OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 23 — Nov. 7, 2011
  • pp: 23350–23363

Exploration of edge-dependent optical selection rules for graphene nanoribbons

H. C. Chung, M. H. Lee, C. P. Chang, and M. F. Lin  »View Author Affiliations

Optics Express, Vol. 19, Issue 23, pp. 23350-23363 (2011)

View Full Text Article

Enhanced HTML    Acrobat PDF (1172 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(160.4760) Materials : Optical properties
(300.1030) Spectroscopy : Absorption
(300.6170) Spectroscopy : Spectra
(310.6860) Thin films : Thin films, optical properties

ToC Category:

Original Manuscript: August 22, 2011
Revised Manuscript: October 8, 2011
Manuscript Accepted: October 8, 2011
Published: November 1, 2011

H. C. Chung, M. H. Lee, C. P. Chang, and M. F. Lin, "Exploration of edge-dependent optical selection rules for graphene nanoribbons," Opt. Express 19, 23350-23363 (2011)

Sort:  Author  |  Year  |  Journal  |  Reset  


  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]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4 Fig. 5

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited