Electronic states of graphene nanoribbons and analytical solutions

Science and Technology of Advanced Materials

Volumn 11, Issue 5, 2010, Pages

  Wakabayashi, Katsunori ^a,b   Sasaki, Ken Ichi ^a   Nakanishi, Takeshi ^c   Enoki, Toshiaki ^d  

^a NATIONAL INSTITUTE FOR MATERIALS SCIENCE   (Japan)

^b JAPAN SCIENCE AND TECHNOLOGY AGENCY   (Japan)

^c NATIONAL INSTITUTE OF ADVANCED INDUSTRIAL SCIENCE AND TECHNOLOGY AIST   (Japan)

^d TOKYO INSTITUTE OF TECHNOLOGY   (Japan)

Author keywords

Analytical solution; Chirality; Edge orientation; Edge state; Graphene; Graphene nanoribbon; Tight binding model; Wave mechanics

Indexed keywords

ANALYTICAL SOLUTIONS; EDGE ORIENTATION; EDGE STATE; GRAPHENE NANORIBBON; GRAPHENES; TIGHT BINDING MODEL; WAVE MECHANICS;

BAND STRUCTURE; BINDING ENERGY; CARBON NANOTUBES; CHIRALITY; ELECTRODYNAMICS; ELECTRON-ELECTRON INTERACTIONS; ELECTRONIC STATES; ENANTIOMERS; HUBBARD MODEL; MECHANICS; QUANTUM THEORY; SPECTROSCOPY; STEREOCHEMISTRY; WAVES;

GRAPHENE;

EID: 78649974225     PISSN: 14686996     EISSN: None     Source Type: Journal    
DOI: 10.1088/1468-6996/11/5/054504     Document Type: Review

References (105)

1. Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 Science 306 666
2. Geim A K and Novoselov K S 2007 Nat. Mater. 6 183
3. Castro Neto A H, Guinea F, Peres N M, Novoselov K S and Geim A K 2009 Rev. Mod. Phys. 81 109
4. Ando T 2005 J. Phys. Soc. Japan 74 777
5. Ando T 2008 Prog. Theor. Phys. Suppl. 176 203
6. Novoselov K S, Geim A K, Morozov S V, Jiang D, Katsnelson M I, Grigorieva I V, Dubonos S V and Firsov A A 2005 Nature 438 197
7. Zhang Y, Tan Y W, Stormer H L and Kim P 2005 Nature 438 201
8. Novoselov K S, McCann E, Morozov S V, Fal'ko V I, Katsnelson M I, Zeitler U, Jiang D, Schedin F and Geim A K 2006 Nat. Phys. 2 177
9. Ando T and Nakanishi T 1998 J. Phys. Soc. Japan 67 1704
10. Ando T, Nakanishi T and Saito R 1998 J. Phys. Soc. Japan 67 2857
11. Katsnelson M I, Novoselov K S and Geim A K 2006 Nat. Phys. 2 620
12. Luk'yanchuk I A and Kopelevich Y 2004 Phys. Rev. Lett. 93 166402
13. Bolotin K I, Sikes K J, Jiang Z, Klima M, Fudenberg G, Hone J, Kim P and Stormer H L 2008 Solid State Commun. 146 351
14. Balandin A A, Ghosh S, Bao W Z, Calizo I, Teweldebrhan D, Miao F and Lau C N 2008 Nano Lett. 8 902
15. Fujita M, Wakabayashi K, Nakada K and Kusakabe K 1996 J. Phys. Soc. Japan 65 1920
16. Nakada K, Fujita M, Dresselhaus G and Dresselhaus M S 1996 Phys. Rev. B 54 17954
17. Wakabayashi K, Fujita M, Ajiki H and Sigrist M 1999 Phys. Rev. B 59 8271
18. Wakabayashi K, Sigrist M and Fujita M 1998 J. Phys. Soc. Japan 67 2089
19. Wakabayashi K 2000 PhD Thesis University of Tsukuba http://www.tulips. tsukuba.ac.jp/dspace/handle/2241/2592
20. Son Y W, Cohen M L and Louie S G 2006 Nature 444 347
21. Son Y M, Cohen M L and Louie S G 2006 Phys. Rev. Lett. 97 216803
22. Kobayashi Y, Fukui K, Enoki T, Kusakabe K and Kaburagi Y 2005 Phys. Rev. B 71 193406
23. Kobayashi Y, Fukui K and Enoki T 2006 Phys. Rev. B 73 125415
24. Niimi Y, Matsui T, Kambara H, Tagami K, Tsukada M and Fukuyama H 2006 Phys. Rev. B 73 085421
25. Sugawara K, Sato T, Souma S, Takahashi T and Suematsu H 2006 Phys. Rev. B 73 045124
26. Wakabayashi K and Harigaya K 2003 J. Phys. Soc. Japan 72 998
27. Yamashiro A, Shimoi Y, Harigaya K and Wakabayashi K 2003 Phys. Rev. B 68 193410
28. Harigaya K and Enoki T 2002 Chem. Phys. Lett. 351 128
29. Yoshioka H 2003 J. Phys. Soc. Japan 72 2145
30. Kumazaki H and Hirashima D S 2008 J. Phys. Soc. Japan 77 044705
31. Hikihara T, Hu X, Lin H-H and Mou C-Y 2003 Phys. Rev. B 68 035432
32. Kusakabe K and Maruyama M 2003 Phys. Rev. B 67 092406
33. Palacios J J, Fernández-Rossier J and Brey L 2008 Phys. Rev. B 77 195428
34. Fernández-Rossier J and Palacios J J 2007 Phys. Rev. Lett. 99 177204
35. Hod O, Barone V and Scuseria G E 2008 Phys. Rev. B 77 035411
36. Hod O, Barone V, Peralta J E and Scuseria G E 2007 Nano Lett. 7 2295
37. Hod O, Peralta J E and Scuseria G E 2007 Phys. Rev. B 76 233401
38. Ezawa M 2008 Physica E 40 1421
39. Ezawa M 2007 Phys. Rev. B 76 245415
40. Kundin K N 2008 ACS Nano 2 516
41. Wassmann T, Seitsonen A P, Saitta M, Lazzeri M and Mauri F 2007 Phys. Rev. Lett. 101 096402
42. Wakabayashi K, Okada S, Tomita R, Fujimoto S and Natsume Y 2010 J. Phys. Soc. Japan 79 034706
43. Dutta S 2009 Phys. Rev. Lett. 102 096601
44. Kan E 2008 J. Am. Chem. Soc. 130 42224
45. Han M Y, Özyilmaz B, Zhang Y and Kim P 2007 Phys. Rev. Lett. 98 206805
46. Chen Z, Lin Y-M, Rooks M J and Avouris P 2007 Physica E 40 228
47. Li X, Wang X, Zhang L, Lee S and Dai H 2008 Science 319 1229
48. Jiao L, Zhang L, Wang X, Diankov G and Dai H 2009 Nature 458 877
49. Kosynkin D V, Higginbotham A L, Sinitskii A, Lomeda J R, Dimiev A, Price B K and Tour J M 2009 Nature 458 872
50. Yang X, Dou X, Rouhanipour A, Zhi L, Räder J and Müllen K 2008 J. Am. Chem. Phys. 130 4216
51. Molitor F, Güttinger J, Stampfer C, Graf D, Ihn T and Ensslin K 2007 Phys. Rev. B 76 245426
52. Wang X, Ouyang Y, Li X, Wang H, Guo J and Dai H 2008 Phys. Rev. Lett. 100 206803
53. Tapaszto L, Dobrik G, Lambin P and Birò L P 2008 Nat. Nanotech. 3 397
54. Stampfer C, Güttinger J, Hellmüller, Ensslin M K and Ihn T 2009 Phys. Rev. Lett. 102 056403
55. Miyazaki H et al 2008 Appl. Phys. Express 1 024001
56. Güttinger, Stampfer C, Libisch F, Frey T, Burgdörfe J, Ihn T and Ensslin K 2009 Phys. Rev. Lett. 103 046810
57. Jia X et al 2009 Science 323 1701
58. Campos L C, Manfrinato V R, Sanchez-Yamgishi J D, Kong J and Jarillo-Herrero P 2009 Nano Lett. 9 2600
59. Cai J et al 2010 Nature 466 470
60. Wakabayashi K and Sigrist M 2000 Phys. Rev. Lett. 84 3390
61. Wakabayashi K 2001 Phys. Rev. B 64 125428
62. Wakabayashi K and Aoki T 2002 Int. J. Mod. Phys. B 16 4897
63. Yamamoto M and Wakabayashi K 2009 Appl. Phys. Lett. 95 082109
64. Rycerz A, Tworzydlo J and Beenakker C W J 2007 Nat. Phys. 3 172
65. Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801
66. Hasan M Z and Kane C L 2010 arXiv:1002.3895
67. Akhmerov A R and Beenakker C W J 2008 Phys. Rev. B 77 205416
68. Cresti A, Grosso G and Parravicini P 2008 Phys. Rev. B 77 233402
69. Nakabayashi J, Yamamoto D and Kurihara S 2009 Phys. Rev. Lett. 102 066803
70. Wakabayashi K and Sigrist M 2008 J. Phys. Soc. Japan 78 034717
71. Beenakker C W J 2006 Phys. Rev. Lett. 97 067007
72. Wakabayashi K, Takane Y and Sigrist M 2007 Phys. Rev. Lett. 99 036601
73. Wakabayashi K, Takane Y and Sigrist M 2009 Carbon 47 124
74. Saito R, Fujita M, Dresselhaus G and Dresselhaus M S 1992 Phys. Rev. B 46 1804
75. Saito R, Fujita M, Dresselhaus G and Dresselhaus M S 1992 Appl. Phys. Lett. 60 2204
76. Wallace P R 1947 Phys. Rev. 71 622
77. Fujita M, Igami M and Nakada K 1997 J. Phys. Soc. Japan 66 1864
78. Miyamoto Y, Nakada K and Fujita M 1999 Phys. Rev. B 59 9858
79. Wimmer M, Akhmerov A R and Guinea F 2010 Phys. Rev. B 82 045409
80. Sasaki K and Wakabayashi K 2010 Phys. Rev. B 82 035421
81. Sasaki K, Yamamoto M, Murakami S, Saito R, Dresselhaus M S, Takai K, Mori T, Enoki T and Wakabayashi K 2009 Phys. Rev. B 80 155450
82. Sasaki K, Saito R, Wakabayashi K and Enoki T 2010 J. Phys. Soc. Japan 79 044603
83. Beenakker C W J 1997 Rev. Mod. Phys. 69 731
84. Büttiker M, Imry Y, Landauer R and Pinhas S 1985 Phys. Rev. B 31 6207
85. Wakabayashi K 2002 J. Phys. Soc. Japan 71 2500
86. Zar̂bo L P and Nikolić B K 2007 Europhys. Lett. 80 47001
87. Yamamoto M, Takane Y and Wakabayashi K 2009 Phys. Rev. B 79 125421
88. Sasaki K, Wakabayashi K and Enoki T 2010 New J. Phys. 12 083023
89. Wakabayashi K, Takane Y, Yamamoto M and Sigrist M 2009 New J. Phys. 11 095016
90. Li T C and Lu S P 2008 Phys. Rev. B 77 085408
91. Louis E, Vergès J A, Guinea F and Chiappe G 2007 Phys. Rev. B 75 085440
92. Mucciolo E R, Castro Neto A H and Lewenkopf C H 2009 Phys. Rev. B 79 075407
93. Areshkin D A, Gunlycke D and White C T 2007 Nano Lett. 7 204
94. Cresti A and Roche S 2009 New J. Phys. 11 095004
95. Lieb E H 1989 Phys. Rev. Lett. 62 1201
96. Pitaevskii L and Stringari S 1991 J. Low. Temp. Phys. 85 377
97. Dagotto E and Rice T M 1996 Science 271 618
98. Makarova T L 2004 Semiconductors 38 615
99. Okada S and Oshiyama A 2001 Phys. Rev. Lett. 87 146803
100. Onipko A 2008 Phys. Rev. B 78 245412
101. Malysheva L and Onipko A 2008 Phys. Rev. Lett. 100 186806
102. Sakai K, Takai K, Fukui K, Nakanishi T and Enoki T 2010 Phys. Rev. B 81 235417
103. Brey L and Fertig H A 2006 Phys. Rev. B 73 235411
104. Rammal R 1985 J. Physique 46 1345
105. Sasaki K, Murakami S and Saito R 2006 Appl. Phys. Lett. 88 113110