Abstract

We investigate theoretically the size-dependence of two-photon absorption (TPA) for circular graphene quantum dots (GQDs) on the basis of electronic energy states obtained by solving the Dirac-Weyl equation analytically under infinite-mass boundary condition. The analytical expressions for TPA coefficient are derived with an arbitrary size-distribution and the transition selection rules are obtained. Results reveal that the intraband transitions in conduction band and valence band contribute much more to TPA than interband transitions. The energy spectrum and TPA peaks are tuned by the size of GQDs.

© 2016 Optical Society of America

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  1. Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
    [Crossref] [PubMed]
  2. A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
    [Crossref] [PubMed]
  3. A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
    [Crossref] [PubMed]
  4. 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(5696), 666–669 (2004).
    [Crossref] [PubMed]
  5. 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(7065), 197–200 (2005).
    [Crossref] [PubMed]
  6. H. Hiura, “Tailoring graphite layers by scanning tunneling microscopy,” Appl. Surf. Sci. 222(1–4), 374–381 (2004).
    [Crossref]
  7. L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
    [Crossref] [PubMed]
  8. Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
    [Crossref] [PubMed]
  9. H. Sun, L. Wu, W. Wei, and X. Qu, “Recent advances in graphene quantum dots for sensing,” Mater. Today 16(11), 433–442 (2013).
    [Crossref]
  10. G. S. He, K. T. Yong, Q. Zheng, Y. Sahoo, A. Baev, A. I. Ryasnyanskiy, and P. N. Prasad, “Multi-photon excitation properties of CdSe quantum dots solutions and optical limiting behavior in infrared range,” Opt. Express 15(20), 12818–12833 (2007).
    [Crossref] [PubMed]
  11. M. Zarenia, A. Chaves, G. A. Farias, and F. M. Peeters, “Energy levels of triangular and hexagonal graphene quantum dots: a comparative study between the tight-binding and the Dirac equation approach,” Phys. Rev. B Condens. Matter 84(24), 245403 (2011).
    [Crossref]
  12. S. Schnez, K. Ensslin, M. Sigrist, and T. Ihn, “Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field,” Phys. Rev. B Condens. Matter 78(19), 195427 (2008).
    [Crossref]
  13. D. R. da Costa, A. Chaves, M. Zarenia, J. M. Pereira, G. A. Farias, and F. M. Peeters, “Geometry and edge effects on the energy levels of graphene quantum rings: a comparison between tight-binding and simplified Dirac models,” Phys. Rev. B Condens. Matter 89(7), 075418 (2014).
    [Crossref]
  14. J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
    [Crossref] [PubMed]
  15. R. P. Choudhary, S. Shukla, K. Vaibhav, P. B. Pawar, and S. Saxena, “Optical properties of few layered graphene quantum dots,” Mater. Res. Express 2(9), 095024 (2015).
    [Crossref]
  16. M. Grujić, M. Zarenia, M. Tadić, and F. M. Peeters, “Interband optical absorption in a circular graphene quantum dot,” Phys. Scr. T149, 014056 (2012).
    [Crossref]
  17. H. D. Ha, M. H. Jang, F. Liu, Y. H. Cho, and T. S. Seo, “Upconversion photoluminescent metal ion sensors via two photon absorption in graphene oxide quantum dots,” Carbon 81(1), 367–375 (2015).
    [Crossref]
  18. M. Grujić and M. Tadić, “Electronic states and optical transitions in a graphene quantum dot in a normal magnetic field,” Serbian J. Electrical Eng. 8(1), 53–62 (2011).
    [Crossref]
  19. D. S. L. Abergel, V. M. Apalkov, and T. Chakraborty, “Interplay between valley polarization and electron-electron interaction in a graphene ring,” Phys. Rev. B Condens. Matter 78(19), 193405 (2008).
    [Crossref]
  20. P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley-degeneracy in graphene rings,” Phys. Rev. B Condens. Matter 76(23), 235404 (2007).
    [Crossref]
  21. X. Feng and W. Ji, “Shape-dependent two-photon absorption in semiconductor nanocrystals,” Opt. Express 17(15), 13140–13150 (2009).
    [Crossref] [PubMed]
  22. W. Y. Wu, J. N. Schulman, T. Y. Hsu, and U. Efron, “Effect of size nonuniformity on the absorption spectrum of a semiconductor quantum dot system,” Appl. Phys. Lett. 51(10), 710–712 (1987).
    [Crossref]

2015 (2)

H. D. Ha, M. H. Jang, F. Liu, Y. H. Cho, and T. S. Seo, “Upconversion photoluminescent metal ion sensors via two photon absorption in graphene oxide quantum dots,” Carbon 81(1), 367–375 (2015).
[Crossref]

R. P. Choudhary, S. Shukla, K. Vaibhav, P. B. Pawar, and S. Saxena, “Optical properties of few layered graphene quantum dots,” Mater. Res. Express 2(9), 095024 (2015).
[Crossref]

2014 (1)

D. R. da Costa, A. Chaves, M. Zarenia, J. M. Pereira, G. A. Farias, and F. M. Peeters, “Geometry and edge effects on the energy levels of graphene quantum rings: a comparison between tight-binding and simplified Dirac models,” Phys. Rev. B Condens. Matter 89(7), 075418 (2014).
[Crossref]

2013 (2)

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[Crossref] [PubMed]

H. Sun, L. Wu, W. Wei, and X. Qu, “Recent advances in graphene quantum dots for sensing,” Mater. Today 16(11), 433–442 (2013).
[Crossref]

2012 (3)

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

M. Grujić, M. Zarenia, M. Tadić, and F. M. Peeters, “Interband optical absorption in a circular graphene quantum dot,” Phys. Scr. T149, 014056 (2012).
[Crossref]

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

2011 (2)

M. Zarenia, A. Chaves, G. A. Farias, and F. M. Peeters, “Energy levels of triangular and hexagonal graphene quantum dots: a comparative study between the tight-binding and the Dirac equation approach,” Phys. Rev. B Condens. Matter 84(24), 245403 (2011).
[Crossref]

M. Grujić and M. Tadić, “Electronic states and optical transitions in a graphene quantum dot in a normal magnetic field,” Serbian J. Electrical Eng. 8(1), 53–62 (2011).
[Crossref]

2010 (1)

Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
[Crossref] [PubMed]

2009 (2)

2008 (2)

D. S. L. Abergel, V. M. Apalkov, and T. Chakraborty, “Interplay between valley polarization and electron-electron interaction in a graphene ring,” Phys. Rev. B Condens. Matter 78(19), 193405 (2008).
[Crossref]

S. Schnez, K. Ensslin, M. Sigrist, and T. Ihn, “Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field,” Phys. Rev. B Condens. Matter 78(19), 195427 (2008).
[Crossref]

2007 (3)

P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley-degeneracy in graphene rings,” Phys. Rev. B Condens. Matter 76(23), 235404 (2007).
[Crossref]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

G. S. He, K. T. Yong, Q. Zheng, Y. Sahoo, A. Baev, A. I. Ryasnyanskiy, and P. N. Prasad, “Multi-photon excitation properties of CdSe quantum dots solutions and optical limiting behavior in infrared range,” Opt. Express 15(20), 12818–12833 (2007).
[Crossref] [PubMed]

2005 (1)

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(7065), 197–200 (2005).
[Crossref] [PubMed]

2004 (2)

H. Hiura, “Tailoring graphite layers by scanning tunneling microscopy,” Appl. Surf. Sci. 222(1–4), 374–381 (2004).
[Crossref]

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(5696), 666–669 (2004).
[Crossref] [PubMed]

1987 (1)

W. Y. Wu, J. N. Schulman, T. Y. Hsu, and U. Efron, “Effect of size nonuniformity on the absorption spectrum of a semiconductor quantum dot system,” Appl. Phys. Lett. 51(10), 710–712 (1987).
[Crossref]

Abergel, D. S. L.

D. S. L. Abergel, V. M. Apalkov, and T. Chakraborty, “Interplay between valley polarization and electron-electron interaction in a graphene ring,” Phys. Rev. B Condens. Matter 78(19), 193405 (2008).
[Crossref]

Ajayan, P. M.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Alemany, L. B.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Apalkov, V. M.

D. S. L. Abergel, V. M. Apalkov, and T. Chakraborty, “Interplay between valley polarization and electron-electron interaction in a graphene ring,” Phys. Rev. B Condens. Matter 78(19), 193405 (2008).
[Crossref]

Baev, A.

Beenakker, C. W. J.

P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley-degeneracy in graphene rings,” Phys. Rev. B Condens. Matter 76(23), 235404 (2007).
[Crossref]

Blanter, Y. M.

P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley-degeneracy in graphene rings,” Phys. Rev. B Condens. Matter 76(23), 235404 (2007).
[Crossref]

Cai, W.

Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
[Crossref] [PubMed]

Cao, X.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Chakraborty, T.

D. S. L. Abergel, V. M. Apalkov, and T. Chakraborty, “Interplay between valley polarization and electron-electron interaction in a graphene ring,” Phys. Rev. B Condens. Matter 78(19), 193405 (2008).
[Crossref]

Chaves, A.

D. R. da Costa, A. Chaves, M. Zarenia, J. M. Pereira, G. A. Farias, and F. M. Peeters, “Geometry and edge effects on the energy levels of graphene quantum rings: a comparison between tight-binding and simplified Dirac models,” Phys. Rev. B Condens. Matter 89(7), 075418 (2014).
[Crossref]

M. Zarenia, A. Chaves, G. A. Farias, and F. M. Peeters, “Energy levels of triangular and hexagonal graphene quantum dots: a comparative study between the tight-binding and the Dirac equation approach,” Phys. Rev. B Condens. Matter 84(24), 245403 (2011).
[Crossref]

Cho, Y. H.

H. D. Ha, M. H. Jang, F. Liu, Y. H. Cho, and T. S. Seo, “Upconversion photoluminescent metal ion sensors via two photon absorption in graphene oxide quantum dots,” Carbon 81(1), 367–375 (2015).
[Crossref]

Choudhary, R. P.

R. P. Choudhary, S. Shukla, K. Vaibhav, P. B. Pawar, and S. Saxena, “Optical properties of few layered graphene quantum dots,” Mater. Res. Express 2(9), 095024 (2015).
[Crossref]

da Costa, D. R.

D. R. da Costa, A. Chaves, M. Zarenia, J. M. Pereira, G. A. Farias, and F. M. Peeters, “Geometry and edge effects on the energy levels of graphene quantum rings: a comparison between tight-binding and simplified Dirac models,” Phys. Rev. B Condens. Matter 89(7), 075418 (2014).
[Crossref]

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(7065), 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(5696), 666–669 (2004).
[Crossref] [PubMed]

Efron, U.

W. Y. Wu, J. N. Schulman, T. Y. Hsu, and U. Efron, “Effect of size nonuniformity on the absorption spectrum of a semiconductor quantum dot system,” Appl. Phys. Lett. 51(10), 710–712 (1987).
[Crossref]

Ensslin, K.

S. Schnez, K. Ensslin, M. Sigrist, and T. Ihn, “Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field,” Phys. Rev. B Condens. Matter 78(19), 195427 (2008).
[Crossref]

Farias, G. A.

D. R. da Costa, A. Chaves, M. Zarenia, J. M. Pereira, G. A. Farias, and F. M. Peeters, “Geometry and edge effects on the energy levels of graphene quantum rings: a comparison between tight-binding and simplified Dirac models,” Phys. Rev. B Condens. Matter 89(7), 075418 (2014).
[Crossref]

M. Zarenia, A. Chaves, G. A. Farias, and F. M. Peeters, “Energy levels of triangular and hexagonal graphene quantum dots: a comparative study between the tight-binding and the Dirac equation approach,” Phys. Rev. B Condens. Matter 84(24), 245403 (2011).
[Crossref]

Feng, X.

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(7065), 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(5696), 666–669 (2004).
[Crossref] [PubMed]

Gao, G.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Gao, W.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Ge, L.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Geim, A. K.

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (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(7065), 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(5696), 666–669 (2004).
[Crossref] [PubMed]

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(7065), 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(5696), 666–669 (2004).
[Crossref] [PubMed]

Grujic, M.

M. Grujić, M. Zarenia, M. Tadić, and F. M. Peeters, “Interband optical absorption in a circular graphene quantum dot,” Phys. Scr. T149, 014056 (2012).
[Crossref]

M. Grujić and M. Tadić, “Electronic states and optical transitions in a graphene quantum dot in a normal magnetic field,” Serbian J. Electrical Eng. 8(1), 53–62 (2011).
[Crossref]

Guo, S.

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[Crossref] [PubMed]

Gupta, B. K.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Ha, H. D.

H. D. Ha, M. H. Jang, F. Liu, Y. H. Cho, and T. S. Seo, “Upconversion photoluminescent metal ion sensors via two photon absorption in graphene oxide quantum dots,” Carbon 81(1), 367–375 (2015).
[Crossref]

Hao, J.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Hayashi, T.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

He, G. S.

Hiura, H.

H. Hiura, “Tailoring graphite layers by scanning tunneling microscopy,” Appl. Surf. Sci. 222(1–4), 374–381 (2004).
[Crossref]

Hsu, T. Y.

W. Y. Wu, J. N. Schulman, T. Y. Hsu, and U. Efron, “Effect of size nonuniformity on the absorption spectrum of a semiconductor quantum dot system,” Appl. Phys. Lett. 51(10), 710–712 (1987).
[Crossref]

Ihn, T.

S. Schnez, K. Ensslin, M. Sigrist, and T. Ihn, “Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field,” Phys. Rev. B Condens. Matter 78(19), 195427 (2008).
[Crossref]

Jang, M. H.

H. D. Ha, M. H. Jang, F. Liu, Y. H. Cho, and T. S. Seo, “Upconversion photoluminescent metal ion sensors via two photon absorption in graphene oxide quantum dots,” Carbon 81(1), 367–375 (2015).
[Crossref]

Ji, R.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Ji, W.

Jiang, D.

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(7065), 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(5696), 666–669 (2004).
[Crossref] [PubMed]

Jiang, H.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Kaipparettu, B. A.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Katsnelson, M. I.

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(7065), 197–200 (2005).
[Crossref] [PubMed]

Lau, S. P.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Li, X.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
[Crossref] [PubMed]

Lin, J.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Liu, F.

H. D. Ha, M. H. Jang, F. Liu, Y. H. Cho, and T. S. Seo, “Upconversion photoluminescent metal ion sensors via two photon absorption in graphene oxide quantum dots,” Carbon 81(1), 367–375 (2015).
[Crossref]

Liu, Z.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Luk, C. M.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Marti, A. A.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Morozov, 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(7065), 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(5696), 666–669 (2004).
[Crossref] [PubMed]

Morpurgo, A. F.

P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley-degeneracy in graphene rings,” Phys. Rev. B Condens. Matter 76(23), 235404 (2007).
[Crossref]

Murali, S.

Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
[Crossref] [PubMed]

Novoselov, K. S.

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (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(7065), 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(5696), 666–669 (2004).
[Crossref] [PubMed]

Pawar, P. B.

R. P. Choudhary, S. Shukla, K. Vaibhav, P. B. Pawar, and S. Saxena, “Optical properties of few layered graphene quantum dots,” Mater. Res. Express 2(9), 095024 (2015).
[Crossref]

Peeters, F. M.

D. R. da Costa, A. Chaves, M. Zarenia, J. M. Pereira, G. A. Farias, and F. M. Peeters, “Geometry and edge effects on the energy levels of graphene quantum rings: a comparison between tight-binding and simplified Dirac models,” Phys. Rev. B Condens. Matter 89(7), 075418 (2014).
[Crossref]

M. Grujić, M. Zarenia, M. Tadić, and F. M. Peeters, “Interband optical absorption in a circular graphene quantum dot,” Phys. Scr. T149, 014056 (2012).
[Crossref]

M. Zarenia, A. Chaves, G. A. Farias, and F. M. Peeters, “Energy levels of triangular and hexagonal graphene quantum dots: a comparative study between the tight-binding and the Dirac equation approach,” Phys. Rev. B Condens. Matter 84(24), 245403 (2011).
[Crossref]

Peng, J.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Pereira, J. M.

D. R. da Costa, A. Chaves, M. Zarenia, J. M. Pereira, G. A. Farias, and F. M. Peeters, “Geometry and edge effects on the energy levels of graphene quantum rings: a comparison between tight-binding and simplified Dirac models,” Phys. Rev. B Condens. Matter 89(7), 075418 (2014).
[Crossref]

Potts, J. R.

Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
[Crossref] [PubMed]

Prasad, P. N.

Qu, X.

H. Sun, L. Wu, W. Wei, and X. Qu, “Recent advances in graphene quantum dots for sensing,” Mater. Today 16(11), 433–442 (2013).
[Crossref]

Recher, P.

P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley-degeneracy in graphene rings,” Phys. Rev. B Condens. Matter 76(23), 235404 (2007).
[Crossref]

Romero-Aburto, R.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Ruoff, R. S.

Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
[Crossref] [PubMed]

Ryasnyanskiy, A. I.

Rycerz, A.

P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley-degeneracy in graphene rings,” Phys. Rev. B Condens. Matter 76(23), 235404 (2007).
[Crossref]

Sahoo, Y.

Saxena, S.

R. P. Choudhary, S. Shukla, K. Vaibhav, P. B. Pawar, and S. Saxena, “Optical properties of few layered graphene quantum dots,” Mater. Res. Express 2(9), 095024 (2015).
[Crossref]

Schnez, S.

S. Schnez, K. Ensslin, M. Sigrist, and T. Ihn, “Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field,” Phys. Rev. B Condens. Matter 78(19), 195427 (2008).
[Crossref]

Schulman, J. N.

W. Y. Wu, J. N. Schulman, T. Y. Hsu, and U. Efron, “Effect of size nonuniformity on the absorption spectrum of a semiconductor quantum dot system,” Appl. Phys. Lett. 51(10), 710–712 (1987).
[Crossref]

Seo, T. S.

H. D. Ha, M. H. Jang, F. Liu, Y. H. Cho, and T. S. Seo, “Upconversion photoluminescent metal ion sensors via two photon absorption in graphene oxide quantum dots,” Carbon 81(1), 367–375 (2015).
[Crossref]

Shukla, S.

R. P. Choudhary, S. Shukla, K. Vaibhav, P. B. Pawar, and S. Saxena, “Optical properties of few layered graphene quantum dots,” Mater. Res. Express 2(9), 095024 (2015).
[Crossref]

Sigrist, M.

S. Schnez, K. Ensslin, M. Sigrist, and T. Ihn, “Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field,” Phys. Rev. B Condens. Matter 78(19), 195427 (2008).
[Crossref]

Song, L.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Suk, J. W.

Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
[Crossref] [PubMed]

Sun, H.

H. Sun, L. Wu, W. Wei, and X. Qu, “Recent advances in graphene quantum dots for sensing,” Mater. Today 16(11), 433–442 (2013).
[Crossref]

Tadic, M.

M. Grujić, M. Zarenia, M. Tadić, and F. M. Peeters, “Interband optical absorption in a circular graphene quantum dot,” Phys. Scr. T149, 014056 (2012).
[Crossref]

M. Grujić and M. Tadić, “Electronic states and optical transitions in a graphene quantum dot in a normal magnetic field,” Serbian J. Electrical Eng. 8(1), 53–62 (2011).
[Crossref]

Tang, L.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Teng, K. S.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Trauzettel, B.

P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley-degeneracy in graphene rings,” Phys. Rev. B Condens. Matter 76(23), 235404 (2007).
[Crossref]

Vaibhav, K.

R. P. Choudhary, S. Shukla, K. Vaibhav, P. B. Pawar, and S. Saxena, “Optical properties of few layered graphene quantum dots,” Mater. Res. Express 2(9), 095024 (2015).
[Crossref]

Vithayathil, S. A.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Wei, W.

H. Sun, L. Wu, W. Wei, and X. Qu, “Recent advances in graphene quantum dots for sensing,” Mater. Today 16(11), 433–442 (2013).
[Crossref]

Wu, C.

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[Crossref] [PubMed]

Wu, H.

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[Crossref] [PubMed]

Wu, L.

H. Sun, L. Wu, W. Wei, and X. Qu, “Recent advances in graphene quantum dots for sensing,” Mater. Today 16(11), 433–442 (2013).
[Crossref]

Wu, W. Y.

W. Y. Wu, J. N. Schulman, T. Y. Hsu, and U. Efron, “Effect of size nonuniformity on the absorption spectrum of a semiconductor quantum dot system,” Appl. Phys. Lett. 51(10), 710–712 (1987).
[Crossref]

Wu, X.

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[Crossref] [PubMed]

Yang, Y.

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[Crossref] [PubMed]

Yong, K. T.

Zarenia, M.

D. R. da Costa, A. Chaves, M. Zarenia, J. M. Pereira, G. A. Farias, and F. M. Peeters, “Geometry and edge effects on the energy levels of graphene quantum rings: a comparison between tight-binding and simplified Dirac models,” Phys. Rev. B Condens. Matter 89(7), 075418 (2014).
[Crossref]

M. Grujić, M. Zarenia, M. Tadić, and F. M. Peeters, “Interband optical absorption in a circular graphene quantum dot,” Phys. Scr. T149, 014056 (2012).
[Crossref]

M. Zarenia, A. Chaves, G. A. Farias, and F. M. Peeters, “Energy levels of triangular and hexagonal graphene quantum dots: a comparative study between the tight-binding and the Dirac equation approach,” Phys. Rev. B Condens. Matter 84(24), 245403 (2011).
[Crossref]

Zeng, S.

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Zhan, X.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Zhang, J.

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[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(5696), 666–669 (2004).
[Crossref] [PubMed]

Zheng, Q.

Zhou, X.

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[Crossref] [PubMed]

Zhu, J. J.

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Zhu, Y.

Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
[Crossref] [PubMed]

ACS Nano (1)

L. Tang, R. Ji, X. Cao, J. Lin, H. Jiang, X. Li, K. S. Teng, C. M. Luk, S. Zeng, J. Hao, and S. P. Lau, “Deep ultraviolet photoluminescence of water-soluble self-passivated graphene quantum dots,” ACS Nano 6(6), 5102–5110 (2012).
[Crossref] [PubMed]

Adv. Mater. (1)

Y. Zhu, S. Murali, W. Cai, X. Li, J. W. Suk, J. R. Potts, and R. S. Ruoff, “Graphene and graphene oxide: synthesis, properties, and applications,” Adv. Mater. 22(35), 3906–3924 (2010).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

W. Y. Wu, J. N. Schulman, T. Y. Hsu, and U. Efron, “Effect of size nonuniformity on the absorption spectrum of a semiconductor quantum dot system,” Appl. Phys. Lett. 51(10), 710–712 (1987).
[Crossref]

Appl. Surf. Sci. (1)

H. Hiura, “Tailoring graphite layers by scanning tunneling microscopy,” Appl. Surf. Sci. 222(1–4), 374–381 (2004).
[Crossref]

Carbon (1)

H. D. Ha, M. H. Jang, F. Liu, Y. H. Cho, and T. S. Seo, “Upconversion photoluminescent metal ion sensors via two photon absorption in graphene oxide quantum dots,” Carbon 81(1), 367–375 (2015).
[Crossref]

Mater. Res. Express (1)

R. P. Choudhary, S. Shukla, K. Vaibhav, P. B. Pawar, and S. Saxena, “Optical properties of few layered graphene quantum dots,” Mater. Res. Express 2(9), 095024 (2015).
[Crossref]

Mater. Today (1)

H. Sun, L. Wu, W. Wei, and X. Qu, “Recent advances in graphene quantum dots for sensing,” Mater. Today 16(11), 433–442 (2013).
[Crossref]

Nano Lett. (1)

J. Peng, W. Gao, B. K. Gupta, Z. Liu, R. Romero-Aburto, L. Ge, L. Song, L. B. Alemany, X. Zhan, G. Gao, S. A. Vithayathil, B. A. Kaipparettu, A. A. Marti, T. Hayashi, J. J. Zhu, and P. M. Ajayan, “Graphene quantum dots derived from carbon fibers,” Nano Lett. 12(2), 844–849 (2012).
[Crossref] [PubMed]

Nanoscale (1)

Y. Zhang, C. Wu, X. Zhou, X. Wu, Y. Yang, H. Wu, S. Guo, and J. Zhang, “Graphene quantum dots/gold electrode and its application in living cell H2O2 detection,” Nanoscale 5(5), 1816–1819 (2013).
[Crossref] [PubMed]

Nat. Mater. (1)

A. K. Geim and K. S. Novoselov, “The rise of graphene,” Nat. Mater. 6(3), 183–191 (2007).
[Crossref] [PubMed]

Nature (1)

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(7065), 197–200 (2005).
[Crossref] [PubMed]

Opt. Express (2)

Phys. Rev. B Condens. Matter (5)

D. S. L. Abergel, V. M. Apalkov, and T. Chakraborty, “Interplay between valley polarization and electron-electron interaction in a graphene ring,” Phys. Rev. B Condens. Matter 78(19), 193405 (2008).
[Crossref]

P. Recher, B. Trauzettel, A. Rycerz, Y. M. Blanter, C. W. J. Beenakker, and A. F. Morpurgo, “Aharonov-Bohm effect and broken valley-degeneracy in graphene rings,” Phys. Rev. B Condens. Matter 76(23), 235404 (2007).
[Crossref]

M. Zarenia, A. Chaves, G. A. Farias, and F. M. Peeters, “Energy levels of triangular and hexagonal graphene quantum dots: a comparative study between the tight-binding and the Dirac equation approach,” Phys. Rev. B Condens. Matter 84(24), 245403 (2011).
[Crossref]

S. Schnez, K. Ensslin, M. Sigrist, and T. Ihn, “Analytic model of the energy spectrum of a graphene quantum dot in a perpendicular magnetic field,” Phys. Rev. B Condens. Matter 78(19), 195427 (2008).
[Crossref]

D. R. da Costa, A. Chaves, M. Zarenia, J. M. Pereira, G. A. Farias, and F. M. Peeters, “Geometry and edge effects on the energy levels of graphene quantum rings: a comparison between tight-binding and simplified Dirac models,” Phys. Rev. B Condens. Matter 89(7), 075418 (2014).
[Crossref]

Phys. Scr. (1)

M. Grujić, M. Zarenia, M. Tadić, and F. M. Peeters, “Interband optical absorption in a circular graphene quantum dot,” Phys. Scr. T149, 014056 (2012).
[Crossref]

Science (2)

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(5696), 666–669 (2004).
[Crossref] [PubMed]

A. K. Geim, “Graphene: status and prospects,” Science 324(5934), 1530–1534 (2009).
[Crossref] [PubMed]

Serbian J. Electrical Eng. (1)

M. Grujić and M. Tadić, “Electronic states and optical transitions in a graphene quantum dot in a normal magnetic field,” Serbian J. Electrical Eng. 8(1), 53–62 (2011).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1 Two-dimensional illustration of a circular GQD with radius R.
Fig. 2
Fig. 2 Energy levels of a circular GQD as a function of angular momentum label m for R = 2 nm in K valley.
Fig. 3
Fig. 3 Energy levels of a circular GQD as a function of the dot radius with m = 0.
Fig. 4
Fig. 4 TPA coefficient of circular GQDs with average size R = 2 nm and corresponding form function F(R) plotted as a function of incident photon energy for (a-b) intraband transitions and (c-d) interband transitions.
Fig. 5
Fig. 5 TPA spectra of circular GQDs with three different radii for (a) interband transitions, (b) intra conduction band transitions, and (c) intra valence band transitions.

Equations (11)

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

H= v F pσ+τV(r) σ z ,
Ψ(r,θ)= e imθ ( χ 1 (r) χ 2 (r) e iθ ).
r 2 2 r 2 χ 1 (r)+r 2 r 2 χ 1 (r)+( ε 2 r 2 m 2 ) χ 1 (r)=0,
χ 1 (r)= D m J m (εr).
χ 2 (r)=i D m J m+1 (εr),
D m =1/ π R 2 [ ( J m+1 ( x m n )) 2 + ( J m+2 ( x m n )) 2 ] =1/ π R 2 C m
W (2) = 2π i,f | M f,i | 2 δ( E f E i 2ω), M f,i = v H f,v int H v,i int E v E i ωiγ ,
H v,i int = m 1 , n 1 |(e v F /c)Aσ| m 0 , n 0 =i C m 0 C m 1 (eA v F /c){ e [ J m 1 +1 ( x m 1 n 1 )] 2 δ m 1 , m 0 +1 δ n 1 , n 0 e + [ J m 0 +1 ( x m 0 n 0 )] 2 δ m 1 , m 0 1 δ n 1 , n 0 },
W (2) = 2π m 0 , m 1 m 2 ,n 2 (eA v F /c) 4 F(R) , F(R)= B 2 T(R)δ( E m 2 ,n E m 0 ,n 2ω), B= C m 0 C m 1 2 C m 2 ( [ J m 1 +1 ( x m 1 n )] 2 [ J m 2 +1 ( x m 2 n )] 2 δ m 2 , m 1 +1 δ m 1 , m 0 +1 + [ J m 1 +1 ( x m 1 n )] 2 [ J m 0 +1 ( x m 0 n )] 2 δ m 2 , m 1 1 δ m 1 , m 0 1 ), T(R)= | 1 E m 1 ,n e E m 0 ,n h ωiγ + 1 E m 1 ,n h E m 0 ,n h ωiγ | 2 .
β=4ω N I 2 W ¯ (2) f(R)dR ,
β= 2πN ε ω ω 4 ε 0 2 c 2 (e v F ) 4 m 0 , m 1 m 2 ,n B 2 T()f().

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