Abstract

We predict the existence of transverse electric (TE) plasmons in bilayer graphene. We find that their plasmonic properties are much more pronounced in bilayer than in monolayer graphene, in a sense that they can get more localized at frequencies just below h̄ω = 0.4 eV for adequate doping values. This is a consequence of the perfectly nested bands in bilayer graphene which are separated by ∼ 0.4 eV.

© 2011 OSA

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  1. D. Pines and P. Nozieres, The Theory of Quantum Liquids (Benjamin, 1966).
  2. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824 (2003).
    [CrossRef] [PubMed]
  3. S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
    [CrossRef]
  4. S. Vedentam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 3447 (2009).
    [CrossRef]
  5. A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength lght in air,” Phys. Rev. Lett. 95, 063901 (2005).
    [CrossRef] [PubMed]
  6. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509 (1968).
    [CrossRef]
  7. V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41 (2007).
    [CrossRef]
  8. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
    [CrossRef] [PubMed]
  9. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788 (2004).
    [CrossRef] [PubMed]
  10. 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 (2004).
    [CrossRef] [PubMed]
  11. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109 (2009).
    [CrossRef]
  12. K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
    [CrossRef]
  13. X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in a graphene bilayer,” Phys. Rev. B 75, 041404 (2007).
    [CrossRef]
  14. G. Borghi, M. Polini, R. Asgari, and A. H. MacDonald, “Dynamical response functions and collective modes of bilayer graphene,” Phys. Rev. B 80, 241402 (2009).
    [CrossRef]
  15. X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in biased bilayer graphene,” Phys. Rev. B 81, 081402 (2010).
    [CrossRef]
  16. R. Sensarma, E. H. Hwang, and S. Das Sarma, “Dynamic screening and low-energy collective modes in bilayer graphene,” Phys. Rev. B 82, 195428 (2010).
  17. B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” N. J. Phys. 8, 318 (2006).
    [CrossRef]
  18. E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
    [CrossRef]
  19. S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
    [CrossRef] [PubMed]
  20. F. Rana, “Graphene terahertz plasmon oscillators,” IEEE Trans. Nanotechnology 7, 91 (2008).
    [CrossRef]
  21. C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).
  22. Y. Liu, R. F. Willis, K. V. Emtsev, and Th. Seyller, “Plasmon dispersion and damping in electrically isolated two-dimensional charge sheets,” Phys. Rev. B 78, 201403 (2008).
  23. M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
    [CrossRef]
  24. E. J. Nicol and J. P. Carbotte, “Optical conductivity of bilayer graphene with and without an asymmetry gap,” Phys. Rev. B 77, 155409 (2008).
    [CrossRef]

2014

Y. Liu, R. F. Willis, K. V. Emtsev, and Th. Seyller, “Plasmon dispersion and damping in electrically isolated two-dimensional charge sheets,” Phys. Rev. B 78, 201403 (2008).

2010

X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in biased bilayer graphene,” Phys. Rev. B 81, 081402 (2010).
[CrossRef]

2009

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

G. Borghi, M. Polini, R. Asgari, and A. H. MacDonald, “Dynamical response functions and collective modes of bilayer graphene,” Phys. Rev. B 80, 241402 (2009).
[CrossRef]

S. Vedentam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 3447 (2009).
[CrossRef]

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

2008

E. J. Nicol and J. P. Carbotte, “Optical conductivity of bilayer graphene with and without an asymmetry gap,” Phys. Rev. B 77, 155409 (2008).
[CrossRef]

F. Rana, “Graphene terahertz plasmon oscillators,” IEEE Trans. Nanotechnology 7, 91 (2008).
[CrossRef]

2007

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41 (2007).
[CrossRef]

X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in a graphene bilayer,” Phys. Rev. B 75, 041404 (2007).
[CrossRef]

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[CrossRef]

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[CrossRef] [PubMed]

2006

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[CrossRef]

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” N. J. Phys. 8, 318 (2006).
[CrossRef]

2005

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength lght in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

2004

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788 (2004).
[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 (2004).
[CrossRef] [PubMed]

2003

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824 (2003).
[CrossRef] [PubMed]

2000

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1968

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

1954

R. Sensarma, E. H. Hwang, and S. Das Sarma, “Dynamic screening and low-energy collective modes in bilayer graphene,” Phys. Rev. B 82, 195428 (2010).

Asgari, R.

G. Borghi, M. Polini, R. Asgari, and A. H. MacDonald, “Dynamical response functions and collective modes of bilayer graphene,” Phys. Rev. B 80, 241402 (2009).
[CrossRef]

Atwater, H. A.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824 (2003).
[CrossRef] [PubMed]

Borghi, G.

G. Borghi, M. Polini, R. Asgari, and A. H. MacDonald, “Dynamical response functions and collective modes of bilayer graphene,” Phys. Rev. B 80, 241402 (2009).
[CrossRef]

Büchner, B.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Buljan, H.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

Carbotte, J. P.

E. J. Nicol and J. P. Carbotte, “Optical conductivity of bilayer graphene with and without an asymmetry gap,” Phys. Rev. B 77, 155409 (2008).
[CrossRef]

Castro Neto, A. H.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

Chakraborty, T.

X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in biased bilayer graphene,” Phys. Rev. B 81, 081402 (2010).
[CrossRef]

X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in a graphene bilayer,” Phys. Rev. B 75, 041404 (2007).
[CrossRef]

Conway, J.

S. Vedentam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 3447 (2009).
[CrossRef]

Das Sarma, S.

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[CrossRef]

R. Sensarma, E. H. Hwang, and S. Das Sarma, “Dynamic screening and low-energy collective modes in bilayer graphene,” Phys. Rev. B 82, 195428 (2010).

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824 (2003).
[CrossRef] [PubMed]

Dubonos, S. V.

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 (2004).
[CrossRef] [PubMed]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824 (2003).
[CrossRef] [PubMed]

Einarsson, E.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Emtsev, K. V.

Y. Liu, R. F. Willis, K. V. Emtsev, and Th. Seyller, “Plasmon dispersion and damping in electrically isolated two-dimensional charge sheets,” Phys. Rev. B 78, 201403 (2008).

Fal’ko, V. I.

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[CrossRef]

Fink, J.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Firsov, A. A.

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 (2004).
[CrossRef] [PubMed]

Geim, A. K.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[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, 666 (2004).
[CrossRef] [PubMed]

Giorgetti, C.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Grigorieva, I. V.

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 (2004).
[CrossRef] [PubMed]

Guinea, F.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” N. J. Phys. 8, 318 (2006).
[CrossRef]

Hambach, R.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Hannewald, K.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Hwang, E. H.

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[CrossRef]

R. Sensarma, E. H. Hwang, and S. Das Sarma, “Dynamic screening and low-energy collective modes in bilayer graphene,” Phys. Rev. B 82, 195428 (2010).

Ibanescu, M.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength lght in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Jablan, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

Jiang, D.

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[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, 666 (2004).
[CrossRef] [PubMed]

Joannopoulos, J. D.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength lght in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Karalis, A.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength lght in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Katsnelson, M. I.

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[CrossRef]

Knupfer, M.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Kramberger, C.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Lee, H.

S. Vedentam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 3447 (2009).
[CrossRef]

Lidorikis, E.

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength lght in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Liu, Y.

Y. Liu, R. F. Willis, K. V. Emtsev, and Th. Seyller, “Plasmon dispersion and damping in electrically isolated two-dimensional charge sheets,” Phys. Rev. B 78, 201403 (2008).

MacDonald, A. H.

G. Borghi, M. Polini, R. Asgari, and A. H. MacDonald, “Dynamical response functions and collective modes of bilayer graphene,” Phys. Rev. B 80, 241402 (2009).
[CrossRef]

Maier, S. A.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

Marinopoulos, A. G.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Maruyama, S.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

McCann, E.

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[CrossRef]

Mikhailov, S. A.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[CrossRef] [PubMed]

Morozov, S. V.

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[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, 666 (2004).
[CrossRef] [PubMed]

Nicol, E. J.

E. J. Nicol and J. P. Carbotte, “Optical conductivity of bilayer graphene with and without an asymmetry gap,” Phys. Rev. B 77, 155409 (2008).
[CrossRef]

Novoselov, K. S.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[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, 666 (2004).
[CrossRef] [PubMed]

Nozieres, P.

D. Pines and P. Nozieres, The Theory of Quantum Liquids (Benjamin, 1966).

Olevano, V.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788 (2004).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Peres, N. M. R.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

Pichler, T.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Pines, D.

D. Pines and P. Nozieres, The Theory of Quantum Liquids (Benjamin, 1966).

Polini, M.

G. Borghi, M. Polini, R. Asgari, and A. H. MacDonald, “Dynamical response functions and collective modes of bilayer graphene,” Phys. Rev. B 80, 241402 (2009).
[CrossRef]

Rana, F.

F. Rana, “Graphene terahertz plasmon oscillators,” IEEE Trans. Nanotechnology 7, 91 (2008).
[CrossRef]

Reining, L.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Rümmeli, M. H.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Schedin, F.

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[CrossRef]

Sensarma, R.

R. Sensarma, E. H. Hwang, and S. Das Sarma, “Dynamic screening and low-energy collective modes in bilayer graphene,” Phys. Rev. B 82, 195428 (2010).

Seyller, Th.

Y. Liu, R. F. Willis, K. V. Emtsev, and Th. Seyller, “Plasmon dispersion and damping in electrically isolated two-dimensional charge sheets,” Phys. Rev. B 78, 201403 (2008).

Shalaev, V. M.

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41 (2007).
[CrossRef]

Smith, D. R.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788 (2004).
[CrossRef] [PubMed]

Soljacic, M.

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength lght in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Sols, F.

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” N. J. Phys. 8, 318 (2006).
[CrossRef]

Sottile, F.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

Staffaroni, M.

S. Vedentam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 3447 (2009).
[CrossRef]

Stauber, T.

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” N. J. Phys. 8, 318 (2006).
[CrossRef]

Tang, J.

S. Vedentam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 3447 (2009).
[CrossRef]

Vedentam, S.

S. Vedentam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 3447 (2009).
[CrossRef]

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Wang, X. F.

X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in biased bilayer graphene,” Phys. Rev. B 81, 081402 (2010).
[CrossRef]

X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in a graphene bilayer,” Phys. Rev. B 75, 041404 (2007).
[CrossRef]

Willis, R. F.

Y. Liu, R. F. Willis, K. V. Emtsev, and Th. Seyller, “Plasmon dispersion and damping in electrically isolated two-dimensional charge sheets,” Phys. Rev. B 78, 201403 (2008).

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788 (2004).
[CrossRef] [PubMed]

Wunsch, B.

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” N. J. Phys. 8, 318 (2006).
[CrossRef]

Yablonovitch, E.

S. Vedentam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 3447 (2009).
[CrossRef]

Zeitler, U.

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[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 (2004).
[CrossRef] [PubMed]

Ziegler, K.

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[CrossRef] [PubMed]

IEEE Trans. Nanotechnology

F. Rana, “Graphene terahertz plasmon oscillators,” IEEE Trans. Nanotechnology 7, 91 (2008).
[CrossRef]

J. Appl. Phys.

S. A. Maier and H. A. Atwater, “Plasmonics: localization and guiding of electromagnetic energy in metal/dielectric structures,” J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

N. J. Phys.

B. Wunsch, T. Stauber, F. Sols, and F. Guinea, “Dynamical polarization of graphene at finite doping,” N. J. Phys. 8, 318 (2006).
[CrossRef]

Nano Lett.

S. Vedentam, H. Lee, J. Tang, J. Conway, M. Staffaroni, and E. Yablonovitch, “A plasmonic dimple lens for nanoscale focusing of light,” Nano Lett. 9, 3447 (2009).
[CrossRef]

Nat. Photonics

V. M. Shalaev, “Optical negative-index metamaterials,” Nat. Photonics 1, 41 (2007).
[CrossRef]

Nat. Phys.

K. S. Novoselov, E. McCann, S. V. Morozov, V. I. Fal’ko, M. I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, and A. K. Geim, “Unconventional quantum Hall effect and Berry’s phase of 2π in bilayer graphene,” Nat. Phys. 2, 177 (2006).
[CrossRef]

Nature

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824 (2003).
[CrossRef] [PubMed]

Phys. Rev. B

E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
[CrossRef]

X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in a graphene bilayer,” Phys. Rev. B 75, 041404 (2007).
[CrossRef]

G. Borghi, M. Polini, R. Asgari, and A. H. MacDonald, “Dynamical response functions and collective modes of bilayer graphene,” Phys. Rev. B 80, 241402 (2009).
[CrossRef]

X. F. Wang and T. Chakraborty, “Coulomb screening and collective excitations in biased bilayer graphene,” Phys. Rev. B 81, 081402 (2010).
[CrossRef]

R. Sensarma, E. H. Hwang, and S. Das Sarma, “Dynamic screening and low-energy collective modes in bilayer graphene,” Phys. Rev. B 82, 195428 (2010).

Y. Liu, R. F. Willis, K. V. Emtsev, and Th. Seyller, “Plasmon dispersion and damping in electrically isolated two-dimensional charge sheets,” Phys. Rev. B 78, 201403 (2008).

M. Jablan, H. Buljan, and M. Soljačić, “Plasmonics in graphene at infrared frequencies,” Phys. Rev. B 80, 245435 (2009).
[CrossRef]

E. J. Nicol and J. P. Carbotte, “Optical conductivity of bilayer graphene with and without an asymmetry gap,” Phys. Rev. B 77, 155409 (2008).
[CrossRef]

Phys. Rev. Lett.

C. Kramberger, R. Hambach, C. Giorgetti, M. H. Rümmeli, M. Knupfer, J. Fink, B. Büchner, L. Reining, E. Einarsson, S. Maruyama, F. Sottile, K. Hannewald, V. Olevano, A. G. Marinopoulos, and T. Pichler, “Linear plasmon dispersion in single-wall carbon nanotubes and the collective excitation spectrum of graphene,” Phys. Rev. Lett. 100, 196803 (2008).

S. A. Mikhailov and K. Ziegler, “New electromagnetic mode in graphene,” Phys. Rev. Lett. 99, 016803 (2007).
[CrossRef] [PubMed]

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

A. Karalis, E. Lidorikis, M. Ibanescu, J. D. Joannopoulos, and M. Soljačić, “Surface-plasmon-assisted guiding of broadband slow and subwavelength lght in air,” Phys. Rev. Lett. 95, 063901 (2005).
[CrossRef] [PubMed]

Rev. Mod. Phys.

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, “The electronic properties of graphene,” Rev. Mod. Phys. 81, 109 (2009).
[CrossRef]

Science

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788 (2004).
[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 (2004).
[CrossRef] [PubMed]

Sov. Phys. Usp.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ɛ and μ,” Sov. Phys. Usp. 10, 509 (1968).
[CrossRef]

Other

D. Pines and P. Nozieres, The Theory of Quantum Liquids (Benjamin, 1966).

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Figures (3)

Fig. 1
Fig. 1

The band-structure of bilayer graphene. The two upper bands (as well as the two lower bands) are perfectly nested and separated by γ ∼ 0.4 eV; q 0 = γ/h̄vF . Horizontal line depicts one possible value of the Fermi level, and arrows denote some of the possible interband electronic transitions. See text for details.

Fig. 2
Fig. 2

The real (red dotted lines) and imaginary (blue solid lines) part of the conductivity of bilayer graphene for two values of doping: μ = 0.4γ (a), and μ = 0.9γ (b). The conductivity is in units of σ 0 = e 2/2, and the frequency is in units of ω 0 = γ/. The δ-functions in ℜσ(ω) at ω = 0 (intraband transitions) and ω = γ/ (transitions from the lower to the upper conduction band depicted as green solid arrows in Fig. 1) are not shown (see [24]).

Fig. 3
Fig. 3

The plasmon dispersion curve Δq = qω/c vs. ω for μ = 0.4γ (a), and μ = 0.9γ (b) is shown as blue solid line. To the right of the vertical red dotted lines plasmons can be damped via excitation of electron-hole pairs, whereas to the left of this line these excitations are forbidden due to the Pauli principle. Black dashed line in (b) (which closely follows the blue line) corresponds to Eq. (8). The wave vector is in units of q 0 = γ/h̄vF , and the frequency is in units of ω 0 = γ/.

Equations (8)

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1 + i σ ( q , ω ) q 2 ω 2 / c 2 2 ɛ 0 ω = 0
1 μ 0 ω i σ ( q , ω ) 2 q 2 ω 2 / c 2 = 0
ɛ ( k ) γ = ± 1 4 + ( h ¯ v F k γ ) 2 ± 1 2 ,
σ ( ω ) = 2 ω π 𝒫 0 σ ( ω ) ω 2 ω 2 d ω ,
σ ( ω ) σ 0 = f ( Ω , 2 μ ) + g ( Ω , μ , γ ) + [ f ( Ω , 2 γ ) + g ( Ω , γ , γ ) ] Θ ( γ μ ) + [ f ( Ω , 2 μ ) + g ( Ω , μ , γ ) ] Θ ( μ γ ) + γ 2 Ω 2 [ Ω π ( 2 μ + γ ) + f ( Ω , 2 μ + γ ) ] + γ 2 Ω 2 [ Ω π γ + f ( Ω , γ ) ] Θ ( γ μ ) + γ 2 Ω 2 [ Ω π ( 2 μ γ ) + f ( Ω , 2 μ γ ) ] Θ ( μ γ ) + a ( μ ) π Ω + 2 Ω b ( μ ) π ( Ω 2 γ 2 ) ,
f ( x , y ) = 1 2 π log | x y x + y | , g ( x , y , z ) = z 2 π ( x z ) log | x 2 y | + ( x + z ) log | x + 2 y | 2 x log | 2 y + z | x 2 z 2 , a ( μ ) = 4 μ ( μ + γ ) 2 μ + γ + 4 μ ( μ γ ) 2 μ γ Θ ( μ γ ) , b ( μ ) = γ 2 [ log 2 μ + γ γ log 2 μ γ γ Θ ( μ γ ) ] ,
Δ q ω 8 ɛ 0 2 c 3 σ ( ω ) 2 .
Δ q γ / 2 < μ < γ ω σ 0 2 2 π 2 ɛ 0 2 c 3 [ h ¯ ω b ( μ ) γ 2 ( h ¯ ω ) 2 ] 2 .

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