Abstract

Within a self-consistent microscopic theory, the conditions for the existence of a strongly Coulomb-correlated phase in graphene is explored, and its fingerprints in the optical spectra are investigated. A second-order semimetal-to-insulator transition is predicted if the effective fine-structure constant exceeds the critical value 1/2. Above this value, the Coulomb interaction opens a gap in the quasiparticle spectrum that increases rapidly with increasing coupling strength. Energetically below the gap, the optical spectra are predicted to exhibit pronounced excitonic resonances that are superimposed on the Drude-like response of the filled graphene π-band. Experimental observation of these excitons could serve as a fingerprint for the existence of the Coulomb-correlated phase. Increasing the coupling constant results in a blueshift and increasing oscillator strength of the dominant resonance.

© 2012 Optical Society of America

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  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, 197–200 (2005).
    [CrossRef]
  2. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, “Experimental observation of the quantum Hall effect and Berry’s phase in graphene,” Nature 438, 201–204 (2005).
    [CrossRef]
  3. R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov, and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers,” Phys. Rev. B 76, 081406 (2007).
    [CrossRef]
  4. Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
    [CrossRef]
  5. S. Y. Zhou, G.-H. Gweon, and A. Lanzara, “Low energy excitations in graphite: the role of dimensionality and lattice defects,” Ann. Phys. 321, 1730 (2006).
    [CrossRef]
  6. A. Bostwick, T. Ohta, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, “Band structure and many body effects in graphene,” Eur. J. Phys. Special Topics 148, 5–13 (2007).
    [CrossRef]
  7. S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
    [CrossRef]
  8. J. González, F. Guinea, and M. A. H. Vozmediano, “Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction,” Phys. Rev. B 59, R2474 (1999).
    [CrossRef]
  9. D. E. Sheehy and J. Schmalian, “Quantum critical scaling in graphene,” Phys. Rev. Lett. 99, 226803 (2007).
    [CrossRef]
  10. L. Fritz, J. Schmalian, M. Müller, and S. Sachdev, “Quantum critical transport in clean graphene,” Phys. Rev. B 78, 085416 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  14. V. Juričić, I. F. Herbut, and G. W. Semenoff, “Coulomb interaction at the metal—insulator critical point in graphene,” Phys. Rev. B 80, 081405 (2009).
    [CrossRef]
  15. J. E. Drut and T. A. Lähde, “Is graphene in vacuum an insulator?,” Phys. Rev. Lett. 102, 026802 (2009).
    [CrossRef]
  16. J. E. Drut and T. A. Lähde, “Lattice field theory simulations of graphene,” Phys. Rev. B 79, 165425 (2009).
    [CrossRef]
  17. L. Yang, J. Deslippe, C.-H. Park, M. L. Cohen, and S. G. Louie, “Excitonic effects on the optical response of graphene and bilayer graphene,” Phys. Rev. Lett. 103, 186802 (2009).
    [CrossRef]
  18. E. Malić, J. Maultzsch, S. Reich, and A. Knorr, “Excitonic absorption spectra of metallic single-walled carbon nanotubes,” Phys. Rev. B 82, 035433 (2010).
    [CrossRef]
  19. A. D. Güçlü, P. Potasz, and P. Hawrylak, “Excitonic absorption in gate-controlled graphene quantum dots,” Phys. Rev. B 82, 155445 (2010).
    [CrossRef]
  20. J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
    [CrossRef]
  21. H. Min, R. Bistritzer, J.-J. Su, and A. H. MacDonald, “Room-temperature superfluidity in graphene bilayers,” Phys. Rev. B 78, 121401 (2008).
    [CrossRef]
  22. O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Collective properties of magnetobiexcitons in quantum wells and graphene superlattices,” Phys. Rev. B 78, 035135 (2008).
    [CrossRef]
  23. O. L. Berman, Y. E. Lozovik, and G. Gumbs, “Bose—Einstein condensation and superfluidity of magnetoexcitons in bilayer graphene,” Phys. Rev. B 77, 155433 (2008).
    [CrossRef]
  24. K. F. Mak, J. Shan, and T. F. Heinz, “Seeing many-body effects in single- and few-layer graphene: observation of two-dimensional saddle-point excitons,” Phys. Rev. Lett. 106, 046401 (2011).
    [CrossRef]
  25. D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
    [CrossRef]
  26. E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84, 205406 (2011).
    [CrossRef]
  27. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, 2009).
  28. J. H. Grönqvist, T. Stroucken, G. Berghäuser, and S. W. Koch, “Excitons in graphene and the influence of the dielectric environment,” arXiv: 1107.5653 (2011).
  29. T. Stroucken, J. H. Grönqvist, and S. W. Koch, “Optical response and ground state of graphene,” Phys. Rev. B 84, 205445 (2011).
    [CrossRef]
  30. P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71, 622–634 (1947).
    [CrossRef]
  31. J. Sabio, F. Sols, and F. Guinea, “Variational approach to the excitonic phase transition in graphene,” Phys. Rev. B 82, 121413 (2010).
    [CrossRef]
  32. O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Gap generation and semimetal—insulator phase transition in graphene,” Phys. Rev. B 81, 075429 (2010).
    [CrossRef]
  33. J. E. Sipe, Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, M5S 1A7, Canada (personal communication, 2010).
  34. O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Supercritical Coulomb center and excitonic instability in graphene,” Phys. Rev. B 80, 165429 (2009).
    [CrossRef]
  35. E. H. Hwang and S. Das Sarma, “Dielectric function, screening, and plasmons in two-dimensional graphene,” Phys. Rev. B 75, 205418 (2007).
    [CrossRef]

2011

K. F. Mak, J. Shan, and T. F. Heinz, “Seeing many-body effects in single- and few-layer graphene: observation of two-dimensional saddle-point excitons,” Phys. Rev. Lett. 106, 046401 (2011).
[CrossRef]

D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
[CrossRef]

E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84, 205406 (2011).
[CrossRef]

T. Stroucken, J. H. Grönqvist, and S. W. Koch, “Optical response and ground state of graphene,” Phys. Rev. B 84, 205445 (2011).
[CrossRef]

2010

J. Sabio, F. Sols, and F. Guinea, “Variational approach to the excitonic phase transition in graphene,” Phys. Rev. B 82, 121413 (2010).
[CrossRef]

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Gap generation and semimetal—insulator phase transition in graphene,” Phys. Rev. B 81, 075429 (2010).
[CrossRef]

A. Sinner and K. Ziegler, “Effect of the Coulomb interaction on the gap in monolayer and bilayer graphene,” Phys. Rev. B 82, 165453 (2010).
[CrossRef]

E. Malić, J. Maultzsch, S. Reich, and A. Knorr, “Excitonic absorption spectra of metallic single-walled carbon nanotubes,” Phys. Rev. B 82, 035433 (2010).
[CrossRef]

A. D. Güçlü, P. Potasz, and P. Hawrylak, “Excitonic absorption in gate-controlled graphene quantum dots,” Phys. Rev. B 82, 155445 (2010).
[CrossRef]

J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
[CrossRef]

2009

V. Juričić, I. F. Herbut, and G. W. Semenoff, “Coulomb interaction at the metal—insulator critical point in graphene,” Phys. Rev. B 80, 081405 (2009).
[CrossRef]

J. E. Drut and T. A. Lähde, “Is graphene in vacuum an insulator?,” Phys. Rev. Lett. 102, 026802 (2009).
[CrossRef]

J. E. Drut and T. A. Lähde, “Lattice field theory simulations of graphene,” Phys. Rev. B 79, 165425 (2009).
[CrossRef]

L. Yang, J. Deslippe, C.-H. Park, M. L. Cohen, and S. G. Louie, “Excitonic effects on the optical response of graphene and bilayer graphene,” Phys. Rev. Lett. 103, 186802 (2009).
[CrossRef]

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Supercritical Coulomb center and excitonic instability in graphene,” Phys. Rev. B 80, 165429 (2009).
[CrossRef]

2008

H. Min, R. Bistritzer, J.-J. Su, and A. H. MacDonald, “Room-temperature superfluidity in graphene bilayers,” Phys. Rev. B 78, 121401 (2008).
[CrossRef]

O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Collective properties of magnetobiexcitons in quantum wells and graphene superlattices,” Phys. Rev. B 78, 035135 (2008).
[CrossRef]

O. L. Berman, Y. E. Lozovik, and G. Gumbs, “Bose—Einstein condensation and superfluidity of magnetoexcitons in bilayer graphene,” Phys. Rev. B 77, 155433 (2008).
[CrossRef]

L. Fritz, J. Schmalian, M. Müller, and S. Sachdev, “Quantum critical transport in clean graphene,” Phys. Rev. B 78, 085416 (2008).
[CrossRef]

2007

D. E. Sheehy and J. Schmalian, “Quantum critical scaling in graphene,” Phys. Rev. Lett. 99, 226803 (2007).
[CrossRef]

A. Bostwick, T. Ohta, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, “Band structure and many body effects in graphene,” Eur. J. Phys. Special Topics 148, 5–13 (2007).
[CrossRef]

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov, and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers,” Phys. Rev. B 76, 081406 (2007).
[CrossRef]

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (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]

2006

D. V. Khveshchenko and W. F. Shively, “Excitonic pairing between nodal fermions,” Phys. Rev. B 73, 115104 (2006).
[CrossRef]

S. Y. Zhou, G.-H. Gweon, and A. Lanzara, “Low energy excitations in graphite: the role of dimensionality and lattice defects,” Ann. Phys. 321, 1730 (2006).
[CrossRef]

2005

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

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

2001

D. V. Khveshchenko, “Ghost excitonic insulator transition in layered graphite,” Phys. Rev. Lett. 87, 246802 (2001).
[CrossRef]

1999

J. González, F. Guinea, and M. A. H. Vozmediano, “Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction,” Phys. Rev. B 59, R2474 (1999).
[CrossRef]

1947

P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71, 622–634 (1947).
[CrossRef]

Abbamonte, P.

J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
[CrossRef]

Berghäuser, G.

J. H. Grönqvist, T. Stroucken, G. Berghäuser, and S. W. Koch, “Excitons in graphene and the influence of the dielectric environment,” arXiv: 1107.5653 (2011).

Berman, O. L.

O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Collective properties of magnetobiexcitons in quantum wells and graphene superlattices,” Phys. Rev. B 78, 035135 (2008).
[CrossRef]

O. L. Berman, Y. E. Lozovik, and G. Gumbs, “Bose—Einstein condensation and superfluidity of magnetoexcitons in bilayer graphene,” Phys. Rev. B 77, 155433 (2008).
[CrossRef]

Bistritzer, R.

H. Min, R. Bistritzer, J.-J. Su, and A. H. MacDonald, “Room-temperature superfluidity in graphene bilayers,” Phys. Rev. B 78, 121401 (2008).
[CrossRef]

Bobkin, E.

E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84, 205406 (2011).
[CrossRef]

Bostwick, A.

A. Bostwick, T. Ohta, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, “Band structure and many body effects in graphene,” Eur. J. Phys. Special Topics 148, 5–13 (2007).
[CrossRef]

Casa, D.

J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
[CrossRef]

Castro Neto, A. H.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

Chae, D.-H.

D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
[CrossRef]

Chuang, K.-C.

R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov, and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers,” Phys. Rev. B 76, 081406 (2007).
[CrossRef]

Cohen, M. L.

L. Yang, J. Deslippe, C.-H. Park, M. L. Cohen, and S. G. Louie, “Excitonic effects on the optical response of graphene and bilayer graphene,” Phys. Rev. Lett. 103, 186802 (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]

de Heer, W. A.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

Deacon, R. S.

R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov, and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers,” Phys. Rev. B 76, 081406 (2007).
[CrossRef]

Deslippe, J.

L. Yang, J. Deslippe, C.-H. Park, M. L. Cohen, and S. G. Louie, “Excitonic effects on the optical response of graphene and bilayer graphene,” Phys. Rev. Lett. 103, 186802 (2009).
[CrossRef]

Drut, J. E.

J. E. Drut and T. A. Lähde, “Lattice field theory simulations of graphene,” Phys. Rev. B 79, 165425 (2009).
[CrossRef]

J. E. Drut and T. A. Lähde, “Is graphene in vacuum an insulator?,” Phys. Rev. Lett. 102, 026802 (2009).
[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, 197–200 (2005).
[CrossRef]

Fedorov, A. V.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

Firsov, A. A.

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

First, P. N.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

Fradkin, E.

J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
[CrossRef]

Fritz, L.

L. Fritz, J. Schmalian, M. Müller, and S. Sachdev, “Quantum critical transport in clean graphene,” Phys. Rev. B 78, 085416 (2008).
[CrossRef]

Gamayun, O. V.

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Gap generation and semimetal—insulator phase transition in graphene,” Phys. Rev. B 81, 075429 (2010).
[CrossRef]

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Supercritical Coulomb center and excitonic instability in graphene,” Phys. Rev. B 80, 165429 (2009).
[CrossRef]

Gan, Y.

J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
[CrossRef]

Geim, A. K.

R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov, and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers,” Phys. Rev. B 76, 081406 (2007).
[CrossRef]

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

Giessen, H.

D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
[CrossRef]

González, J.

J. González, F. Guinea, and M. A. H. Vozmediano, “Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction,” Phys. Rev. B 59, R2474 (1999).
[CrossRef]

Gorbar, E. V.

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Gap generation and semimetal—insulator phase transition in graphene,” Phys. Rev. B 81, 075429 (2010).
[CrossRef]

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Supercritical Coulomb center and excitonic instability in graphene,” Phys. Rev. B 80, 165429 (2009).
[CrossRef]

Grigorieva, I. V.

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

Grönqvist, J. H.

T. Stroucken, J. H. Grönqvist, and S. W. Koch, “Optical response and ground state of graphene,” Phys. Rev. B 84, 205445 (2011).
[CrossRef]

J. H. Grönqvist, T. Stroucken, G. Berghäuser, and S. W. Koch, “Excitons in graphene and the influence of the dielectric environment,” arXiv: 1107.5653 (2011).

Güçlü, A. D.

A. D. Güçlü, P. Potasz, and P. Hawrylak, “Excitonic absorption in gate-controlled graphene quantum dots,” Phys. Rev. B 82, 155445 (2010).
[CrossRef]

Guinea, F.

J. Sabio, F. Sols, and F. Guinea, “Variational approach to the excitonic phase transition in graphene,” Phys. Rev. B 82, 121413 (2010).
[CrossRef]

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

J. González, F. Guinea, and M. A. H. Vozmediano, “Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction,” Phys. Rev. B 59, R2474 (1999).
[CrossRef]

Gumbs, G.

O. L. Berman, Y. E. Lozovik, and G. Gumbs, “Bose—Einstein condensation and superfluidity of magnetoexcitons in bilayer graphene,” Phys. Rev. B 77, 155433 (2008).
[CrossRef]

Gusynin, V. P.

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Gap generation and semimetal—insulator phase transition in graphene,” Phys. Rev. B 81, 075429 (2010).
[CrossRef]

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Supercritical Coulomb center and excitonic instability in graphene,” Phys. Rev. B 80, 165429 (2009).
[CrossRef]

Gweon, G.-H.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

S. Y. Zhou, G.-H. Gweon, and A. Lanzara, “Low energy excitations in graphite: the role of dimensionality and lattice defects,” Ann. Phys. 321, 1730 (2006).
[CrossRef]

Han, M. Y.

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef]

Haug, H.

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, 2009).

Hawrylak, P.

A. D. Güçlü, P. Potasz, and P. Hawrylak, “Excitonic absorption in gate-controlled graphene quantum dots,” Phys. Rev. B 82, 155445 (2010).
[CrossRef]

Heinz, T. F.

K. F. Mak, J. Shan, and T. F. Heinz, “Seeing many-body effects in single- and few-layer graphene: observation of two-dimensional saddle-point excitons,” Phys. Rev. Lett. 106, 046401 (2011).
[CrossRef]

Henriksen, E. A.

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef]

Herbut, I. F.

V. Juričić, I. F. Herbut, and G. W. Semenoff, “Coulomb interaction at the metal—insulator critical point in graphene,” Phys. Rev. B 80, 081405 (2009).
[CrossRef]

Horn, K.

A. Bostwick, T. Ohta, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, “Band structure and many body effects in graphene,” Eur. J. Phys. Special Topics 148, 5–13 (2007).
[CrossRef]

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]

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, 197–200 (2005).
[CrossRef]

Jiang, Z.

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef]

Joe, Y. I.

J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
[CrossRef]

Juricic, V.

V. Juričić, I. F. Herbut, and G. W. Semenoff, “Coulomb interaction at the metal—insulator critical point in graphene,” Phys. Rev. B 80, 081405 (2009).
[CrossRef]

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, 197–200 (2005).
[CrossRef]

Kezerashvili, R. Y.

O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Collective properties of magnetobiexcitons in quantum wells and graphene superlattices,” Phys. Rev. B 78, 035135 (2008).
[CrossRef]

Khveshchenko, D. V.

D. V. Khveshchenko and W. F. Shively, “Excitonic pairing between nodal fermions,” Phys. Rev. B 73, 115104 (2006).
[CrossRef]

D. V. Khveshchenko, “Ghost excitonic insulator transition in layered graphite,” Phys. Rev. Lett. 87, 246802 (2001).
[CrossRef]

Kim, P.

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef]

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

Klitzing, K. v.

D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
[CrossRef]

Knorr, A.

E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84, 205406 (2011).
[CrossRef]

E. Malić, J. Maultzsch, S. Reich, and A. Knorr, “Excitonic absorption spectra of metallic single-walled carbon nanotubes,” Phys. Rev. B 82, 035433 (2010).
[CrossRef]

Koch, S. W.

T. Stroucken, J. H. Grönqvist, and S. W. Koch, “Optical response and ground state of graphene,” Phys. Rev. B 84, 205445 (2011).
[CrossRef]

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, 2009).

J. H. Grönqvist, T. Stroucken, G. Berghäuser, and S. W. Koch, “Excitons in graphene and the influence of the dielectric environment,” arXiv: 1107.5653 (2011).

Lähde, T. A.

J. E. Drut and T. A. Lähde, “Lattice field theory simulations of graphene,” Phys. Rev. B 79, 165425 (2009).
[CrossRef]

J. E. Drut and T. A. Lähde, “Is graphene in vacuum an insulator?,” Phys. Rev. Lett. 102, 026802 (2009).
[CrossRef]

Lanzara, A.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

S. Y. Zhou, G.-H. Gweon, and A. Lanzara, “Low energy excitations in graphite: the role of dimensionality and lattice defects,” Ann. Phys. 321, 1730 (2006).
[CrossRef]

Lee, D.-H.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

Lippitz, M.

D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
[CrossRef]

Louie, S. G.

L. Yang, J. Deslippe, C.-H. Park, M. L. Cohen, and S. G. Louie, “Excitonic effects on the optical response of graphene and bilayer graphene,” Phys. Rev. Lett. 103, 186802 (2009).
[CrossRef]

Lozovik, Y. E.

O. L. Berman, Y. E. Lozovik, and G. Gumbs, “Bose—Einstein condensation and superfluidity of magnetoexcitons in bilayer graphene,” Phys. Rev. B 77, 155433 (2008).
[CrossRef]

O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Collective properties of magnetobiexcitons in quantum wells and graphene superlattices,” Phys. Rev. B 78, 035135 (2008).
[CrossRef]

MacDonald, A. H.

H. Min, R. Bistritzer, J.-J. Su, and A. H. MacDonald, “Room-temperature superfluidity in graphene bilayers,” Phys. Rev. B 78, 121401 (2008).
[CrossRef]

Mak, K. F.

K. F. Mak, J. Shan, and T. F. Heinz, “Seeing many-body effects in single- and few-layer graphene: observation of two-dimensional saddle-point excitons,” Phys. Rev. Lett. 106, 046401 (2011).
[CrossRef]

Malic, E.

E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84, 205406 (2011).
[CrossRef]

E. Malić, J. Maultzsch, S. Reich, and A. Knorr, “Excitonic absorption spectra of metallic single-walled carbon nanotubes,” Phys. Rev. B 82, 035433 (2010).
[CrossRef]

Maultzsch, J.

E. Malić, J. Maultzsch, S. Reich, and A. Knorr, “Excitonic absorption spectra of metallic single-walled carbon nanotubes,” Phys. Rev. B 82, 035433 (2010).
[CrossRef]

McChesney, J. L.

A. Bostwick, T. Ohta, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, “Band structure and many body effects in graphene,” Eur. J. Phys. Special Topics 148, 5–13 (2007).
[CrossRef]

Min, H.

H. Min, R. Bistritzer, J.-J. Su, and A. H. MacDonald, “Room-temperature superfluidity in graphene bilayers,” Phys. Rev. B 78, 121401 (2008).
[CrossRef]

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, 197–200 (2005).
[CrossRef]

Müller, M.

L. Fritz, J. Schmalian, M. Müller, and S. Sachdev, “Quantum critical transport in clean graphene,” Phys. Rev. B 78, 085416 (2008).
[CrossRef]

Nicholas, R. J.

R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov, and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers,” Phys. Rev. B 76, 081406 (2007).
[CrossRef]

Novoselov, K. S.

R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov, and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers,” Phys. Rev. B 76, 081406 (2007).
[CrossRef]

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

Ohta, T.

A. Bostwick, T. Ohta, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, “Band structure and many body effects in graphene,” Eur. J. Phys. Special Topics 148, 5–13 (2007).
[CrossRef]

Park, C.-H.

L. Yang, J. Deslippe, C.-H. Park, M. L. Cohen, and S. G. Louie, “Excitonic effects on the optical response of graphene and bilayer graphene,” Phys. Rev. Lett. 103, 186802 (2009).
[CrossRef]

Potasz, P.

A. D. Güçlü, P. Potasz, and P. Hawrylak, “Excitonic absorption in gate-controlled graphene quantum dots,” Phys. Rev. B 82, 155445 (2010).
[CrossRef]

Reed, J. P.

J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
[CrossRef]

Reich, S.

E. Malić, J. Maultzsch, S. Reich, and A. Knorr, “Excitonic absorption spectra of metallic single-walled carbon nanotubes,” Phys. Rev. B 82, 035433 (2010).
[CrossRef]

Rotenberg, E.

A. Bostwick, T. Ohta, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, “Band structure and many body effects in graphene,” Eur. J. Phys. Special Topics 148, 5–13 (2007).
[CrossRef]

Sabio, J.

J. Sabio, F. Sols, and F. Guinea, “Variational approach to the excitonic phase transition in graphene,” Phys. Rev. B 82, 121413 (2010).
[CrossRef]

Sachdev, S.

L. Fritz, J. Schmalian, M. Müller, and S. Sachdev, “Quantum critical transport in clean graphene,” Phys. Rev. B 78, 085416 (2008).
[CrossRef]

Schmalian, J.

L. Fritz, J. Schmalian, M. Müller, and S. Sachdev, “Quantum critical transport in clean graphene,” Phys. Rev. B 78, 085416 (2008).
[CrossRef]

D. E. Sheehy and J. Schmalian, “Quantum critical scaling in graphene,” Phys. Rev. Lett. 99, 226803 (2007).
[CrossRef]

Schwartz, M. E.

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef]

Semenoff, G. W.

V. Juričić, I. F. Herbut, and G. W. Semenoff, “Coulomb interaction at the metal—insulator critical point in graphene,” Phys. Rev. B 80, 081405 (2009).
[CrossRef]

Seyller, T.

A. Bostwick, T. Ohta, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, “Band structure and many body effects in graphene,” Eur. J. Phys. Special Topics 148, 5–13 (2007).
[CrossRef]

Shan, J.

K. F. Mak, J. Shan, and T. F. Heinz, “Seeing many-body effects in single- and few-layer graphene: observation of two-dimensional saddle-point excitons,” Phys. Rev. Lett. 106, 046401 (2011).
[CrossRef]

Sheehy, D. E.

D. E. Sheehy and J. Schmalian, “Quantum critical scaling in graphene,” Phys. Rev. Lett. 99, 226803 (2007).
[CrossRef]

Shively, W. F.

D. V. Khveshchenko and W. F. Shively, “Excitonic pairing between nodal fermions,” Phys. Rev. B 73, 115104 (2006).
[CrossRef]

Sinner, A.

A. Sinner and K. Ziegler, “Effect of the Coulomb interaction on the gap in monolayer and bilayer graphene,” Phys. Rev. B 82, 165453 (2010).
[CrossRef]

Sipe, J. E.

J. E. Sipe, Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, M5S 1A7, Canada (personal communication, 2010).

Smet, J.

D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
[CrossRef]

Sols, F.

J. Sabio, F. Sols, and F. Guinea, “Variational approach to the excitonic phase transition in graphene,” Phys. Rev. B 82, 121413 (2010).
[CrossRef]

Stormer, H. L.

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef]

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

Stroucken, T.

T. Stroucken, J. H. Grönqvist, and S. W. Koch, “Optical response and ground state of graphene,” Phys. Rev. B 84, 205445 (2011).
[CrossRef]

J. H. Grönqvist, T. Stroucken, G. Berghäuser, and S. W. Koch, “Excitons in graphene and the influence of the dielectric environment,” arXiv: 1107.5653 (2011).

Su, J.-J.

H. Min, R. Bistritzer, J.-J. Su, and A. H. MacDonald, “Room-temperature superfluidity in graphene bilayers,” Phys. Rev. B 78, 121401 (2008).
[CrossRef]

Tan, Y.-W.

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

Tung, L. C.

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef]

Uchoa, B.

J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
[CrossRef]

Utikal, T.

D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
[CrossRef]

Vozmediano, M. A. H.

J. González, F. Guinea, and M. A. H. Vozmediano, “Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction,” Phys. Rev. B 59, R2474 (1999).
[CrossRef]

Wallace, P. R.

P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71, 622–634 (1947).
[CrossRef]

Wang, Y.-J.

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef]

Weisenburger, S.

D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
[CrossRef]

Winzer, T.

E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84, 205406 (2011).
[CrossRef]

Yang, L.

L. Yang, J. Deslippe, C.-H. Park, M. L. Cohen, and S. G. Louie, “Excitonic effects on the optical response of graphene and bilayer graphene,” Phys. Rev. Lett. 103, 186802 (2009).
[CrossRef]

Zhang, Y.

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

Zhou, S. Y.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

S. Y. Zhou, G.-H. Gweon, and A. Lanzara, “Low energy excitations in graphite: the role of dimensionality and lattice defects,” Ann. Phys. 321, 1730 (2006).
[CrossRef]

Ziegler, K.

A. Sinner and K. Ziegler, “Effect of the Coulomb interaction on the gap in monolayer and bilayer graphene,” Phys. Rev. B 82, 165453 (2010).
[CrossRef]

Ann. Phys.

S. Y. Zhou, G.-H. Gweon, and A. Lanzara, “Low energy excitations in graphite: the role of dimensionality and lattice defects,” Ann. Phys. 321, 1730 (2006).
[CrossRef]

Eur. J. Phys. Special Topics

A. Bostwick, T. Ohta, J. L. McChesney, T. Seyller, K. Horn, and E. Rotenberg, “Band structure and many body effects in graphene,” Eur. J. Phys. Special Topics 148, 5–13 (2007).
[CrossRef]

Nano Lett.

D.-H. Chae, T. Utikal, S. Weisenburger, H. Giessen, K. v. Klitzing, M. Lippitz, and J. Smet, “Excitonic fano resonance in free-standing graphene,” Nano Lett. 11, 1379–1382 (2011).
[CrossRef]

Nat. Mater.

S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, “Substrate-induced bandgap opening in epitaxial graphene,” Nat. Mater. 6, 770–775 (2007).
[CrossRef]

Nature

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

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

Phys. Rev.

P. R. Wallace, “The band theory of graphite,” Phys. Rev. 71, 622–634 (1947).
[CrossRef]

Phys. Rev. B

J. Sabio, F. Sols, and F. Guinea, “Variational approach to the excitonic phase transition in graphene,” Phys. Rev. B 82, 121413 (2010).
[CrossRef]

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Gap generation and semimetal—insulator phase transition in graphene,” Phys. Rev. B 81, 075429 (2010).
[CrossRef]

O. V. Gamayun, E. V. Gorbar, and V. P. Gusynin, “Supercritical Coulomb center and excitonic instability in graphene,” Phys. Rev. B 80, 165429 (2009).
[CrossRef]

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

T. Stroucken, J. H. Grönqvist, and S. W. Koch, “Optical response and ground state of graphene,” Phys. Rev. B 84, 205445 (2011).
[CrossRef]

E. Malic, T. Winzer, E. Bobkin, and A. Knorr, “Microscopic theory of absorption and ultrafast many-particle kinetics in graphene,” Phys. Rev. B 84, 205406 (2011).
[CrossRef]

H. Min, R. Bistritzer, J.-J. Su, and A. H. MacDonald, “Room-temperature superfluidity in graphene bilayers,” Phys. Rev. B 78, 121401 (2008).
[CrossRef]

O. L. Berman, R. Y. Kezerashvili, and Y. E. Lozovik, “Collective properties of magnetobiexcitons in quantum wells and graphene superlattices,” Phys. Rev. B 78, 035135 (2008).
[CrossRef]

O. L. Berman, Y. E. Lozovik, and G. Gumbs, “Bose—Einstein condensation and superfluidity of magnetoexcitons in bilayer graphene,” Phys. Rev. B 77, 155433 (2008).
[CrossRef]

R. S. Deacon, K.-C. Chuang, R. J. Nicholas, K. S. Novoselov, and A. K. Geim, “Cyclotron resonance study of the electron and hole velocity in graphene monolayers,” Phys. Rev. B 76, 081406 (2007).
[CrossRef]

J. González, F. Guinea, and M. A. H. Vozmediano, “Marginal-Fermi-liquid behavior from two-dimensional Coulomb interaction,” Phys. Rev. B 59, R2474 (1999).
[CrossRef]

L. Fritz, J. Schmalian, M. Müller, and S. Sachdev, “Quantum critical transport in clean graphene,” Phys. Rev. B 78, 085416 (2008).
[CrossRef]

A. Sinner and K. Ziegler, “Effect of the Coulomb interaction on the gap in monolayer and bilayer graphene,” Phys. Rev. B 82, 165453 (2010).
[CrossRef]

D. V. Khveshchenko and W. F. Shively, “Excitonic pairing between nodal fermions,” Phys. Rev. B 73, 115104 (2006).
[CrossRef]

V. Juričić, I. F. Herbut, and G. W. Semenoff, “Coulomb interaction at the metal—insulator critical point in graphene,” Phys. Rev. B 80, 081405 (2009).
[CrossRef]

J. E. Drut and T. A. Lähde, “Lattice field theory simulations of graphene,” Phys. Rev. B 79, 165425 (2009).
[CrossRef]

E. Malić, J. Maultzsch, S. Reich, and A. Knorr, “Excitonic absorption spectra of metallic single-walled carbon nanotubes,” Phys. Rev. B 82, 035433 (2010).
[CrossRef]

A. D. Güçlü, P. Potasz, and P. Hawrylak, “Excitonic absorption in gate-controlled graphene quantum dots,” Phys. Rev. B 82, 155445 (2010).
[CrossRef]

Phys. Rev. Lett.

L. Yang, J. Deslippe, C.-H. Park, M. L. Cohen, and S. G. Louie, “Excitonic effects on the optical response of graphene and bilayer graphene,” Phys. Rev. Lett. 103, 186802 (2009).
[CrossRef]

J. E. Drut and T. A. Lähde, “Is graphene in vacuum an insulator?,” Phys. Rev. Lett. 102, 026802 (2009).
[CrossRef]

D. V. Khveshchenko, “Ghost excitonic insulator transition in layered graphite,” Phys. Rev. Lett. 87, 246802 (2001).
[CrossRef]

D. E. Sheehy and J. Schmalian, “Quantum critical scaling in graphene,” Phys. Rev. Lett. 99, 226803 (2007).
[CrossRef]

Z. Jiang, E. A. Henriksen, L. C. Tung, Y.-J. Wang, M. E. Schwartz, M. Y. Han, P. Kim, and H. L. Stormer, “Infrared spectroscopy of Landau levels of graphene,” Phys. Rev. Lett. 98, 197403 (2007).
[CrossRef]

K. F. Mak, J. Shan, and T. F. Heinz, “Seeing many-body effects in single- and few-layer graphene: observation of two-dimensional saddle-point excitons,” Phys. Rev. Lett. 106, 046401 (2011).
[CrossRef]

Science

J. P. Reed, B. Uchoa, Y. I. Joe, Y. Gan, D. Casa, E. Fradkin, and P. Abbamonte, “The effective fine-structure constant of freestanding graphene measured in graphite,” Science 330, 805–808 (2010).
[CrossRef]

Other

H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, 2009).

J. H. Grönqvist, T. Stroucken, G. Berghäuser, and S. W. Koch, “Excitons in graphene and the influence of the dielectric environment,” arXiv: 1107.5653 (2011).

J. E. Sipe, Department of Physics, University of Toronto, 60 St. George St., Toronto, Ontario, M5S 1A7, Canada (personal communication, 2010).

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Figures (5)

Fig. 1.
Fig. 1.

Lattice structure of a graphene sheet. The upper part shows the real space lattice consisting of the equivalent sublattices A and B. The sublattices are connected by a translation by δi. The lower part shows the reciprocal lattice with the Dirac points K±, the Γ, and the M point. In our representation, the first Brillouin zone is centered at the Γ point.

Fig. 2.
Fig. 2.

(a) Ratio of the Coulomb and kinetic energy for different values of the coupling strength αG for the solutions of the gap equations (9) and (10). (b) Total energy density versus coupling strength for these same solutions.

Fig. 3.
Fig. 3.

(a) Schematic representation of the single-particle dispersion of the noninteracting system (left) and the interacting mean-field Hamiltonian (right). (b) Energy gap in the bands (11) as a function of the coupling strength αG. The shaded area indicates a decreasing accuracy of the linear approximation, and the dash-dotted line marks the transition energy EcEv of TB bands, Eq. (1), at the M point, where the linear approximation fails completely.

Fig. 4.
Fig. 4.

Optical matrix elements in k space. The figures show different symmetry properties of the optical matrix elements π(k) of Eq. (13). The first Brillouin zone, centered on a Γ point, is marked by a hexagon. (a) shows the magnitude |π(k)|. This magnitude is zero at the Γ points, and maximal at the K points. (b) and (c) show the magnitudes of the x- and y-components, respectively. The lower part shows the inter- and intraband contributions to the optical matrix element in (d) and (e), respectively. At the M points, intraband transitions are forbidden, while at the K points, inter- and intraband transitions contribute equally.

Fig. 5.
Fig. 5.

Computed linear optical spectra for αG=0.9 (green solid line), αG=1.0 (blue long-dashed line), αG=1.1 (purple dashed line), and αG=1.2 (pink short-dashed line). The upper part shows the transmission spectra, the middle part the true absorption spectra, and the lower part the imaginary part of the linear susceptibility. The shaded area indicates the regime of unbound (continuum) solutions; the dotted line shows the effective gap.

Equations (36)

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ϕ(r)=1d5/2132πcosϑre-r/2d
Ekc/v=±γ|f(k)|,
f(K±+k)=-3a2e-iπ/6(kx±iky).
H0=vFτkΨ^τkkστΨ^τk,
HC=12kkq:Ψ^k+qΨ^kV(q)Ψ^kqΨ^k:
V(q)=2πe2ϵqF(qd)
F(qd)=d3rd3reiq·(ρρ)e-q|z-z||ϕ(r)|2|ϕ(r)|2,
λH/vF=τk¯Ψ¯τk¯kστΨ¯τk¯+αG2k¯k¯q¯:Ψ¯k¯+q¯Ψ¯k¯F(q¯d/λ)q¯Ψ¯kq¯Ψ¯k¯:.
|Ψ=CeβB^|0,
0=k(2Σ¯kδf¯k-2Ω¯kδP¯k),
Σ¯k=vFkkV(k-k)cos(θ-θ)f¯k,
Ω¯k=kV(k-k)P¯k
Ω¯k=12kV(k-k)Ω¯kΣ¯k2+Ω¯k2,
Σ¯k=vFk-12kV(k-k)cos(θ-θ)(1-Σ¯kΣ¯k2+Ω¯k2),
Ekc/ν=±Ω¯k2+Σ¯k2.
H^I=-em0ckA·(k-e2cA)(a^ka^k+b^kb^k)-em0ck(π(k)·Aa^kb^k+h.c.),
π(k)=ieik·δid3xϕ*(r)pϕ(r-δi)=-i2M3a2kf(k)
π±(k)=i2Mae-iπ/6u±=-|π|e-iπ/6u±
H^0+H^I[p]=vFτkΨ^τk(ke*cA)στΨ^τk.
H^I[p]=e|π|m0ckA±cosθ(e^ke^k+h^-kh^-k-1)±ie|π|m0ckA±sinθ(e^kh^-k-h^-ke^k),
ΔA±-n2c22t2Aτ±=-4πcj±.
j±=-e2n0m0cA±(z=0,t)f(z)+e|π|m0k[(1-2fk)cosθImPksinθ]f(z)=-e2n0m0cA±(z=0,t)f(z)+j[p]±f(z)
A(z,ω)=A0(ω)eiqzz+2πinωj(ω)eiqz|z|,
A(0,ω)=A0(ω)-2πie2n0m0ncωA(0,ω)+2πinωj[p](ω)=A0(ω)+2πinωj[p](ω)1+iωp2(qz)n2ω2,
ωp(q)=2πe2n0m0q
limω0A(0,ω)=2πωcj[p](ω)
A(0,ω)=A0(ω)1+iωcnω-i2πωncχ(ω),
r(ω)=-iωc-2πω2cχ(ω)nω+i(ωc-2πω2cχ(ω)),
α(ω)=4πωncIm[χ(ω)]|1+iωcnω-i2πωncχ(ω)|2.
Pk=P¯k+ΔPk,
fk=f¯k+Δfk.
i(ddt+γ)ΔPk=2(Σ¯k+ΔΣk)ΔPk-(1-2f¯k-2Δfk)ΔΩk+2ΔΣkP¯k+2Ω¯kΔfk,
(ddt+γ)Δfk=-2Im[ΔPk*ΔΩk]-2Im[P¯kΔΩk+Ω¯kΔPk],
ΔΣk=-kV(k-k)cos(θ-θ)Δfk±kV(k-k)sin(θ-θ)ImΔPk+e|π|m0cA±cosθ,
ΔΩk=kV(k-k)[ReΔPk+icos(θ-θ)ImΔPk]ie|π|m0cA±sinθikV(k-k)sin(θ-θ)Δfk
(it-2Σ¯k+iγ)ΔPk-2Ω¯kΔfk=Qk,(it+iγ)Δfk-Ω¯kΔPk+Ω¯kΔPk*=Sk,

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