Abstract

Optical selection rules for one-dimensional graphene nanoribbons are explored based on the tight-binding model. A theoretical explanation, through analyzing the velocity matrix elements and the features of the wavefunctions, can account for the selection rules, which depend on the edge structure of the nanoribbon, i.e., armchair or zigzag edges. The selection rule of armchair nanoribbons is ΔJ = Jc – Jv = 0, and the optical transitions occur from the conduction to the valence subbands of the same index. Such a selection rule originates in the relationships between two sublattices and between the conduction and valence subbands. On the other hand, zigzag nanoribbons exhibit the selection rule |ΔJ| = odd, which results from the alternatively changing symmetry property as the subband index increases. Furthermore, an efficient theoretical prediction on transition energies is obtained by the application of selection rules, and the energies of the band-edge states become experimentally attainable via optical measurements.

© 2011 OSA

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  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
    [CrossRef] [PubMed]
  2. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
    [CrossRef] [PubMed]
  3. R. F. Service, “Materials science carbon sheets an atom thick give rise to graphene dreams,” Science 324, 875–877 (2009).
    [CrossRef] [PubMed]
  4. N. M. R. Peres, “Graphene, new physics in two dimensions,” Europhys. News 40, 17–20 (2009).
    [CrossRef]
  5. M. I. Katsnelson, “Graphene: carbon in two dimensions,” Mater. Today 10, 20–27 (2007).
    [CrossRef]
  6. A. K. Geim, “Graphene: Status and prospects,” Science 324, 1530–1534 (2009).
    [CrossRef] [PubMed]
  7. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
    [CrossRef] [PubMed]
  8. S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
    [CrossRef] [PubMed]
  9. F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
    [CrossRef] [PubMed]
  10. S. V. Morozov, K. S. Novoselov, and A. K. Geim, “Electron transport in graphene,” Phys. Usp. 51, 744–748 (2008).
    [CrossRef]
  11. S. Cho and M. S. Fuhrer, “Charge transport and inhomogeneity near the minimum conductivity point in graphene,” Phys. Rev. B 77, 081402 (2008).
    [CrossRef]
  12. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
    [CrossRef] [PubMed]
  13. Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum hall effect and berry’s phase in graphene,” Nature 438, 201–204 (2005).
    [CrossRef] [PubMed]
  14. J. W. Bai, X. F. Duan, and Y. Huang, “Rational fabrication of graphene nanoribbons using a nanowire etch mask,” Nano Lett. 9, 2083–2087 (2009).
    [CrossRef] [PubMed]
  15. A. Fasoli, A. Colli, A. Lombardo, and A. C. Ferrari, “Fabrication of graphene nanoribbons via nanowire lithography,” Phys. Status Solidi B-Basic Solid State Phys. 246, 2514–2517 (2009).
    [CrossRef]
  16. V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
    [CrossRef]
  17. J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
    [CrossRef]
  18. L. Tapaszto, G. Dobrik, P. Lambin, and L. P. Biro, “Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography,” Nat. Nanotechnol. 3, 397–401 (2008).
    [CrossRef] [PubMed]
  19. M. Y. Han, B. Ozyilmaz, Y. B. Zhang, and P. Kim, “Energy band-gap engineering of graphene nanoribbons,” Phys. Rev. Lett. 98, 206805 (2007).
    [CrossRef] [PubMed]
  20. C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
    [CrossRef] [PubMed]
  21. D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
    [CrossRef] [PubMed]
  22. F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
    [CrossRef]
  23. M. C. Paiva, W. Xu, M. F. Proenca, R. M. Novais, E. Laegsgaard, and F. Besenbacher, “Unzipping of functionalized multiwall carbon nanotubes induced by stm,” Nano Lett. 10, 1764–1768 (2010).
    [CrossRef] [PubMed]
  24. A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
    [CrossRef] [PubMed]
  25. R. H. Miwa, R. G. A. Veiga, and G. P. Srivastava, “Structural, electronic, and magnetic properties of pristine and oxygen-adsorbed graphene nanoribbons,” Appl. Surf. Sci. 256, 5776–5782 (2010).
    [CrossRef]
  26. S. Dutta and S. K. Pati, “Novel properties of graphene nanoribbons: a review,” J. Mater. Chem. 20, 8207–8223 (2010).
    [CrossRef]
  27. H. C. Chung, Y. C. Huang, M. H. Lee, C. C. Chang, and M. F. Lin, “Quasi-landau levels in bilayer zigzag graphene nanoribbons,” Physica E 42, 711–714 (2010).
    [CrossRef]
  28. T. Nomura, D. Yamamoto, and S. Kurihara, “Electric field effects in zigzag edged graphene nanoribbons,” J. Phys.: Conf. Ser. 200, 062015 (2010).
    [CrossRef]
  29. J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
    [CrossRef] [PubMed]
  30. H. C. Chung, M. H. Lee, C. P. Chang, Y. C. Huang, and M. F. Lin, “Effects of transverse electric fields on quasi-landau levels in zigzag graphene nanoribbons,” J. Phys. Soc. Jpn. 80, 044602 (2011).
    [CrossRef]
  31. A. Cresti and S. Roche, “Range and correlation effects in edge disordered graphene nanoribbons,” New. J. Phys. 11, 095004 (2009).
    [CrossRef]
  32. Y. O. Klymenko and O. Shevtsov, “Low-energy electron transport in semimetal graphene ribbon junctions,” Eur. Phys. J. B 72, 203–209 (2009).
    [CrossRef]
  33. E. Perfetto, G. Stefanucci, and M. Cini, “Time-dependent transport in graphene nanoribbons,” Phys. Rev. B 82, 035446 (2010).
    [CrossRef]
  34. J. Jiang, W. Lu, and J. Bernholc, “Edge states and optical transition energies in carbon nanoribbons,” Phys. Rev. Lett. 101, 246803 (2008).
    [CrossRef] [PubMed]
  35. M. F. Lin and F. L. Shyu, “Optical properties of nanographite ribbons,” J. Phys. Soc. Jpn. 69, 3529–3532 (2000).
    [CrossRef]
  36. H. Hsu and L. E. Reichl, “Selection rule for the optical absorption of graphene nanoribbons,” Phys. Rev. B 76, 045418 (2007).
    [CrossRef]
  37. C. W. Chiu, S. H. Lee, S. C. Chen, F. L. Shyu, and M. F. Lin, “Absorption spectra of aa-stacked graphite,” New. J. Phys. 12, 083060 (2010).
    [CrossRef]
  38. L. Van Hove, “The occurrence of singularities in the elastic frequency distribution of a crystal,” Phys. Rev. 89, 1189 (1953).
    [CrossRef]
  39. E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
    [CrossRef]
  40. J. C. Charlier, X. Gonze, and J. P. Michenaud, “First-principles study of the electronic properties of graphite,” Phys. Rev. B 43, 4579–4589 (1991).
    [CrossRef]
  41. G. Dresselhaus and M. S. Dresselhaus, “Fourier expansion for electronic energy bands in silicon and germanium,” Phys. Rev. 160, 649–679 (1967).
    [CrossRef]
  42. L. G. Johnson and G. Dresselhaus, “Optical properies of graphite,” Phys. Rev. B 7, 2275–2285 (1973).
    [CrossRef]
  43. N. V. Smith, “Photoemission spectra and band structures of d-band metals .7. extensions of the combined interpolation scheme,” Phys. Rev. B 19, 5019–5027 (1979).
    [CrossRef]
  44. L. C. Lew Yan Voon and L. R. Ram-Mohan, “Tight-binding representation of the optical matrix-elements - theory and applications,” Phys. Rev. B 47, 15500–15508 (1993).
    [CrossRef]

2011 (1)

H. C. Chung, M. H. Lee, C. P. Chang, Y. C. Huang, and M. F. Lin, “Effects of transverse electric fields on quasi-landau levels in zigzag graphene nanoribbons,” J. Phys. Soc. Jpn. 80, 044602 (2011).
[CrossRef]

2010 (10)

E. Perfetto, G. Stefanucci, and M. Cini, “Time-dependent transport in graphene nanoribbons,” Phys. Rev. B 82, 035446 (2010).
[CrossRef]

C. W. Chiu, S. H. Lee, S. C. Chen, F. L. Shyu, and M. F. Lin, “Absorption spectra of aa-stacked graphite,” New. J. Phys. 12, 083060 (2010).
[CrossRef]

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

M. C. Paiva, W. Xu, M. F. Proenca, R. M. Novais, E. Laegsgaard, and F. Besenbacher, “Unzipping of functionalized multiwall carbon nanotubes induced by stm,” Nano Lett. 10, 1764–1768 (2010).
[CrossRef] [PubMed]

R. H. Miwa, R. G. A. Veiga, and G. P. Srivastava, “Structural, electronic, and magnetic properties of pristine and oxygen-adsorbed graphene nanoribbons,” Appl. Surf. Sci. 256, 5776–5782 (2010).
[CrossRef]

S. Dutta and S. K. Pati, “Novel properties of graphene nanoribbons: a review,” J. Mater. Chem. 20, 8207–8223 (2010).
[CrossRef]

H. C. Chung, Y. C. Huang, M. H. Lee, C. C. Chang, and M. F. Lin, “Quasi-landau levels in bilayer zigzag graphene nanoribbons,” Physica E 42, 711–714 (2010).
[CrossRef]

T. Nomura, D. Yamamoto, and S. Kurihara, “Electric field effects in zigzag edged graphene nanoribbons,” J. Phys.: Conf. Ser. 200, 062015 (2010).
[CrossRef]

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

2009 (10)

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

R. F. Service, “Materials science carbon sheets an atom thick give rise to graphene dreams,” Science 324, 875–877 (2009).
[CrossRef] [PubMed]

N. M. R. Peres, “Graphene, new physics in two dimensions,” Europhys. News 40, 17–20 (2009).
[CrossRef]

A. K. Geim, “Graphene: Status and prospects,” Science 324, 1530–1534 (2009).
[CrossRef] [PubMed]

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

J. W. Bai, X. F. Duan, and Y. Huang, “Rational fabrication of graphene nanoribbons using a nanowire etch mask,” Nano Lett. 9, 2083–2087 (2009).
[CrossRef] [PubMed]

A. Fasoli, A. Colli, A. Lombardo, and A. C. Ferrari, “Fabrication of graphene nanoribbons via nanowire lithography,” Phys. Status Solidi B-Basic Solid State Phys. 246, 2514–2517 (2009).
[CrossRef]

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
[CrossRef] [PubMed]

A. Cresti and S. Roche, “Range and correlation effects in edge disordered graphene nanoribbons,” New. J. Phys. 11, 095004 (2009).
[CrossRef]

Y. O. Klymenko and O. Shevtsov, “Low-energy electron transport in semimetal graphene ribbon junctions,” Eur. Phys. J. B 72, 203–209 (2009).
[CrossRef]

2008 (5)

J. Jiang, W. Lu, and J. Bernholc, “Edge states and optical transition energies in carbon nanoribbons,” Phys. Rev. Lett. 101, 246803 (2008).
[CrossRef] [PubMed]

S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
[CrossRef] [PubMed]

L. Tapaszto, G. Dobrik, P. Lambin, and L. P. Biro, “Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography,” Nat. Nanotechnol. 3, 397–401 (2008).
[CrossRef] [PubMed]

S. V. Morozov, K. S. Novoselov, and A. K. Geim, “Electron transport in graphene,” Phys. Usp. 51, 744–748 (2008).
[CrossRef]

S. Cho and M. S. Fuhrer, “Charge transport and inhomogeneity near the minimum conductivity point in graphene,” Phys. Rev. B 77, 081402 (2008).
[CrossRef]

2007 (5)

M. Y. Han, B. Ozyilmaz, Y. B. Zhang, and P. Kim, “Energy band-gap engineering of graphene nanoribbons,” Phys. Rev. Lett. 98, 206805 (2007).
[CrossRef] [PubMed]

F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
[CrossRef] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[CrossRef] [PubMed]

M. I. Katsnelson, “Graphene: carbon in two dimensions,” Mater. Today 10, 20–27 (2007).
[CrossRef]

H. Hsu and L. E. Reichl, “Selection rule for the optical absorption of graphene nanoribbons,” Phys. Rev. B 76, 045418 (2007).
[CrossRef]

2006 (2)

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

2005 (3)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum hall effect and berry’s phase in graphene,” Nature 438, 201–204 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
[CrossRef] [PubMed]

2004 (1)

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

2000 (1)

M. F. Lin and F. L. Shyu, “Optical properties of nanographite ribbons,” J. Phys. Soc. Jpn. 69, 3529–3532 (2000).
[CrossRef]

1993 (1)

L. C. Lew Yan Voon and L. R. Ram-Mohan, “Tight-binding representation of the optical matrix-elements - theory and applications,” Phys. Rev. B 47, 15500–15508 (1993).
[CrossRef]

1991 (1)

J. C. Charlier, X. Gonze, and J. P. Michenaud, “First-principles study of the electronic properties of graphite,” Phys. Rev. B 43, 4579–4589 (1991).
[CrossRef]

1979 (1)

N. V. Smith, “Photoemission spectra and band structures of d-band metals .7. extensions of the combined interpolation scheme,” Phys. Rev. B 19, 5019–5027 (1979).
[CrossRef]

1973 (1)

L. G. Johnson and G. Dresselhaus, “Optical properies of graphite,” Phys. Rev. B 7, 2275–2285 (1973).
[CrossRef]

1967 (1)

G. Dresselhaus and M. S. Dresselhaus, “Fourier expansion for electronic energy bands in silicon and germanium,” Phys. Rev. 160, 649–679 (1967).
[CrossRef]

1953 (1)

L. Van Hove, “The occurrence of singularities in the elastic frequency distribution of a crystal,” Phys. Rev. 89, 1189 (1953).
[CrossRef]

Amemiya, K.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

Angelini, G.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Bai, J. W.

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

J. W. Bai, X. F. Duan, and Y. Huang, “Rational fabrication of graphene nanoribbons using a nanowire etch mask,” Nano Lett. 9, 2083–2087 (2009).
[CrossRef] [PubMed]

Barros, E. B.

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

Berger, C.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Bernholc, J.

J. Jiang, W. Lu, and J. Bernholc, “Edge states and optical transition energies in carbon nanoribbons,” Phys. Rev. Lett. 101, 246803 (2008).
[CrossRef] [PubMed]

Besenbacher, F.

M. C. Paiva, W. Xu, M. F. Proenca, R. M. Novais, E. Laegsgaard, and F. Besenbacher, “Unzipping of functionalized multiwall carbon nanotubes induced by stm,” Nano Lett. 10, 1764–1768 (2010).
[CrossRef] [PubMed]

Biro, L. P.

L. Tapaszto, G. Dobrik, P. Lambin, and L. P. Biro, “Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography,” Nat. Nanotechnol. 3, 397–401 (2008).
[CrossRef] [PubMed]

Blake, P.

F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
[CrossRef] [PubMed]

Booth, T. J.

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
[CrossRef] [PubMed]

Botello-Mendez, A.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

Brown, N.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Campos-Delgado, J.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

Cano-Marquez, A. G.

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

Capaz, R. B.

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

Cataldo, F.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Chang, C. C.

H. C. Chung, Y. C. Huang, M. H. Lee, C. C. Chang, and M. F. Lin, “Quasi-landau levels in bilayer zigzag graphene nanoribbons,” Physica E 42, 711–714 (2010).
[CrossRef]

Chang, C. P.

H. C. Chung, M. H. Lee, C. P. Chang, Y. C. Huang, and M. F. Lin, “Effects of transverse electric fields on quasi-landau levels in zigzag graphene nanoribbons,” J. Phys. Soc. Jpn. 80, 044602 (2011).
[CrossRef]

Charlier, J. C.

J. C. Charlier, X. Gonze, and J. P. Michenaud, “First-principles study of the electronic properties of graphite,” Phys. Rev. B 43, 4579–4589 (1991).
[CrossRef]

Chen, S. C.

C. W. Chiu, S. H. Lee, S. C. Chen, F. L. Shyu, and M. F. Lin, “Absorption spectra of aa-stacked graphite,” New. J. Phys. 12, 083060 (2010).
[CrossRef]

Cheng, R.

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

Chiu, C. W.

C. W. Chiu, S. H. Lee, S. C. Chen, F. L. Shyu, and M. F. Lin, “Absorption spectra of aa-stacked graphite,” New. J. Phys. 12, 083060 (2010).
[CrossRef]

Cho, S.

S. Cho and M. S. Fuhrer, “Charge transport and inhomogeneity near the minimum conductivity point in graphene,” Phys. Rev. B 77, 081402 (2008).
[CrossRef]

Chung, H. C.

H. C. Chung, M. H. Lee, C. P. Chang, Y. C. Huang, and M. F. Lin, “Effects of transverse electric fields on quasi-landau levels in zigzag graphene nanoribbons,” J. Phys. Soc. Jpn. 80, 044602 (2011).
[CrossRef]

H. C. Chung, Y. C. Huang, M. H. Lee, C. C. Chang, and M. F. Lin, “Quasi-landau levels in bilayer zigzag graphene nanoribbons,” Physica E 42, 711–714 (2010).
[CrossRef]

Cini, M.

E. Perfetto, G. Stefanucci, and M. Cini, “Time-dependent transport in graphene nanoribbons,” Phys. Rev. B 82, 035446 (2010).
[CrossRef]

Colli, A.

A. Fasoli, A. Colli, A. Lombardo, and A. C. Ferrari, “Fabrication of graphene nanoribbons via nanowire lithography,” Phys. Status Solidi B-Basic Solid State Phys. 246, 2514–2517 (2009).
[CrossRef]

Compagnini, G.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Conrad, E. H.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Cresti, A.

A. Cresti and S. Roche, “Range and correlation effects in edge disordered graphene nanoribbons,” New. J. Phys. 11, 095004 (2009).
[CrossRef]

Cricenti, A.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Cullen, D. A.

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

de Heer, W. A.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Dimiev, A.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
[CrossRef] [PubMed]

Dobrik, G.

L. Tapaszto, G. Dobrik, P. Lambin, and L. P. Biro, “Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography,” Nat. Nanotechnol. 3, 397–401 (2008).
[CrossRef] [PubMed]

Dresselhaus, G.

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

L. G. Johnson and G. Dresselhaus, “Optical properies of graphite,” Phys. Rev. B 7, 2275–2285 (1973).
[CrossRef]

G. Dresselhaus and M. S. Dresselhaus, “Fourier expansion for electronic energy bands in silicon and germanium,” Phys. Rev. 160, 649–679 (1967).
[CrossRef]

Dresselhaus, M. S.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

G. Dresselhaus and M. S. Dresselhaus, “Fourier expansion for electronic energy bands in silicon and germanium,” Phys. Rev. 160, 649–679 (1967).
[CrossRef]

Duan, X. F.

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

J. W. Bai, X. F. Duan, and Y. Huang, “Rational fabrication of graphene nanoribbons using a nanowire etch mask,” Nano Lett. 9, 2083–2087 (2009).
[CrossRef] [PubMed]

Dubonos, S. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Dutta, S.

S. Dutta and S. K. Pati, “Novel properties of graphene nanoribbons: a review,” J. Mater. Chem. 20, 8207–8223 (2010).
[CrossRef]

Elias, D. C.

S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
[CrossRef] [PubMed]

Endo, M.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

Enoki, T.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

Espinosa-Gonzalez, C. G.

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

Fasoli, A.

A. Fasoli, A. Colli, A. Lombardo, and A. C. Ferrari, “Fabrication of graphene nanoribbons via nanowire lithography,” Phys. Status Solidi B-Basic Solid State Phys. 246, 2514–2517 (2009).
[CrossRef]

Ferrari, A. C.

A. Fasoli, A. Colli, A. Lombardo, and A. C. Ferrari, “Fabrication of graphene nanoribbons via nanowire lithography,” Phys. Status Solidi B-Basic Solid State Phys. 246, 2514–2517 (2009).
[CrossRef]

Firsov, A. A.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

First, P. N.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Fuhrer, M. S.

S. Cho and M. S. Fuhrer, “Charge transport and inhomogeneity near the minimum conductivity point in graphene,” Phys. Rev. B 77, 081402 (2008).
[CrossRef]

Geim, A. K.

A. K. Geim, “Graphene: Status and prospects,” Science 324, 1530–1534 (2009).
[CrossRef] [PubMed]

S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
[CrossRef] [PubMed]

S. V. Morozov, K. S. Novoselov, and A. K. Geim, “Electron transport in graphene,” Phys. Usp. 51, 744–748 (2008).
[CrossRef]

F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
[CrossRef] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[CrossRef] [PubMed]

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Gonze, X.

J. C. Charlier, X. Gonze, and J. P. Michenaud, “First-principles study of the electronic properties of graphite,” Phys. Rev. B 43, 4579–4589 (1991).
[CrossRef]

Grigorieva, I. V.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Han, M. Y.

M. Y. Han, B. Ozyilmaz, Y. B. Zhang, and P. Kim, “Energy band-gap engineering of graphene nanoribbons,” Phys. Rev. Lett. 98, 206805 (2007).
[CrossRef] [PubMed]

Hao, S. J.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

Hass, J.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Hayashi, T.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

Higginbotham, A. L.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
[CrossRef] [PubMed]

Hill, E. W.

F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
[CrossRef] [PubMed]

Hofmann, M.

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

Hsu, H.

H. Hsu and L. E. Reichl, “Selection rule for the optical absorption of graphene nanoribbons,” Phys. Rev. B 76, 045418 (2007).
[CrossRef]

Huang, Y.

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

J. W. Bai, X. F. Duan, and Y. Huang, “Rational fabrication of graphene nanoribbons using a nanowire etch mask,” Nano Lett. 9, 2083–2087 (2009).
[CrossRef] [PubMed]

Huang, Y. C.

H. C. Chung, M. H. Lee, C. P. Chang, Y. C. Huang, and M. F. Lin, “Effects of transverse electric fields on quasi-landau levels in zigzag graphene nanoribbons,” J. Phys. Soc. Jpn. 80, 044602 (2011).
[CrossRef]

H. C. Chung, Y. C. Huang, M. H. Lee, C. C. Chang, and M. F. Lin, “Quasi-landau levels in bilayer zigzag graphene nanoribbons,” Physica E 42, 711–714 (2010).
[CrossRef]

Jaszczak, J. A.

S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
[CrossRef] [PubMed]

Jiang, D.

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Jiang, J.

J. Jiang, W. Lu, and J. Bernholc, “Edge states and optical transition energies in carbon nanoribbons,” Phys. Rev. Lett. 101, 246803 (2008).
[CrossRef] [PubMed]

Johnson, L. G.

L. G. Johnson and G. Dresselhaus, “Optical properies of graphite,” Phys. Rev. B 7, 2275–2285 (1973).
[CrossRef]

Joly, V. L. J.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

Jorio, A.

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

Katsnelson, M. I.

S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
[CrossRef] [PubMed]

M. I. Katsnelson, “Graphene: carbon in two dimensions,” Mater. Today 10, 20–27 (2007).
[CrossRef]

F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

Khotkevich, V. V.

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
[CrossRef] [PubMed]

Kiguchi, M.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

Kim, P.

M. Y. Han, B. Ozyilmaz, Y. B. Zhang, and P. Kim, “Energy band-gap engineering of graphene nanoribbons,” Phys. Rev. Lett. 98, 206805 (2007).
[CrossRef] [PubMed]

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum hall effect and berry’s phase in graphene,” Nature 438, 201–204 (2005).
[CrossRef] [PubMed]

Kim, Y. A.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

Klymenko, Y. O.

Y. O. Klymenko and O. Shevtsov, “Low-energy electron transport in semimetal graphene ribbon junctions,” Eur. Phys. J. B 72, 203–209 (2009).
[CrossRef]

Kosynkin, D. V.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
[CrossRef] [PubMed]

Kurihara, S.

T. Nomura, D. Yamamoto, and S. Kurihara, “Electric field effects in zigzag edged graphene nanoribbons,” J. Phys.: Conf. Ser. 200, 062015 (2010).
[CrossRef]

Laegsgaard, E.

M. C. Paiva, W. Xu, M. F. Proenca, R. M. Novais, E. Laegsgaard, and F. Besenbacher, “Unzipping of functionalized multiwall carbon nanotubes induced by stm,” Nano Lett. 10, 1764–1768 (2010).
[CrossRef] [PubMed]

Lambin, P.

L. Tapaszto, G. Dobrik, P. Lambin, and L. P. Biro, “Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography,” Nat. Nanotechnol. 3, 397–401 (2008).
[CrossRef] [PubMed]

Lee, M. H.

H. C. Chung, M. H. Lee, C. P. Chang, Y. C. Huang, and M. F. Lin, “Effects of transverse electric fields on quasi-landau levels in zigzag graphene nanoribbons,” J. Phys. Soc. Jpn. 80, 044602 (2011).
[CrossRef]

H. C. Chung, Y. C. Huang, M. H. Lee, C. C. Chang, and M. F. Lin, “Quasi-landau levels in bilayer zigzag graphene nanoribbons,” Physica E 42, 711–714 (2010).
[CrossRef]

Lee, S. H.

C. W. Chiu, S. H. Lee, S. C. Chen, F. L. Shyu, and M. F. Lin, “Absorption spectra of aa-stacked graphite,” New. J. Phys. 12, 083060 (2010).
[CrossRef]

Lew Yan Voon, L. C.

L. C. Lew Yan Voon and L. R. Ram-Mohan, “Tight-binding representation of the optical matrix-elements - theory and applications,” Phys. Rev. B 47, 15500–15508 (1993).
[CrossRef]

Li, T. B.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Li, X. B.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Liao, L.

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

Lin, M. F.

H. C. Chung, M. H. Lee, C. P. Chang, Y. C. Huang, and M. F. Lin, “Effects of transverse electric fields on quasi-landau levels in zigzag graphene nanoribbons,” J. Phys. Soc. Jpn. 80, 044602 (2011).
[CrossRef]

H. C. Chung, Y. C. Huang, M. H. Lee, C. C. Chang, and M. F. Lin, “Quasi-landau levels in bilayer zigzag graphene nanoribbons,” Physica E 42, 711–714 (2010).
[CrossRef]

C. W. Chiu, S. H. Lee, S. C. Chen, F. L. Shyu, and M. F. Lin, “Absorption spectra of aa-stacked graphite,” New. J. Phys. 12, 083060 (2010).
[CrossRef]

M. F. Lin and F. L. Shyu, “Optical properties of nanographite ribbons,” J. Phys. Soc. Jpn. 69, 3529–3532 (2000).
[CrossRef]

Lombardo, A.

A. Fasoli, A. Colli, A. Lombardo, and A. C. Ferrari, “Fabrication of graphene nanoribbons via nanowire lithography,” Phys. Status Solidi B-Basic Solid State Phys. 246, 2514–2517 (2009).
[CrossRef]

Lomeda, J. R.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
[CrossRef] [PubMed]

Lopez-Urias, F.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

Lu, W.

J. Jiang, W. Lu, and J. Bernholc, “Edge states and optical transition energies in carbon nanoribbons,” Phys. Rev. Lett. 101, 246803 (2008).
[CrossRef] [PubMed]

Marchenkov, A. N.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Margaritondo, G.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Mayou, D.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Mendes, J.

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

Michenaud, J. P.

J. C. Charlier, X. Gonze, and J. P. Michenaud, “First-principles study of the electronic properties of graphite,” Phys. Rev. B 43, 4579–4589 (1991).
[CrossRef]

Miwa, R. H.

R. H. Miwa, R. G. A. Veiga, and G. P. Srivastava, “Structural, electronic, and magnetic properties of pristine and oxygen-adsorbed graphene nanoribbons,” Appl. Surf. Sci. 256, 5776–5782 (2010).
[CrossRef]

Morelos-Gomez, A.

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

Morozov, S. V.

S. V. Morozov, K. S. Novoselov, and A. K. Geim, “Electron transport in graphene,” Phys. Usp. 51, 744–748 (2008).
[CrossRef]

S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
[CrossRef] [PubMed]

F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
[CrossRef] [PubMed]

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Muramatsu, H.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

Naud, C.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Nomura, T.

T. Nomura, D. Yamamoto, and S. Kurihara, “Electric field effects in zigzag edged graphene nanoribbons,” J. Phys.: Conf. Ser. 200, 062015 (2010).
[CrossRef]

Novais, R. M.

M. C. Paiva, W. Xu, M. F. Proenca, R. M. Novais, E. Laegsgaard, and F. Besenbacher, “Unzipping of functionalized multiwall carbon nanotubes induced by stm,” Nano Lett. 10, 1764–1768 (2010).
[CrossRef] [PubMed]

Novoselov, K. S.

S. V. Morozov, K. S. Novoselov, and A. K. Geim, “Electron transport in graphene,” Phys. Usp. 51, 744–748 (2008).
[CrossRef]

S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
[CrossRef] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[CrossRef] [PubMed]

F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
[CrossRef] [PubMed]

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Ozyilmaz, B.

M. Y. Han, B. Ozyilmaz, Y. B. Zhang, and P. Kim, “Energy band-gap engineering of graphene nanoribbons,” Phys. Rev. Lett. 98, 206805 (2007).
[CrossRef] [PubMed]

Paiva, M. C.

M. C. Paiva, W. Xu, M. F. Proenca, R. M. Novais, E. Laegsgaard, and F. Besenbacher, “Unzipping of functionalized multiwall carbon nanotubes induced by stm,” Nano Lett. 10, 1764–1768 (2010).
[CrossRef] [PubMed]

Palleschi, G.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Patane, G.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Pati, S. K.

S. Dutta and S. K. Pati, “Novel properties of graphene nanoribbons: a review,” J. Mater. Chem. 20, 8207–8223 (2010).
[CrossRef]

Peres, N. M. R.

N. M. R. Peres, “Graphene, new physics in two dimensions,” Europhys. News 40, 17–20 (2009).
[CrossRef]

Perfetto, E.

E. Perfetto, G. Stefanucci, and M. Cini, “Time-dependent transport in graphene nanoribbons,” Phys. Rev. B 82, 035446 (2010).
[CrossRef]

Price, B. K.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
[CrossRef] [PubMed]

Proenca, M. F.

M. C. Paiva, W. Xu, M. F. Proenca, R. M. Novais, E. Laegsgaard, and F. Besenbacher, “Unzipping of functionalized multiwall carbon nanotubes induced by stm,” Nano Lett. 10, 1764–1768 (2010).
[CrossRef] [PubMed]

Ramirez-Gonzalez, D.

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

Ram-Mohan, L. R.

L. C. Lew Yan Voon and L. R. Ram-Mohan, “Tight-binding representation of the optical matrix-elements - theory and applications,” Phys. Rev. B 47, 15500–15508 (1993).
[CrossRef]

Reichl, L. E.

H. Hsu and L. E. Reichl, “Selection rule for the optical absorption of graphene nanoribbons,” Phys. Rev. B 76, 045418 (2007).
[CrossRef]

Ribic, P. R.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Roche, S.

A. Cresti and S. Roche, “Range and correlation effects in edge disordered graphene nanoribbons,” New. J. Phys. 11, 095004 (2009).
[CrossRef]

Rodriguez-Macias, F. J.

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

Samsonidze, G. G.

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

Schedin, F.

S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
[CrossRef] [PubMed]

F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
[CrossRef] [PubMed]

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
[CrossRef] [PubMed]

Service, R. F.

R. F. Service, “Materials science carbon sheets an atom thick give rise to graphene dreams,” Science 324, 875–877 (2009).
[CrossRef] [PubMed]

Shailos, A.

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

Shevtsov, O.

Y. O. Klymenko and O. Shevtsov, “Low-energy electron transport in semimetal graphene ribbon junctions,” Eur. Phys. J. B 72, 203–209 (2009).
[CrossRef]

Shull, R. D.

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

Shyu, F. L.

C. W. Chiu, S. H. Lee, S. C. Chen, F. L. Shyu, and M. F. Lin, “Absorption spectra of aa-stacked graphite,” New. J. Phys. 12, 083060 (2010).
[CrossRef]

M. F. Lin and F. L. Shyu, “Optical properties of nanographite ribbons,” J. Phys. Soc. Jpn. 69, 3529–3532 (2000).
[CrossRef]

Sinitskii, A.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
[CrossRef] [PubMed]

Smith, D. J.

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

Smith, N. V.

N. V. Smith, “Photoemission spectra and band structures of d-band metals .7. extensions of the combined interpolation scheme,” Phys. Rev. B 19, 5019–5027 (1979).
[CrossRef]

Song, Z. M.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Souza, A. G.

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

Srivastava, G. P.

R. H. Miwa, R. G. A. Veiga, and G. P. Srivastava, “Structural, electronic, and magnetic properties of pristine and oxygen-adsorbed graphene nanoribbons,” Appl. Surf. Sci. 256, 5776–5782 (2010).
[CrossRef]

Stefanucci, G.

E. Perfetto, G. Stefanucci, and M. Cini, “Time-dependent transport in graphene nanoribbons,” Phys. Rev. B 82, 035446 (2010).
[CrossRef]

Stormer, H. L.

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum hall effect and berry’s phase in graphene,” Nature 438, 201–204 (2005).
[CrossRef] [PubMed]

Sumii, R.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

Takai, K.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

Tan, Y. W.

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum hall effect and berry’s phase in graphene,” Nature 438, 201–204 (2005).
[CrossRef] [PubMed]

Tapaszto, L.

L. Tapaszto, G. Dobrik, P. Lambin, and L. P. Biro, “Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography,” Nat. Nanotechnol. 3, 397–401 (2008).
[CrossRef] [PubMed]

Terrones, H.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

Terrones, M.

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

Tour, J. M.

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
[CrossRef] [PubMed]

Tristan-Lopez, F.

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

Ursini, O.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Valentini, F.

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Van Hove, L.

L. Van Hove, “The occurrence of singularities in the elastic frequency distribution of a crystal,” Phys. Rev. 89, 1189 (1953).
[CrossRef]

Vega-Cantu, Y. I.

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

Veiga, R. G. A.

R. H. Miwa, R. G. A. Veiga, and G. P. Srivastava, “Structural, electronic, and magnetic properties of pristine and oxygen-adsorbed graphene nanoribbons,” Appl. Surf. Sci. 256, 5776–5782 (2010).
[CrossRef]

Wang, K. L.

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

Wang, M. S.

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

Wu, X. S.

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

Xiu, F. X.

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

Xu, W.

M. C. Paiva, W. Xu, M. F. Proenca, R. M. Novais, E. Laegsgaard, and F. Besenbacher, “Unzipping of functionalized multiwall carbon nanotubes induced by stm,” Nano Lett. 10, 1764–1768 (2010).
[CrossRef] [PubMed]

Yamamoto, D.

T. Nomura, D. Yamamoto, and S. Kurihara, “Electric field effects in zigzag edged graphene nanoribbons,” J. Phys.: Conf. Ser. 200, 062015 (2010).
[CrossRef]

Zhang, Y.

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

Zhang, Y. B.

M. Y. Han, B. Ozyilmaz, Y. B. Zhang, and P. Kim, “Energy band-gap engineering of graphene nanoribbons,” Phys. Rev. Lett. 98, 206805 (2007).
[CrossRef] [PubMed]

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum hall effect and berry’s phase in graphene,” Nature 438, 201–204 (2005).
[CrossRef] [PubMed]

Appl. Surf. Sci. (1)

R. H. Miwa, R. G. A. Veiga, and G. P. Srivastava, “Structural, electronic, and magnetic properties of pristine and oxygen-adsorbed graphene nanoribbons,” Appl. Surf. Sci. 256, 5776–5782 (2010).
[CrossRef]

Carbon (1)

F. Cataldo, G. Compagnini, G. Patane, O. Ursini, G. Angelini, P. R. Ribic, G. Margaritondo, A. Cricenti, G. Palleschi, and F. Valentini, “Graphene nanoribbons produced by the oxidative unzipping of single-wall carbon nanotubes,” Carbon 48, 2596–2602 (2010).
[CrossRef]

Chem. Phys. Lett. (1)

J. Campos-Delgado, Y. A. Kim, T. Hayashi, A. Morelos-Gomez, M. Hofmann, H. Muramatsu, M. Endo, H. Terrones, R. D. Shull, M. S. Dresselhaus, and M. Terrones, “Thermal stability studies of cvd-grown graphene nanoribbons: Defect annealing and loop formation,” Chem. Phys. Lett. 469, 177–182 (2009).
[CrossRef]

Eur. Phys. J. B (1)

Y. O. Klymenko and O. Shevtsov, “Low-energy electron transport in semimetal graphene ribbon junctions,” Eur. Phys. J. B 72, 203–209 (2009).
[CrossRef]

Europhys. News (1)

N. M. R. Peres, “Graphene, new physics in two dimensions,” Europhys. News 40, 17–20 (2009).
[CrossRef]

J. Mater. Chem. (1)

S. Dutta and S. K. Pati, “Novel properties of graphene nanoribbons: a review,” J. Mater. Chem. 20, 8207–8223 (2010).
[CrossRef]

J. Phys. Soc. Jpn. (2)

M. F. Lin and F. L. Shyu, “Optical properties of nanographite ribbons,” J. Phys. Soc. Jpn. 69, 3529–3532 (2000).
[CrossRef]

H. C. Chung, M. H. Lee, C. P. Chang, Y. C. Huang, and M. F. Lin, “Effects of transverse electric fields on quasi-landau levels in zigzag graphene nanoribbons,” J. Phys. Soc. Jpn. 80, 044602 (2011).
[CrossRef]

J. Phys.: Conf. Ser. (1)

T. Nomura, D. Yamamoto, and S. Kurihara, “Electric field effects in zigzag edged graphene nanoribbons,” J. Phys.: Conf. Ser. 200, 062015 (2010).
[CrossRef]

Mater. Today (1)

M. I. Katsnelson, “Graphene: carbon in two dimensions,” Mater. Today 10, 20–27 (2007).
[CrossRef]

Nano Lett. (3)

M. C. Paiva, W. Xu, M. F. Proenca, R. M. Novais, E. Laegsgaard, and F. Besenbacher, “Unzipping of functionalized multiwall carbon nanotubes induced by stm,” Nano Lett. 10, 1764–1768 (2010).
[CrossRef] [PubMed]

A. G. Cano-Marquez, F. J. Rodriguez-Macias, J. Campos-Delgado, C. G. Espinosa-Gonzalez, F. Tristan-Lopez, D. Ramirez-Gonzalez, D. A. Cullen, D. J. Smith, M. Terrones, and Y. I. Vega-Cantu, “Ex-mwnts: Graphene sheets and ribbons produced by lithium intercalation and exfoliation of carbon nanotubes,” Nano Lett. 9, 1527–1533 (2009).
[CrossRef] [PubMed]

J. W. Bai, X. F. Duan, and Y. Huang, “Rational fabrication of graphene nanoribbons using a nanowire etch mask,” Nano Lett. 9, 2083–2087 (2009).
[CrossRef] [PubMed]

Nat. Mater. (2)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6, 183–191 (2007).
[CrossRef] [PubMed]

F. Schedin, A. K. Geim, S. V. Morozov, E. W. Hill, P. Blake, M. I. Katsnelson, and K. S. Novoselov, “Detection of individual gas molecules adsorbed on graphene,” Nat. Mater. 6, 652–655 (2007).
[CrossRef] [PubMed]

Nat. Nanotechnol. (2)

L. Tapaszto, G. Dobrik, P. Lambin, and L. P. Biro, “Tailoring the atomic structure of graphene nanoribbons by scanning tunnelling microscope lithography,” Nat. Nanotechnol. 3, 397–401 (2008).
[CrossRef] [PubMed]

J. W. Bai, R. Cheng, F. X. Xiu, L. Liao, M. S. Wang, A. Shailos, K. L. Wang, Y. Huang, and X. F. Duan, “Very large magnetoresistance in graphene nanoribbons,” Nat. Nanotechnol. 5, 655–659 (2010).
[CrossRef] [PubMed]

Nature (3)

D. V. Kosynkin, A. L. Higginbotham, A. Sinitskii, J. R. Lomeda, A. Dimiev, B. K. Price, and J. M. Tour, “Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons,” Nature 458, 872–876 (2009).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, “Two-dimensional gas of massless dirac fermions in graphene,” Nature 438, 197–200 (2005).
[CrossRef] [PubMed]

Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum hall effect and berry’s phase in graphene,” Nature 438, 201–204 (2005).
[CrossRef] [PubMed]

New. J. Phys. (2)

A. Cresti and S. Roche, “Range and correlation effects in edge disordered graphene nanoribbons,” New. J. Phys. 11, 095004 (2009).
[CrossRef]

C. W. Chiu, S. H. Lee, S. C. Chen, F. L. Shyu, and M. F. Lin, “Absorption spectra of aa-stacked graphite,” New. J. Phys. 12, 083060 (2010).
[CrossRef]

Phys. Rep. (1)

E. B. Barros, A. Jorio, G. G. Samsonidze, R. B. Capaz, A. G. Souza, J. Mendes, G. Dresselhaus, and M. S. Dresselhaus, “Review on the symmetry-related properties of carbon nanotubes,” Phys. Rep. 431, 261–302 (2006).
[CrossRef]

Phys. Rev. (2)

L. Van Hove, “The occurrence of singularities in the elastic frequency distribution of a crystal,” Phys. Rev. 89, 1189 (1953).
[CrossRef]

G. Dresselhaus and M. S. Dresselhaus, “Fourier expansion for electronic energy bands in silicon and germanium,” Phys. Rev. 160, 649–679 (1967).
[CrossRef]

Phys. Rev. B (8)

L. G. Johnson and G. Dresselhaus, “Optical properies of graphite,” Phys. Rev. B 7, 2275–2285 (1973).
[CrossRef]

N. V. Smith, “Photoemission spectra and band structures of d-band metals .7. extensions of the combined interpolation scheme,” Phys. Rev. B 19, 5019–5027 (1979).
[CrossRef]

L. C. Lew Yan Voon and L. R. Ram-Mohan, “Tight-binding representation of the optical matrix-elements - theory and applications,” Phys. Rev. B 47, 15500–15508 (1993).
[CrossRef]

J. C. Charlier, X. Gonze, and J. P. Michenaud, “First-principles study of the electronic properties of graphite,” Phys. Rev. B 43, 4579–4589 (1991).
[CrossRef]

H. Hsu and L. E. Reichl, “Selection rule for the optical absorption of graphene nanoribbons,” Phys. Rev. B 76, 045418 (2007).
[CrossRef]

E. Perfetto, G. Stefanucci, and M. Cini, “Time-dependent transport in graphene nanoribbons,” Phys. Rev. B 82, 035446 (2010).
[CrossRef]

V. L. J. Joly, M. Kiguchi, S. J. Hao, K. Takai, T. Enoki, R. Sumii, K. Amemiya, H. Muramatsu, T. Hayashi, Y. A. Kim, M. Endo, J. Campos-Delgado, F. Lopez-Urias, A. Botello-Mendez, H. Terrones, M. Terrones, and M. S. Dresselhaus, “Observation of magnetic edge state in graphene nanoribbons,” Phys. Rev. B 81, 245428 (2010).
[CrossRef]

S. Cho and M. S. Fuhrer, “Charge transport and inhomogeneity near the minimum conductivity point in graphene,” Phys. Rev. B 77, 081402 (2008).
[CrossRef]

Phys. Rev. Lett. (3)

M. Y. Han, B. Ozyilmaz, Y. B. Zhang, and P. Kim, “Energy band-gap engineering of graphene nanoribbons,” Phys. Rev. Lett. 98, 206805 (2007).
[CrossRef] [PubMed]

S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, “Giant intrinsic carrier mobilities in graphene and its bilayer,” Phys. Rev. Lett. 100, 016602 (2008).
[CrossRef] [PubMed]

J. Jiang, W. Lu, and J. Bernholc, “Edge states and optical transition energies in carbon nanoribbons,” Phys. Rev. Lett. 101, 246803 (2008).
[CrossRef] [PubMed]

Phys. Status Solidi B-Basic Solid State Phys. (1)

A. Fasoli, A. Colli, A. Lombardo, and A. C. Ferrari, “Fabrication of graphene nanoribbons via nanowire lithography,” Phys. Status Solidi B-Basic Solid State Phys. 246, 2514–2517 (2009).
[CrossRef]

Phys. Usp. (1)

S. V. Morozov, K. S. Novoselov, and A. K. Geim, “Electron transport in graphene,” Phys. Usp. 51, 744–748 (2008).
[CrossRef]

Physica E (1)

H. C. Chung, Y. C. Huang, M. H. Lee, C. C. Chang, and M. F. Lin, “Quasi-landau levels in bilayer zigzag graphene nanoribbons,” Physica E 42, 711–714 (2010).
[CrossRef]

Proc. Natl. Acad. Sci. U. S. A. (1)

K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, “Two-dimensional atomic crystals,” Proc. Natl. Acad. Sci. U. S. A. 102, 10451–10453 (2005).
[CrossRef] [PubMed]

Science (4)

R. F. Service, “Materials science carbon sheets an atom thick give rise to graphene dreams,” Science 324, 875–877 (2009).
[CrossRef] [PubMed]

A. K. Geim, “Graphene: Status and prospects,” Science 324, 1530–1534 (2009).
[CrossRef] [PubMed]

C. Berger, Z. M. Song, X. B. Li, X. S. Wu, N. Brown, C. Naud, D. Mayou, T. B. Li, J. Hass, A. N. Marchenkov, E. H. Conrad, P. N. First, and W. A. de Heer, “Electronic confinement and coherence in patterned epitaxial graphene,” Science 312, 1191–1196 (2006).
[CrossRef] [PubMed]

K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, “Electric field effect in atomically thin carbon films,” Science 306, 666–669 (2004).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1
Fig. 1

Energy dispersions and geometric structures for Ny = 69 AGNR and ZGNR. The conduction (valence) subbands of the corresponding indices Jc (Jv) are depicted in red (blue) color. The dashed-line rectangles represent primitive unit cells. The numbers of the mth dimer line are on the right side of the hexagonal lattice. The notations in the rectangles denote the A and B atoms on the mth dimer line.

Fig. 2
Fig. 2

Wavefunctions of subband index Jc = 1–3 (red dots) and Jv = 1 and 2 (blue dots) at kx = 0 for Ny = 69 AGNR.

Fig. 3
Fig. 3

Wavefunctions of subband index Jc = 1–3 (red dots) and Jv = 1 and 2 (blue dots) at kx = 2π/3 for Ny = 69 ZGNR.

Fig. 4
Fig. 4

Absorption spectra for the Ny = 69 AGNR and ZGNR.

Fig. 5
Fig. 5

The first five consecutive transition energies with respect to the ribbon width Ny for AGNR and ZGNR. The notations •, ○ and ▪ correspond to AGNRs of Ny = 3m, 3m + 1, and 3m + 2, respectively.

Equations (21)

Equations on this page are rendered with MathJax. Learn more.

| Ψ = l = 1 2 N y C l | ϕ l or | Ψ = m = 1 N y A m | a m + m = 1 N y B m | b m ,
H l , l = { γ 0 exp [ i k x ( b ) ] , if l = l + 1 , l is odd , γ 0 exp [ i k x ( b / 2 ) ] , if l = l + 1 , l is even , γ 0 exp [ i k x ( b / 2 ) ] , if l = l + 3 , l is odd , 0 , otherwise .
H l , l = { 2 γ 0 cos ( k x a / 2 ) , if l = l + 1 , l is odd , γ 0 , if l = l + 1 , l is even , 0 , otherwise ,
| Ψ h = m = 1 , 2 , 3 , ... [ A 3 m h | a 3 m + A 3 m + 1 h | a 3 m + 1 + A 3 m + 2 h | a 3 m + 2 + B 3 m h | b 3 m + B 3 m + 1 h | b 3 m + 1 + B 3 m + 2 h | b 3 m + 2 ] ,
A m h ( J h ) = ± B m h ( J h ) .
A m c ( J ) = ± A m v ( J ) .
| Ψ h = odd [ A o h | a o + B o h | b o ] + even [ A e h | a e + B e h | b e ] ,
A m c ( J c ) = ( 1 ) J c + 1 B N y + 1 m c ( J c ) , A m v ( J v ) = ( 1 ) J v B N y + 1 m v ( J v ) ,
A m c ( J c ) = ( 1 ) J c B N y + 1 m c ( J c ) , A m v ( J v ) = ( 1 ) J v + 1 B N y + 1 m v ( J v ) ,
A ( ω ) J h , J h 1 stB . Z . d k x 2 π | Ψ h ( k x , J h ) | e ^ p m e | Ψ h ( k x , J h ) | 2 × Im { f [ E h ( k x , J h ) ] f [ E h ( k x , J h ) ] E h ( k x , J h ) E h ( k x , J h ) ω i Γ } ,
M h h ( k x ) Ψ h ( k x , J h ) | e ^ p m e | Ψ h ( k x , J h ) .
p ( k ) = m e h ¯ k H ( k ) .
M h h ( k x ) = 1 h ¯ l , l = 1 2 N y C l h * ( k x ) C l h ( k x ) H l , l ( k x ) k x ,
b γ 0 m = 1 N y [ s A m c * ( J c ) A m v ( J v ) + t A m c * ( J c ) A m v ( J v ) ] + b γ 0 2 m = 1 N y 1 [ t A m c * ( J c ) A m + 1 v ( J v ) + s A m c * ( J c ) A m + 1 v ( J v ) ] + b γ 0 2 m = 2 N y [ t A m c * ( J c ) A m 1 v ( J v ) + s A m c * ( J c ) A m 1 v ( J v ) ] .
{ A 2 = Δ ± A 1 , A m 1 + A m + 1 = Δ ± A m , if m = 2 , 3 , 4 , , N y 1 , A N y 1 = Δ ± A N y ,
b γ 0 m = 1 N y [ s A m c * ( J c ) A m v ( J v ) + t A m c * ( J c ) A m v ( J v ) Δ s 2 t A m c * ( J c ) A m v ( J v ) + Δ s 2 s A m c * ( J c ) A m v ( J v ) ] = ( t s ) ( 1 Δ s 2 ) b γ 0 m = 1 N y A m c * ( J c ) A m v ( J v ) ,
M v c ( k x = 0 ) = u ( t s ) ( 1 Δ s 2 ) b γ 0 1 2 δ J c , J v = ± ( 1 Δ ± 2 ) b γ 0 δ J c , J v ,
h m = 1 N y [ A m c * ( J c ) B m v ( J v ) + B m c * ( J c ) A m v ( J v ) ] ,
h m = 1 N y [ A m c * ( J c ) B m v ( J v ) + ( 1 ) J c + 1 A N y + 1 m c * ( J c ) ( 1 ) J v B N y + 1 m v ( J v ) ] .
[ 1 + ( 1 ) J c + J v + 1 ] h m = 1 N y A m c * ( J c ) B m v ( J v ) .
M v c ( k x = 2 π 3 ) = { 2 h m = 1 N y A m c * ( J c ) B m v ( J v ) , if Δ J = odd , 0 , if Δ J = even ,

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