Skip to main content
Log in

Theoretical polarization dependence of the two-phonon double-resonant Raman spectra of graphene

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

The experimental Raman spectra of graphene exhibit a few intense two-phonon bands, which are enhanced through double-resonant scattering processes. Though there are many theoretical papers on this topic, none of them predicts the spectra within a single model. Here, we present results for the two-phonon Raman spectra of graphene calculated by means of the quantum-mechanical perturbation theory. The electronic and phonon dispersions, electronic lifetime, electron-photon and electron-phonon matrix elements, are all obtained within a density-functional-theory-based non-orthogonal tight-binding model. We study systematically the overtone and combination two-phonon Raman bands, and, in particular, the energy and polarization dependence of their Raman shift and intensity. We find that the ratio of the integrated intensities for parallel and cross polarized light for all two-phonon bands is between 0.33 and 0.42. Our results are in good agreement with the available experimental data.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A.K. Geim, K.S. Novoselov, Nature Materials 6, 183 (2007)

    Article  ADS  Google Scholar 

  2. F. Bonaccorso, Z. Sun, T. Hasan, A.C. Ferrari, Nature Photonics 4, 611 (2010)

    Article  ADS  Google Scholar 

  3. A.C. Ferrari, J.C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K.S. Novoselov, S. Roth, A.K. Geim, Phys. Rev. Lett. 97, 187401 (2006)

    Article  ADS  Google Scholar 

  4. L.M. Malard, M.A. Pimenta, G. Dresselhaus, M.S. Dresselhaus, Phys. Rep. 473, 51 (2009)

    Article  ADS  Google Scholar 

  5. M.S. Dresselhaus, A. Jorio, M. Hofmann, G. Dresselhaus, R. Saito, Nano Lett. 10, 751 (2010)

    Article  ADS  Google Scholar 

  6. V. Zólyomi, J. Koltai, J. Kürti, Phys. Stat. Sol. B 248, 2435 (2011)

    Article  ADS  Google Scholar 

  7. C. Thomsen, S. Reich, Phys. Rev. Lett. 85, 5214 (2000)

    Article  ADS  Google Scholar 

  8. S. Reich, C. Thomsen, Phil. Trans. R. Soc. Lond. A 362, 2271 (2004)

    Article  ADS  Google Scholar 

  9. R. Saito, A. Jorio, A.G. SouzaFilho, G. Dresselhaus, M.S. Dresselhaus, M.A. Pimenta, Phys. Rev. Lett. 88, 027401 (2002)

    Article  ADS  Google Scholar 

  10. A. Grüneis, R. Saito, T. Kimura, L.G. Cançado, M.A. Pimenta, A. Jorio, A.G. SouzaFilho, G. Dresselhaus, M.S. Dresselhaus, Phys. Rev. B 65, 155405 (2002)

    Article  ADS  Google Scholar 

  11. D.L. Mafra, G. Samsonidze, L.M. Malard, D.C. Elias, J.C. Brant, F. Plentz, E.S. Alves, M.A. Pimenta, Phys. Rev. B 76, 233407 (2007)

    Article  ADS  Google Scholar 

  12. A. Grüneis, J. Serrano, A. Bosak, M. Lazzeri, S.L. Molodtsov, L. Wirtz, C. Attaccalite, M. Krisch, A. Rubio, F. Mauri, T. Pichler, Phys. Rev. B 80, 085423 (2009)

    Article  ADS  Google Scholar 

  13. D.M. Basko, S. Piscanec, A.C. Ferrari, Phys. Rev. B 80, 165413 (2009)

    Article  ADS  Google Scholar 

  14. L.G. Cançado, M.A. Pimenta, R. Saito, A. Jorio, L.O. Ladeira, A. Grüneis, A.G. SouzaFilho, G. Dresselhaus, M.S. Dresselhaus, Phys. Rev. B 66, 035415 (2002)

    Article  ADS  Google Scholar 

  15. J. Maultzsch, S. Reich, C. Thomsen, Phys. Rev. B 70, 155403 (2004)

    Article  ADS  Google Scholar 

  16. R. Narula, S. Reich, Phys. Rev. B 78, 165422 (2008)

    Article  ADS  Google Scholar 

  17. P. Venezuela, M. Lazzeri, F. Mauri, Phys. Rev. B 84, 035433 (2011)

    Article  ADS  Google Scholar 

  18. R. Narula, N. Bonini, N. Marzari, S. Reich, Phys. Stat. Sol. B 248, 2635 (2011)

    Article  ADS  Google Scholar 

  19. D. Yoon, H. Moon, Y.-W. Son, G. Samsonidze, B.H. Park, J.B. Kim, Y.P. Lee, H. Cheong, Nano Lett. 8, 4270 (2008)

    Article  ADS  Google Scholar 

  20. D. Porezag, T. Frauenheim, T. Köhler, G. Seifert, R. Kaschner, Phys. Rev. B 51, 12947 (1995)

    Article  ADS  Google Scholar 

  21. V.N. Popov, L. Henrard, Phys. Rev. B 70, 115407 (2004)

    Article  ADS  Google Scholar 

  22. V.N. Popov, Ph. Lambin, Phys. Rev. B 73, 085407 (2006)

    Article  ADS  Google Scholar 

  23. V.N. Popov, L. Henrard, Ph. Lambin, Phys. Rev. B 72, 035436 (2005)

    Article  ADS  Google Scholar 

  24. V.N. Popov, Ph. Lambin, Phys. Rev. B 74, 075415 (2006)

    Article  ADS  Google Scholar 

  25. R.M. Martin, L.M. Falicov, in Light Scattering in Solids, edited by M. Cardona (Springer-Verlag, Berlin, 1983), Vol. 8

  26. J. Kürti, V. Zólyomi, A. Grüneis, H. Kuzmany, Phys. Rev. B 65, 165433 (2002)

    Article  ADS  Google Scholar 

  27. L.G. Cançado, A. Jorio, M.A. Pimenta, Phys. Rev. B 76, 064304 (2007)

    Article  ADS  Google Scholar 

  28. M. Lazzeri, C. Attaccalite, L. Wirtz, F. Mauri, Phys. Rev. B 78, 081406(R) (2008)

    Article  ADS  Google Scholar 

  29. F. Alzina, H. Tao, J. Moser, Y. García, A. Bachtold, C.M. Sotomayor-Torres, Phys. Rev. B 82, 075422 (2010)

    Article  ADS  Google Scholar 

  30. K. Sato, J.S. Park, R. Saito, C. Cong, T. Yu, C.H. Lui, T.F. Heinz, G. Dresselhaus, M.S. Dresselhaus, Phys. Rev. B 84, 035419 (2011)

    Article  ADS  Google Scholar 

  31. C. Cong, T. Yu, R. Saito, G.F. Dresselhaus, M.S. Dresselhaus, ACS Nano 5, 1600 (2011)

    Article  Google Scholar 

  32. D.M. Basko, Phys. Rev. B 78, 125418 (2008)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. N. Popov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Popov, V.N., Lambin, P. Theoretical polarization dependence of the two-phonon double-resonant Raman spectra of graphene. Eur. Phys. J. B 85, 418 (2012). https://doi.org/10.1140/epjb/e2012-30684-x

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2012-30684-x

Keywords

Navigation