Abstract
Graphene is a one atomic thickness carbon sheet, where the low-energy electronic states of graphene are described by the massless Dirac Fermions. The orientation of edge in graphene determines energy spectrum of the π-electrons. Zigzag edges possess edge localized states with energies close to the Fermi level. However, armchair edges do not have such localized states. In this chapter, we shall introduce the nanoscale and edge shape effect on electronic properties of graphene. Starting from the basic description of electronic states of graphene nanoribbons on the basis of tight-binding model and massless Dirac equation, we briefly introduce the transport properties of disordered graphene nanoribbons and nanojunctions.
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K.S. Novoselov, A.K. Geim, S.V. Morozov et. al., Science 306, 666 (2004)
A.K. Geim and K.S. Novoselov, Nat. Mater. 6, 183 (2007)
A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, and A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)
T. Ando, J. Phys. Soc. Jpn.74, 777 (2005)
T. Ando, Prog. Theor. Phys. Suppl. 176, 203 (2008)
K.S. Novoselov, A.K. Geim, S.V. Morozov, et. al., Nature 438, 197 (2005)
Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature 438, 201 (2005)
K.S. Novoselov et.al., Nat. Phys. 2, 177 (2006)
T. Ando and T. Nakanishi, J. Phys. Soc. Jpn. 67, 1704 (1998)
I.A. Luk’yanchuk and Y. Kopelevich Y, Phys. Rev. Lett. 93, 166402 (2004)
K.I. Bolotin, K.J. Sikes, Z. Jiang et al., Solid State Comm. 146, 351 (2008)
A.A. Balandin, S.Ghosh, W.Z. Bao, et al., Nano Lett. 8, 902 (2008)
M. Fujita, K. Wakabayashi, K. Nakada, and K. Kusakabe, J. Phys. Soc. Jpn. 65, 1920 (1996)
K. Nakada, M. Fujita, G. Dresselhaus, M.S. Dresselhaus, Phys. Rev. B54, 17954 (1996)
K. Wakabayashi, M. Fujita, H. Ajiki, M. Sigrist, Phys. Rev. B59, 8271 (1999)
K. Wakabayashi, M. Sigrist, and M. Fujita, J. Phys. Soc. Jpn. 67, 2089 (1998)
K. Wakabayashi, Dissertation, University of Tsukuba, (2000) http://www.tulips.tsukuba.ac.jp/dspace/handle/2241/2592
Y.W. Son, M.L. Cohen, and S.G. Louie, Nature 444, 347 (2006)
Y.W. Son, M.L. Cohen, S.G. Louie, Phys. Rev. Lett. 97, 216803 (2006)
Y. Kobayashi et. al., Phys. Rev.B71, 193406 (2005)
Y. Kobayashi et. al., Phys. Rev.B73, 125415 (2006)
Y. Niimi et. al., Phys. Rev.B73, 085421 (2006)
K.A. Ritter and J.W. Lyding, Nature Mat. 8, 235 (2009)
K. Sugawara, T. Sato, S. Souma et al., Phys. Rev. B73, 045124 (2006)
M. Y. Han MY et. al., Phys. Rev. Lett. 98, 206805 (2007)
Z. Chen et.al., Physica E 40, 228 (2007)
X. Li et.al., Science 319, 1229 (2008)
L. Jiao et.al., Nature 458, 877 (2009)
D.V. Kosynkin et.al., Nature 458, 872 (2009)
X. Yang et.al., J. Am. Chem. Phys. 130, 4216 (2008)
X. Jia et.al., Science 323, 1701 (2009)
L.C. Campos, V.R. Manfrinato, J.D. Sanchez-Yamgishi, J. Kong and P. Jarillo-Herrero, Nano Lett. 9, 2600 (2009)
J. Cai, P. Ruffieux, R. Jaafar, M. Bieri, T. Braun, S. Blankenburg, M. Muoth, A.P. Seitsonen, M. Saleh, X. Feng, K. Müllen, and R. Fasel, Nature 466, 470 (2010)
K. Wakabayashi, M. Sigrist, Phys. Rev. Lett. 84, 3390 (2000)
K. Wakabayashi, Phys. Rev. B64, 125428 (2001)
M. Yamamoto and K. Wakabayashi, Appl. Phys. Lett. 95, 082109 (2009)
K. Wakabayashi, T. Aoki, Int. J. Mod. Phys. B 16, 4897 (2002)
A. Rycerz, J. Tworzydlo, C.W.J. Beenakker, Nat. Phys. 3, 172 (2007)
C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)
K. Wakabayashi, J. Phys. Soc. Jpn. 79, 034706 (2010)
S. Dutta, Phys. Rev. Lett. 102, 096601 (2009)
E. Kan, J. Am. Chem. Soc. 130, 42224 (2008)
F. Molitor et.al., Phys. Rev. B76, 245426 (2007)
X. Wang et.al., Phys. Rev. Lett. 100, 206803 (2008)
L. Tapaszto et.al., Nat. Nanotech 3, 397 (2008)
C. Stampfer et.al., Phys. Rev. Lett. 102, 056403 (2009)
L. Campos et.al., Nano Lett. 9, 2600 (2009)
H. Miyazaki et.al., Appl. Phys. Exp. 1, 024001 (2008)
J. Güttinger et.al., Phys. Rev. Lett. 103, 046810 (2009)
K. Wakabayashi, Y. Takane, M. Sigrist, Phys. Rev. Lett. 99, 036601 (2007)
K. Wakabayashi, Y. Takane, M. Sigrist, Carbon 47, 124 (2009)
P.R. Wallace, Phys. Rev. 71, 622 (1947)
M. Fujita, M. Igami, K. Nakada, J. Phys. Soc. Jpn. 66, 1864 (1997)
O. Hod et.al., Phys. Rev. B77, 035411 (2008)
K. Wakabayashi, K. Sasaki, T. Nakanishi, T. Enoki, Sci. Tech. Adv. Mat. 11, 054504 (2010)
A. Onipko, Phys. Rev. B78, 245412 (2008)
S. Compernolle, L. Chibotaru, A. Ceulemans, J. Chem. Phys. 119, 2854 (2003)
K. Sasaki, K. Wakabayashi, T. Enoki, J. Phys. Soc. Jpn. 80, 054710 (2011)
K. Sasaki and K. Wakabayashi, Phys. Rev. B82, 035421 (2010)
K. Sasaki, M. Yamamoto, S. Murakami, R. Saito, M. S. Dresselhaus, K. Takai, T. Mori, T. Enoki, K. Wakabayashi, Phys. Rev. B80, 155450 (2009)
K. Sasaki, R. Saito, K. Wakabayashi, T. Enoki, J. Phys. Soc. Jpn. 79, 044603 (2010)
C. Cong, T. Yu, H. Wang, ACS Nano, 4, 3175 (2010)
C. Casiraghi, A. Hartschuh, H. Qian, S. Piscanec, C. Georgi, A. Fasoli, K. S. Novoselov, D. M. Basko and A. C. Ferrari, Nano Lett, 9 1433 (2009)
M. Begliarbekov, O. Sul, S. Kalliakos, E.-H. Yang, S. Strauf, Appl. Phys. Lett. 97, 031908 (2010)
L. Brey, H.A. Fertig, Phys. Rev. B73, 235411 (2006)
C.W.J. Beenakker, Rev. Mod. Phys. 69, 731 (1997)
M. Büttiker, Y. Imry, R. Landauer, S. Pinhas, Phys. Rev. B31, 6207 (1985)
T. Ando, Phys. Rev. B44, 8017 (1991)
T.C. Li, S.P. Lu, Phys. Rev. B77 085408 (2008)
E. Louis, J.A. Vergés, F. Guinea, G. Chiappe, Phys. Rev. B75 085440 (2007)
E. R. Mucciolo et.al., Phys. Rev. B79, 075407 (2009)
S. Ihnatsenka, G. Kirczenow, Phys. Rev. B80 201407(R) (2009)
Y. Takane, K. Wakabayashi, J. Phys. Soc. Jpn. 76, 053701 (2007)
Y. Takane, K. Wakabayashi, J. Phys. Soc. Jpn. 77, 054702 (2008)
K. Wakabayashi, J. Phys. Soc. Jpn. 71, 2500 (2002)
T. Ando, H. Suzuura, J. Phys. Soc. Jpn. 71, 2753 (2002)
S. Das Sarma, S. Adam, E.H. Hwang, E. Rossi, Rev. Mod. Phys. 83, 407 (2011)
H. Suzuura, T. Ando, Phys. Rev. Lett. 89, 266603 (2002)
D.A. Areshkin, D. Gunlycke, C.T. White, Nano Lett. 7, 204 (2007)
A. Cresti, S. Roche, New J. Phys. 11, 095004 (2009)
A. Cresti, S. Roche, Phys. Rev. B79, 233404 (2009)
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Wakabayashi, K. (2011). Electronic Properties of Graphene Nanoribbons. In: Raza, H. (eds) Graphene Nanoelectronics. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22984-8_9
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DOI: https://doi.org/10.1007/978-3-642-22984-8_9
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