Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations

doi:10.1088/1674-1056/25/6/068105

摘要/Abstract

摘要：

In graphene, conductance electrons behave as massless relativistic particles and obey an analogue of the Dirac equation in two dimensions with a chiral nature. For this reason, the bounding of electrons in graphene in the form of geometries of quantum dots is impossible. In gapless graphene, due to its unique electronic band structure, there is a minimal conductivity at Dirac points, that is, in the limit of zero doping. This creates a problem for using such a highly motivated new material in electronic devices. One of the ways to overcome this problem is the creation of a band gap in the graphene band structure, which is made by inversion symmetry breaking (symmetry of sublattices). We investigate the confined states of the massless Dirac fermions in an impured graphene by the short-range perturbations for “local chemical potential” and “local gap”. The calculated energy spectrum exhibits quite different features with and without the perturbations. A characteristic equation for bound states (BSs) has been obtained. It is surprisingly found that the relation between the radial functions of sublattices wave functions, i.e., f_m⁺(r), g_m⁺(r), and f_m^-(r), g_m^-(r), can be established by SO(2) group.

关键词: monolayer gapped graphene, quantum dots, bound states, inversion symmetry breaking

Abstract:

Key words: monolayer gapped graphene, quantum dots, bound states, inversion symmetry breaking

中图分类号: (Electrical and magnetic properties related to treatment conditions)

81.40.Rs

72.10.Bg (General formulation of transport theory) 72.10.Fk (Scattering by point defects, dislocations, surfaces, and other imperfections (including Kondo effect))

Mohsen Yarmohammadi, Malek Zareyan. Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations[J]. 中国物理B, 2016, 25(6): 68105-068105.

Mohsen Yarmohammadi, Malek Zareyan. Bound states of Dirac fermions in monolayer gapped graphene in the presence of local perturbations[J]. Chin. Phys. B, 2016, 25(6): 68105-068105.

参考文献 48

[1]	Katsnelson M I, Novoselov K S and Geim A K 2006 Nat. Phys. 2 620
[2]	Milton Pereira J Jr, Vasilopoulos P and Peeters F M 2007 Appl. Phys. Lett. 90 132122
[3]	Castro Neto A H, Peres N M R, Novoselov K S and Geim A K 2009 Rev. Mod. Phys. 81 109
[4]	Recher P, Trauzettel B, Blanter Y M, Beenakker C and Morpurgo A 2007 Phys. Rev. B 76 235404
[5]	Wunsch B, Stauber T and Guinea F 2008 Phys. Rev. B 77 035316
[6]	Romanovsky I, Yannouleas C and Landman U 2013 Phys. Rev. B 87 165431
[7]	Ponomarenko L A, Katsnelson M I, Yang R, Hill E W, Novoselov K S and Geim A K 2008 Science 320 356
[8]	Volk C, Neumann C, Kazarski S, Fringes S, Engels S, Haupt F, Muller A and Stampfer C 2013 Nat. Commun. 4 1753
[9]	Stampfer C, Guttinger J, Hellmuller S, Molitor F, Ensslin K and Ihn T 2009 Phys. Rev. Lett. 102 056403
[10]	Baringhaus J, Ruan M, Edler F, Tejeda A, Sicot M, Taleb-Ibrahimi A, Li A P, Jiang Z, Conrad E H, Berger C, Tegenkamp C and De Heer W A 2014 Nature 506 349
[11]	Silvestrov P and Efetov K 2007 Phys. Rev. Lett. 98 016802
[12]	De Martino A, Dell'Anna L and Egger R 2007 Phys. Rev. Lett. 98 066802
[13]	Peres N, Rodrigues J, Stauber T and Dos Santos J L 2009 J. Phys.: Condens. Matter 21 344202
[14]	Rusponi S, Papagno M, Moras P, Vlaic S, Etzkorn M, Sheverdyaeva P, Pacile D, Brune H and Carbone C 2010 Phys. Rev. Lett. 105 246803
[15]	Hunt B, Sanchez-Yamagishi J, Young A, Yankowitz M, LeRoy B J, Watanabe K, Taniguchi T, Moon P, Koshino M, Jarillo-Herrero P and Ashoori R C 2013 Science 340 1427
[16]	Fuhrer M S 2013 Science 340 1413
[17]	Lima J R 2015 Phys. Lett. A 379 179
[18]	Maksimova G, Azarova E, Telezhnikov A and Burdov V 2012 Phys. Rev. B 86 205422
[19]	Liu W, Wang Z F, Shi Q W, Yang J and Liu F 2009 Phys. Rev. B 80 233405
[20]	Jackiw R 2012 Phys. Scr. 85 014005
[21]	Ferreira G J and Loss D 2013 Phys. Rev. Lett. 111 106802
[22]	Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[23]	Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[24]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Grigorieva I V and Firsov A A 2004 Science 306 666
[25]	Novoselov K S, Geim A K, Morozov S V, Jiang D, Dubonos S V and Firsov A A 2005 Nature 438 197
[26]	Zhang Y, Tan Y W, Stormer H L and Kim P 2005 Nature 438 201
[27]	Berger C, Song Z, Li X, Wu X, Brown N, Naud C, Mayou D, Li T, Hass J, Marchenkov A N, Conrad E H, First P N and De Heer W A 2006 Science 312 1191
[28]	Zhou S Y, Gweon G H, Graf J, Fedorov A V, Spataru C D, Diehl R D, Kopelevich Y, Lee D H, Louie S G and Lanzara A 2006 Nat. Phys. 2 595
[29]	Chen H Y, Apalkov V and Chakraborty T 2007 Phys. Rev. Lett. 98 186803
[30]	Matulis A and Peeters F M 2008 Phys. Rev. B 77 115423
[31]	Hewageegana P and Apalkov V 2008 Phys. Rev. B 77 245426
[32]	Milton Pereira J Jr, Peeters F M and Vasilopoulos P 2007 Phys. Rev. B 75 125433
[33]	De Martino A, Dell'Anna L and Egger R 2007 Phys. Rev. Lett. 98 066802
[34]	Park S and Sim H S 2008 Phys. Rev. B 77 075433
[35]	Ramezani Masir M and Peeters F M 2009 Phys. Rev. B 79 155451
[36]	Scalapino D J 1995 Phys. Rep. 250 329
[37]	Keldysh L V 1963 J. Exp. Theor. Phys. 45 365
[38]	Ktitorov S A and Tamarchenko V I 1977 Sov. Phys. 19 2070
[39]	Castro Neto A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2008 Rev. Mod. Phys 80 1337
[40]	Zhou S Y, Gweon G H, Fedorov A V, Castro Neto A H and Lanzara A 2007 Nat. Mater. 6 770
[41]	Aleiner I L and Efetov K B 2006 Phys. Rev. Lett. 97 236801
[42]	Basko D M 2008 Phys. Rev. B 78 115432
[43]	Beenakker C W J 2008 Rev. Mod. Phys. 80 1337
[44]	Wallace P R 1947 Phys. Rev. 71 622
[45]	Lherbier A, Blaze X, Niquet Y M, Triozon F and Roche S 2008 Phys. Rev. Lett. 101 036808
[46]	Dong S H and Ma Z Q 2002 Phys. Lett. A 15 171
[47]	Chau Nguyen H, Nguyen N T T and Lien Nguyen V 2015 arXiv: 1511.00535v1 [cond-mat.mes-hall]
[48]	Novikov D S 2007 Phys. Rev. B 76 245435