Abstract

A uniform Fermi level profile is typically assumed in the analysis of a gated graphene nanoribbon, whose Fermi level is actually nonuniform in the experimental measurements. Here, we show that the uniform Fermi level has to be downshifted when it is used to analyze a backgated graphene nanoribbon array (GNRA). The plasmonic extinction behaviors of the GNRAs are perfectly preserved by assuming properly scaled uniform Fermi levels. The scaling factor is independent of the average value of the actual Fermi level profile, but it is a function of the ratio of the nanoribbon width to the distance of the nanoribbons from the backgate. This study facilitates the data postprocessing in the experiments, and may be helpful for analyzing the electron behaviors in GNRAs.

© 2014 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. J. G. de Abajo, Science 339, 917 (2013).
    [CrossRef]
  2. F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, Nano Lett. 11, 3370 (2011).
  3. M. Jablan, H. Buljan, and M. Soljacic, Phys. Rev. B 80, 245435 (2009).
  4. J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, ACS Nano 6, 431 (2012).
    [CrossRef]
  5. J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).
  6. H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
    [CrossRef]
  7. L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
    [CrossRef]
  8. V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, Nano Lett. 13, 2541 (2013).
  9. A. Vakil and N. Engheta, Science 332, 1291 (2011).
    [CrossRef]
  10. P.-Y. Chen and A. Alu, ACS Nano 5, 5855 (2011).
    [CrossRef]
  11. W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).
  12. V. V. Popov, T. Y. Bagaeva, T. Otsuji, and V. Ryzhii, Phys. Rev. B 81, 073404 (2010).
  13. S. He, X. Zhang, and Y. He, Opt. Express 21, 30664 (2013).
    [CrossRef]
  14. X. Shi, D. Han, Y. Dai, Z. Yu, Y. Sun, H. Chen, X. Liu, and J. Zi, Opt. Express 21, 28438 (2013).
    [CrossRef]
  15. J. T. Kim, Y.-J. Yu, H. Choi, and C.-G. Choi, Opt. Express 22, 803 (2014).
    [CrossRef]
  16. J. Tao, X. Yu, B. Hu, A. Dubrovkin, and Q. J. Wang, Opt. Lett. 39, 271 (2014).
    [CrossRef]
  17. P. G. Silvestrov and K. B. Efetov, Phys. Rev. B 77, 155436 (2008).
  18. F. T. Vasko and I. V. Zozoulenko, Appl. Phys. Lett. 97, 092115 (2010).
    [CrossRef]
  19. S. Thongrattanasiri, I. Silveiro, and F. J. G. de Abajo, Appl. Phys. Lett. 100, 201105 (2012).
    [CrossRef]
  20. V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, J. Phys. Condens. Matter 19, 026222 (2007).
    [CrossRef]
  21. X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, Science 319, 1229 (2008).
    [CrossRef]

2014 (2)

2013 (7)

X. Shi, D. Han, Y. Dai, Z. Yu, Y. Sun, H. Chen, X. Liu, and J. Zi, Opt. Express 21, 28438 (2013).
[CrossRef]

S. He, X. Zhang, and Y. He, Opt. Express 21, 30664 (2013).
[CrossRef]

F. J. G. de Abajo, Science 339, 917 (2013).
[CrossRef]

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, Nano Lett. 13, 2541 (2013).

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

2012 (2)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

S. Thongrattanasiri, I. Silveiro, and F. J. G. de Abajo, Appl. Phys. Lett. 100, 201105 (2012).
[CrossRef]

2011 (4)

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

P.-Y. Chen and A. Alu, ACS Nano 5, 5855 (2011).
[CrossRef]

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, Nano Lett. 11, 3370 (2011).

2010 (2)

V. V. Popov, T. Y. Bagaeva, T. Otsuji, and V. Ryzhii, Phys. Rev. B 81, 073404 (2010).

F. T. Vasko and I. V. Zozoulenko, Appl. Phys. Lett. 97, 092115 (2010).
[CrossRef]

2009 (1)

M. Jablan, H. Buljan, and M. Soljacic, Phys. Rev. B 80, 245435 (2009).

2008 (2)

P. G. Silvestrov and K. B. Efetov, Phys. Rev. B 77, 155436 (2008).

X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, Science 319, 1229 (2008).
[CrossRef]

2007 (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, J. Phys. Condens. Matter 19, 026222 (2007).
[CrossRef]

Ajayan, P. M.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

Alu, A.

P.-Y. Chen and A. Alu, ACS Nano 5, 5855 (2011).
[CrossRef]

Atwater, H. A.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, Nano Lett. 13, 2541 (2013).

Avouris, P.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

Bagaeva, T. Y.

V. V. Popov, T. Y. Bagaeva, T. Otsuji, and V. Ryzhii, Phys. Rev. B 81, 073404 (2010).

Bechtel, H. A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Brar, V. W.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, Nano Lett. 13, 2541 (2013).

Buljan, H.

M. Jablan, H. Buljan, and M. Soljacic, Phys. Rev. B 80, 245435 (2009).

Carbotte, J. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, J. Phys. Condens. Matter 19, 026222 (2007).
[CrossRef]

Chan, W.-M.

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

Chang, D. E.

F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, Nano Lett. 11, 3370 (2011).

Chen, H.

Chen, P.-Y.

P.-Y. Chen and A. Alu, ACS Nano 5, 5855 (2011).
[CrossRef]

Choi, C.-G.

Choi, H.

Christensen, J.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

Dai, H.

X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, Science 319, 1229 (2008).
[CrossRef]

Dai, Y.

de Abajo, F. J. G.

F. J. G. de Abajo, Science 339, 917 (2013).
[CrossRef]

S. Thongrattanasiri, I. Silveiro, and F. J. G. de Abajo, Appl. Phys. Lett. 100, 201105 (2012).
[CrossRef]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, Nano Lett. 11, 3370 (2011).

Dubrovkin, A.

Efetov, K. B.

P. G. Silvestrov and K. B. Efetov, Phys. Rev. B 77, 155436 (2008).

Engheta, N.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Freitag, M.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

Gao, W.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

Geng, B.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Girit, C.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Guinea, F.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

Gusynin, V. P.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, J. Phys. Condens. Matter 19, 026222 (2007).
[CrossRef]

Han, D.

Hao, Z.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

He, S.

He, Y.

Horng, J.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Hu, B.

Jablan, M.

M. Jablan, H. Buljan, and M. Soljacic, Phys. Rev. B 80, 245435 (2009).

Jang, M. S.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, Nano Lett. 13, 2541 (2013).

Jin, Z.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

Ju, L.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Kevek, J. W.

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

Kim, J. T.

Kono, J.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

Koppens, F. H. L.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, Nano Lett. 11, 3370 (2011).

Lee, S.

X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, Science 319, 1229 (2008).
[CrossRef]

Li, X.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, Science 319, 1229 (2008).
[CrossRef]

Liang, X.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Liu, X.

Lopez, J. J.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, Nano Lett. 13, 2541 (2013).

Low, T.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

Manjavacas, A.

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

Manolatou, C.

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

Martin, M.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

McEuen, P. L.

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

Nene, P.

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

Otsuji, T.

V. V. Popov, T. Y. Bagaeva, T. Otsuji, and V. Ryzhii, Phys. Rev. B 81, 073404 (2010).

Popov, V. V.

V. V. Popov, T. Y. Bagaeva, T. Otsuji, and V. Ryzhii, Phys. Rev. B 81, 073404 (2010).

Rana, F.

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

Ryzhii, V.

V. V. Popov, T. Y. Bagaeva, T. Otsuji, and V. Ryzhii, Phys. Rev. B 81, 073404 (2010).

Sharapov, S. G.

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, J. Phys. Condens. Matter 19, 026222 (2007).
[CrossRef]

Shen, Y. R.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Sherrott, M.

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, Nano Lett. 13, 2541 (2013).

Shi, G.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

Shi, X.

Shu, J.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

Silveiro, I.

S. Thongrattanasiri, I. Silveiro, and F. J. G. de Abajo, Appl. Phys. Lett. 100, 201105 (2012).
[CrossRef]

Silvestrov, P. G.

P. G. Silvestrov and K. B. Efetov, Phys. Rev. B 77, 155436 (2008).

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljacic, Phys. Rev. B 80, 245435 (2009).

Strait, J. H.

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

Sun, Y.

Tao, J.

Thongrattanasiri, S.

S. Thongrattanasiri, I. Silveiro, and F. J. G. de Abajo, Appl. Phys. Lett. 100, 201105 (2012).
[CrossRef]

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

Tiwari, S.

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

Vajtai, R.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

Vakil, A.

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Vasko, F. T.

F. T. Vasko and I. V. Zozoulenko, Appl. Phys. Lett. 97, 092115 (2010).
[CrossRef]

Wang, F.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Wang, Q. J.

Wang, X.

X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, Science 319, 1229 (2008).
[CrossRef]

Wu, Y.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

Xia, F.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

Xu, Q.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

Yan, H.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

Yu, X.

Yu, Y.-J.

Yu, Z.

Zettl, A.

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Zhang, L.

X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, Science 319, 1229 (2008).
[CrossRef]

Zhang, Q.

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

Zhang, X.

Zhu, W.

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

Zi, J.

Zozoulenko, I. V.

F. T. Vasko and I. V. Zozoulenko, Appl. Phys. Lett. 97, 092115 (2010).
[CrossRef]

ACS Nano (2)

J. Christensen, A. Manjavacas, S. Thongrattanasiri, F. H. L. Koppens, and F. J. G. de Abajo, ACS Nano 6, 431 (2012).
[CrossRef]

P.-Y. Chen and A. Alu, ACS Nano 5, 5855 (2011).
[CrossRef]

Appl. Phys. Lett. (2)

F. T. Vasko and I. V. Zozoulenko, Appl. Phys. Lett. 97, 092115 (2010).
[CrossRef]

S. Thongrattanasiri, I. Silveiro, and F. J. G. de Abajo, Appl. Phys. Lett. 100, 201105 (2012).
[CrossRef]

J. Phys. Condens. Matter (1)

V. P. Gusynin, S. G. Sharapov, and J. P. Carbotte, J. Phys. Condens. Matter 19, 026222 (2007).
[CrossRef]

Nano Lett. (3)

W. Gao, G. Shi, Z. Jin, J. Shu, Q. Zhang, R. Vajtai, P. M. Ajayan, J. Kono, and Q. Xu, Nano Lett. 13, 3698 (2013).

F. H. L. Koppens, D. E. Chang, and F. J. G. de Abajo, Nano Lett. 11, 3370 (2011).

V. W. Brar, M. S. Jang, M. Sherrott, J. J. Lopez, and H. A. Atwater, Nano Lett. 13, 2541 (2013).

Nat. Nanotechnol. (1)

L. Ju, B. Geng, J. Horng, C. Girit, M. Martin, Z. Hao, H. A. Bechtel, X. Liang, A. Zettl, Y. R. Shen, and F. Wang, Nat. Nanotechnol. 6, 630 (2011).
[CrossRef]

Nat. Photonics (1)

H. Yan, T. Low, W. Zhu, Y. Wu, M. Freitag, X. Li, F. Guinea, P. Avouris, and F. Xia, Nat. Photonics 7, 394 (2013).
[CrossRef]

Opt. Express (3)

Opt. Lett. (1)

Phys. Rev. B (4)

M. Jablan, H. Buljan, and M. Soljacic, Phys. Rev. B 80, 245435 (2009).

J. H. Strait, P. Nene, W.-M. Chan, C. Manolatou, S. Tiwari, F. Rana, J. W. Kevek, and P. L. McEuen, Phys. Rev. B 87, 241410 (2013).

V. V. Popov, T. Y. Bagaeva, T. Otsuji, and V. Ryzhii, Phys. Rev. B 81, 073404 (2010).

P. G. Silvestrov and K. B. Efetov, Phys. Rev. B 77, 155436 (2008).

Science (3)

X. Li, X. Wang, L. Zhang, S. Lee, and H. Dai, Science 319, 1229 (2008).
[CrossRef]

F. J. G. de Abajo, Science 339, 917 (2013).
[CrossRef]

A. Vakil and N. Engheta, Science 332, 1291 (2011).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1.
Fig. 1.

(a) Fermi level profiles normalized to their average values of backgated graphene for w/d=1 (solid), 4 (dashed), and 20 (dotted). The backgated configuration and light polarization direction are shown in the inset. (b) Equivalent relative permittivity (real part) of backgated graphene (EF=0.4eV). (c) Extinction spectra of a GNRA (w=100nm) with uniform Fermi level (dotted) and nonuniform Fermi level with w/d=1 (solid) and w/d=4 (dashed) under doping level of EF=0.4eV. (d) Snapshot of Ex near field of a backgated GNRA with w=d=100nm and EF=0.4eV at extinction maximum of 34.47 THz.

Fig. 2.
Fig. 2.

Resonance frequency (a) νp and extinction maximum (b) αp varying with the average Fermi level EF. Solid, nonuniform EF profiles (d=w); dashed, uniform EF profiles. In the inset of (b), w is equal to 100, 200, and 300 nm along the dashed arrows.

Fig. 3.
Fig. 3.

(a) The quantities of s1 and s2 varying with the average Fermi level for w/d=1. (b) The same for Δαp. The solid, dashed, and dotted lines correspond with w=100, 200, and 300 nm, respectively. (c) Extinction spectra of GNRA with w=100nm and EF=0.2, 0.4, and 0.6 eV for the actual Fermi level profiles (solid) and the uniform Fermi levels given by EFeff=0.91EF (dashed). Insets show the zoomed regions around the extinction peaks.

Fig. 4.
Fig. 4.

(a) Dependence of the derivative of s1 with respect to the average Fermi level on w/d. (b) The same for the scaling factor, f. Circles show the computed data. Lines in (a) and (b) are fitted curves given by Eqs. (2) and (3), respectively. Insets show the zoomed regions for small w/d.

Equations (4)

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

s1=0.09EF,s2=0.1EF,(forw/d=1)
s1EF={[(w/d)36.2(w/d)2+96]/1000,w/d30.12(w/d)0.41exp(0.042w/d),w/d>3,
f={[(w/d)3+6.2(w/d)2+904]/1000,w/d310.12(w/d)0.41exp(0.042w/d),w/d>3,
EFeff=fEF.

Metrics