]
[8] Novoselov K S, Jiang Z, Zhang Y, Morozov S V, Stormer H L, Zeitler U, Maan J C, Boebinger G S, Kim P, Geim A K 2007 Science 315 1379
[9] Ci L, Xu Z, Wang L, Gao W, Ding F, Kelly K F, Yakobson B I, Ajayan P M 2008 Nano Res. 1 116
[10] Ezawa M 2006 Phys. Rev. B 73 045432
[11] Son Y W, Cohen M L, Louie S G 2006 Phys. Rev. Lett. 97 216803
[12] Cervantes S F, Csányi G, Piscanec S, Ferrari A C 2008 Phys. Rev. B 77 165427
[13] Ezawa M 2008 Phys. Rev. B 77 155411
[14] Wang W L, Meng S, Kaxiras E 2008 Nano Lett. 8 241
[15] Fernández R J, Palacios J J 2007 Phys. Rev. Lett. 99 177204
[16] Ezawa M 2007 Phys. Rev. B 76 245415
[17] Di C A, Wei D C, Yu G, Liu Y Q, Guo Y L, Zhu D B 2008 Adv. Mater. 20 3289
[18] Wei D C, Liu Y Q, Zhang H L, Huang L P, Wu B, Chen J Y, Yu G 2009 J. Am. Chem. Soc. 131 11147
[19] Geim A K 2009 Science 324 530
[20] Westervelt R M 2008 Science 320 324
[21] Son Y, Cohen M L, Louie S G 2006 Nature 444 347
[22] Kobayashi Y, Fukui K, Enoki T, Kusakabe K, Kaburagi Y 2005 Phys. Rev. B 71 193406
[23] Elias D C, Nair R R, Mohiuddin T M G, Morozov S V, Blake P, Halsall M P, Ferrari A C, Boukhvalov D W, Katsnelson M I, Geim A K, Novoselov K S 2009 Science 323 610
[24] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[25] Perdew J P, Wang Y 1992 Phys. Rev. B 45 13244
[26] Delley B 1990 J. Chem. Phys. 92 508
[27] Delley B 2000 J. Chem. Phys. 113 7756
[28] Girit , Meyer J C, Erni R, Rossell M D, Kisielowski C, Yang L, Park C H, Crommie M F, Cohen M L, Louie S G, Zettl A 2009 Science 323 1705
[29] Huang L F, Li Y L, Ni M Y, Wang X L, Zhang G R, Zeng Z 2009 Acta Phys. Sin. 58 S306 (in Chinese) [黄良锋、 李延龄、 倪美燕、 王贤龙、 张国仁、 曾 雉 2009 物理学报 58 S306]
[30] Lee C G, Wei X D, Kysar J W, Hone J 2008 Science 321 385
[31] Yang Z, Yan Y L, Zhao W J, Lei X L, Ge G X, Luo Y H 2007 Acta Phys. Sin. 56 2590 (in Chinese) [杨 致、 闫玉丽、 赵文杰、 雷雪玲、 葛桂贤、 罗有华 2007 物理学报 56 2590]
[32] Zheng X H, Dai Z X, Wang X L, Zeng Z 2009 Acta Phys. Sin. 58 S259 (in Chinese) [郑小宏、 戴振翔、 王贤龙、 曾 熊 2009 物理学报 58 S259]
[33] Lieb E H 1989 Phys. Rev. Lett. 62 1201
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[1] 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
[2] 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
[3] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
[4] Tan C L, Tan Z B, Ma L, Chen J, Yang F, Qu F M, Liu G T, Yang H F, Yang C L, Lü L 2009 Acta Phys. Sin. 58 5726 (in Chinese) [谭长玲、 谭振兵、 马 丽、 陈 军、 杨 帆、 屈凡明、 刘广同、 杨海方、 杨昌黎、 吕 力 2009 物理学报 58 5726]
[5] Hu H X, Zhang Z H, Liu X H, Qiu M, Ding K H 2009 Acta Phys. Sin. 58 7165 (in Chinese) [胡海鑫、 张振华、 刘新海、 邱 明、 丁开和 2009 物理学报 58 7165]
[6] Tombros N, Jozsa C, Popinciuc M, Jonkman H T, Wees B J 2007 Nature 448 571
[7] Ouyang F P, Xu Hui, Wei Chen 2008 Acta Phys. Sin. 57 1073 (in Chinese) [欧阳方平、 徐 慧、 魏 辰 2008 物理学报 57 1073]
[8] Novoselov K S, Jiang Z, Zhang Y, Morozov S V, Stormer H L, Zeitler U, Maan J C, Boebinger G S, Kim P, Geim A K 2007 Science 315 1379
[9] Ci L, Xu Z, Wang L, Gao W, Ding F, Kelly K F, Yakobson B I, Ajayan P M 2008 Nano Res. 1 116
[10] Ezawa M 2006 Phys. Rev. B 73 045432
[11] Son Y W, Cohen M L, Louie S G 2006 Phys. Rev. Lett. 97 216803
[12] Cervantes S F, Csányi G, Piscanec S, Ferrari A C 2008 Phys. Rev. B 77 165427
[13] Ezawa M 2008 Phys. Rev. B 77 155411
[14] Wang W L, Meng S, Kaxiras E 2008 Nano Lett. 8 241
[15] Fernández R J, Palacios J J 2007 Phys. Rev. Lett. 99 177204
[16] Ezawa M 2007 Phys. Rev. B 76 245415
[17] Di C A, Wei D C, Yu G, Liu Y Q, Guo Y L, Zhu D B 2008 Adv. Mater. 20 3289
[18] Wei D C, Liu Y Q, Zhang H L, Huang L P, Wu B, Chen J Y, Yu G 2009 J. Am. Chem. Soc. 131 11147
[19] Geim A K 2009 Science 324 530
[20] Westervelt R M 2008 Science 320 324
[21] Son Y, Cohen M L, Louie S G 2006 Nature 444 347
[22] Kobayashi Y, Fukui K, Enoki T, Kusakabe K, Kaburagi Y 2005 Phys. Rev. B 71 193406
[23] Elias D C, Nair R R, Mohiuddin T M G, Morozov S V, Blake P, Halsall M P, Ferrari A C, Boukhvalov D W, Katsnelson M I, Geim A K, Novoselov K S 2009 Science 323 610
[24] Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865
[25] Perdew J P, Wang Y 1992 Phys. Rev. B 45 13244
[26] Delley B 1990 J. Chem. Phys. 92 508
[27] Delley B 2000 J. Chem. Phys. 113 7756
[28] Girit , Meyer J C, Erni R, Rossell M D, Kisielowski C, Yang L, Park C H, Crommie M F, Cohen M L, Louie S G, Zettl A 2009 Science 323 1705
[29] Huang L F, Li Y L, Ni M Y, Wang X L, Zhang G R, Zeng Z 2009 Acta Phys. Sin. 58 S306 (in Chinese) [黄良锋、 李延龄、 倪美燕、 王贤龙、 张国仁、 曾 雉 2009 物理学报 58 S306]
[30] Lee C G, Wei X D, Kysar J W, Hone J 2008 Science 321 385
[31] Yang Z, Yan Y L, Zhao W J, Lei X L, Ge G X, Luo Y H 2007 Acta Phys. Sin. 56 2590 (in Chinese) [杨 致、 闫玉丽、 赵文杰、 雷雪玲、 葛桂贤、 罗有华 2007 物理学报 56 2590]
[32] Zheng X H, Dai Z X, Wang X L, Zeng Z 2009 Acta Phys. Sin. 58 S259 (in Chinese) [郑小宏、 戴振翔、 王贤龙、 曾 熊 2009 物理学报 58 S259]
[33] Lieb E H 1989 Phys. Rev. Lett. 62 1201
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