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Based on the tight-binding model, the energy spectrum and persistent currents of mesoscopic graphene rings with armchair edges are studied analytically and numerically. Characters of the persistent currents changing with Aharonov-Bohm (A-B) magnetic flux in rings in different geometry are investigated in datail. The periodicity and special symmetry of energy spectrum and persistent currents changing with the magnetic flux are revealed. It is demonstrated that the persistent currents are determined by the geometric structures of the rings; the quantum states with small eigen-energies may carry much larger currents than those quantum states with eigen-energies far away from zero.
[1] Bttiker M, Imry Y, Landauer R 1983 Phys. Lett. A 96 365
[2] Cheung H F, Gefen Y, Riedel E, Shih W H 1987 Phys. Rev. B 37 11
[3] Cheung H F, Riedel E, Gefen Y 1989 Phys Rev. Lett 62 5
[4] Levy L P, Dolan G, Dunsmuir J, Bouchiat H 1990 Phys. Rev. Lett. 64 2074
[5] Chandrasekhar V, Webb R A, Brady M J, Ketchen M B, Gallagher W J, Kleinsasser A 1991 Phys. Rev. Lett. 67 3578
[6] Bleszynski-Jayich A C, Shanks W E, Peaudecerf B, Ginossar E, Oppen F, Glazman L, Harris J G E 2009 Science 326 272
[7] Deng W J, Liu Y Y, Gong C D 1994 Acta Phys. Sin. 43 03 (in Chinese) [邓文基, 刘有延, 龚昌德 1994 43 03]
[8] Louis E, Verge's J A, Chiappe G 1998 Phys. Rev. B 58 11
[9] Lin M F, Chun D S 1998 Phys. Rev. B 57 11
[10] Zhang Z H, Yuan J H, Qiu M, Peng J C, Xiao F L 2006 J. Appl. Phys. 99 104311
[11] Szopa M, Marganska M, Zipper E 2002 Phys. Lett. A 299 593
[12] Huang B L, Chang M C Mou C Y 2012 J. Phys. Condens. Matter 24 245304
[13] Dutta P, Maiti S, Karmakar S N 2012 Euro. phys. J. B 85 4
[14] Szopa M, Margañska M, Zipper E Lisowski M 2004 Phys. Rev. B 70 075406
[15] Ma M M, Ding J W, Xu N 2009 Nanoscale 1 387
[16] Ma M M, Ding J W 2010 Solid State Commun. 150 1196
[17] Chen H B, Xu N, Ding J W 2008 Solid State Commun. 146 12
[18] Bolivar N, Medina E, Berche B 2014 Phys. Rev. B 89 125413
[19] Michetti P Recher P 2011 Phys. Rev. B 83 125420
[20] Benjamin C, Jayannavar A M 2014 Appl. Phys. Lett. 104 053112
[21] Deng W Y, Zhu R, Deng W J 2013 Acta Phys. Sin. 62 067301 (in Chinese) [邓伟胤, 朱瑞, 邓文基 2013 62 067301]
[22] Deng W Y, Zhu R, Deng W J 2013 Acta Phys. Sin. 62 087301 (in Chinese) [邓伟胤, 朱瑞, 邓文基 2013 62 087301]
[23] Bahamon D A, Pereira A L C, Schulz P A 2009 Phys. Rev. B 79 125414
[24] Russo S, Oostinga J B, Wehenkel D, Heersche H B, Sobhani S S, Vandersypen L M K, Morpurgo A F 2008 Phys. Rev. B 77 085413
[25] Lin M F, Shung K 1995 Phys. Rev. B 52 11
[26] Hatsugai Y, Kohmoto M 1990 Phys. Rev. B 42 13
[27] Guo H M, Feng S P 2012 Chin. Phys. B 21 077303
[28] Shyu F L 2010 J. Phys.: Condens. Matter. 22 025302
[29] Zhang Z H, Yang Z Q, Wang X, Yuan J H, Zhang H, Qiu M, Peng J C 2005 J. Phys.: Condens. Matter. 17 4111
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[1] Bttiker M, Imry Y, Landauer R 1983 Phys. Lett. A 96 365
[2] Cheung H F, Gefen Y, Riedel E, Shih W H 1987 Phys. Rev. B 37 11
[3] Cheung H F, Riedel E, Gefen Y 1989 Phys Rev. Lett 62 5
[4] Levy L P, Dolan G, Dunsmuir J, Bouchiat H 1990 Phys. Rev. Lett. 64 2074
[5] Chandrasekhar V, Webb R A, Brady M J, Ketchen M B, Gallagher W J, Kleinsasser A 1991 Phys. Rev. Lett. 67 3578
[6] Bleszynski-Jayich A C, Shanks W E, Peaudecerf B, Ginossar E, Oppen F, Glazman L, Harris J G E 2009 Science 326 272
[7] Deng W J, Liu Y Y, Gong C D 1994 Acta Phys. Sin. 43 03 (in Chinese) [邓文基, 刘有延, 龚昌德 1994 43 03]
[8] Louis E, Verge's J A, Chiappe G 1998 Phys. Rev. B 58 11
[9] Lin M F, Chun D S 1998 Phys. Rev. B 57 11
[10] Zhang Z H, Yuan J H, Qiu M, Peng J C, Xiao F L 2006 J. Appl. Phys. 99 104311
[11] Szopa M, Marganska M, Zipper E 2002 Phys. Lett. A 299 593
[12] Huang B L, Chang M C Mou C Y 2012 J. Phys. Condens. Matter 24 245304
[13] Dutta P, Maiti S, Karmakar S N 2012 Euro. phys. J. B 85 4
[14] Szopa M, Margañska M, Zipper E Lisowski M 2004 Phys. Rev. B 70 075406
[15] Ma M M, Ding J W, Xu N 2009 Nanoscale 1 387
[16] Ma M M, Ding J W 2010 Solid State Commun. 150 1196
[17] Chen H B, Xu N, Ding J W 2008 Solid State Commun. 146 12
[18] Bolivar N, Medina E, Berche B 2014 Phys. Rev. B 89 125413
[19] Michetti P Recher P 2011 Phys. Rev. B 83 125420
[20] Benjamin C, Jayannavar A M 2014 Appl. Phys. Lett. 104 053112
[21] Deng W Y, Zhu R, Deng W J 2013 Acta Phys. Sin. 62 067301 (in Chinese) [邓伟胤, 朱瑞, 邓文基 2013 62 067301]
[22] Deng W Y, Zhu R, Deng W J 2013 Acta Phys. Sin. 62 087301 (in Chinese) [邓伟胤, 朱瑞, 邓文基 2013 62 087301]
[23] Bahamon D A, Pereira A L C, Schulz P A 2009 Phys. Rev. B 79 125414
[24] Russo S, Oostinga J B, Wehenkel D, Heersche H B, Sobhani S S, Vandersypen L M K, Morpurgo A F 2008 Phys. Rev. B 77 085413
[25] Lin M F, Shung K 1995 Phys. Rev. B 52 11
[26] Hatsugai Y, Kohmoto M 1990 Phys. Rev. B 42 13
[27] Guo H M, Feng S P 2012 Chin. Phys. B 21 077303
[28] Shyu F L 2010 J. Phys.: Condens. Matter. 22 025302
[29] Zhang Z H, Yang Z Q, Wang X, Yuan J H, Zhang H, Qiu M, Peng J C 2005 J. Phys.: Condens. Matter. 17 4111
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