Advertisement

Graphene properties from curved space Dirac equation

  • Antonio GalleratiEmail author
Regular Article
  • 34 Downloads

Abstract.

A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In particular, we study how the new description affects the characteristics of the sample, writing an appropriate conductivity Kubo formula for the modified background. Finally, we provide a theoretical analysis for the particular case of a cylindrical graphene sample.

References

  1. 1.
    W.H. Zurek, Phys. Rep. 276, 177 (1996)ADSCrossRefGoogle Scholar
  2. 2.
    G.E. Volovik, Phys. Rep. 351, 195 (2001)ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    C. Bäuerle, Y.M. Bunkov, S. Fisher, H. Godfrin, G. Pickett, Nature 382, 332 (1996)ADSCrossRefGoogle Scholar
  4. 4.
    J.M. Maldacena, Int. J. Theor. Phys. 38, 1113 (1999) hep-th/9711200CrossRefGoogle Scholar
  5. 5.
    E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998) hep-th/9802150ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    S.S. Gubser, I.R. Klebanov, A.M. Polyakov, Phys. Lett. B 428, 105 (1998) hep-th/9802109ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    G. Modanese, Europhys. Lett. 35, 413 (1996)ADSCrossRefGoogle Scholar
  8. 8.
    M. Agop, C.G. Buzea, P. Nica, Physica C 339, 120 (2000)ADSCrossRefGoogle Scholar
  9. 9.
    G.A. Ummarino, A. Gallerati, Eur. Phys. J. C 77, 549 (2017)ADSCrossRefGoogle Scholar
  10. 10.
    V. Ruutu, V. Eltsov, A. Gill, T. Kibble, M. Krusius, Y.G. Makhlin, B. Placais, G. Volovik, W. Xu, Nature 382, 334 (1996)ADSCrossRefGoogle Scholar
  11. 11.
    A. Vilenkin, E.P.S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press, 2000)Google Scholar
  12. 12.
    J.C. Teo, C.L. Kane, Phys. Rev. B 82, 115120 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    J. Rodriguez-Laguna, L. Tarruell, M. Lewenstein, A. Celi, Phys. Rev. A 95, 013627 (2017) arXiv:1606.0950ADSCrossRefGoogle Scholar
  14. 14.
    A. Kosior, M. Lewenstein, A. Celi, SciPost Phys. 5, 061 (2018) arXiv:1804.1132ADSCrossRefGoogle Scholar
  15. 15.
    M. Vozmediano, M. Katsnelson, F. Guinea, Phys. Rep. 496, 109 (2010)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    A. Cortijo, M.A. Vozmediano, Nucl. Phys. B 763, 293 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)ADSCrossRefGoogle Scholar
  18. 18.
    K. Novoselov, D. Jiang, F. Schedin, T. Booth, V. Khotkevich, S. Morozov, A. Geim, Proc. Natl. Acad. Sci. U.S.A. 102, 10451 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    K. Novoselov, A.K. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grigorieva, S. Dubonos, A. Firsov, Nature 438, 197 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    V. Gusynin, S. Sharapov, J. Carbotte, Phys. Rev. Lett. 96, 256802 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    A.C. Neto, F. Guinea, N.M. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    M. Katsnelson, K. Novoselov, Solid State Commun. 143, 3 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    A. Iorio, G. Lambiase, Phys. Rev. D 90, 025006 (2014) arXiv:1308.0265ADSCrossRefGoogle Scholar
  25. 25.
    O. Boada, A. Celi, J.I. Latorre, M. Lewenstein, New J. Phys. 13, 035002 (2011) arXiv:1010.1716ADSCrossRefGoogle Scholar
  26. 26.
    Y. Zhang, Y.-W. Tan, H.L. Stormer, P. Kim, Nature 438, 201 (2005)ADSCrossRefGoogle Scholar
  27. 27.
    C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)ADSCrossRefGoogle Scholar
  28. 28.
    S. Morozov, K. Novoselov, M. Katsnelson, F. Schedin, L. Ponomarenko, D. Jiang, A. Geim, Phys. Rev. Lett. 97, 016801 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    N. Levy, S. Burke, K. Meaker, M. Panlasigui, A. Zettl, F. Guinea, A.C. Neto, M. Crommie, Science 329, 544 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    A. Iorio, G. Lambiase, Phys. Lett. B 716, 334 (2012) arXiv:1108.2340ADSCrossRefGoogle Scholar
  31. 31.
    S. Stankovich, D.A. Dikin, G.H. Dommett, K.M. Kohlhaas, E.J. Zimney, E.A. Stach, R.D. Piner, S.T. Nguyen, R.S. Ruoff, Nature 442, 282 (2006)ADSCrossRefGoogle Scholar
  32. 32.
    M. Katsnelson, K. Novoselov, A. Geim, Nat. Phys. 2, 620 (2006)CrossRefGoogle Scholar
  33. 33.
    N. Stander, B. Huard, D. Goldhaber-Gordon, Phys. Rev. Lett. 102, 026807 (2009)ADSCrossRefGoogle Scholar
  34. 34.
    G.W. Gibbons, Commun. Math. Phys. 44, 245 (1975)ADSCrossRefGoogle Scholar
  35. 35.
    N. Dombey, A. Calogeracos, Phys. Rep. 315, 41 (1999)ADSCrossRefGoogle Scholar
  36. 36.
    F. Belgiorno, M. Martellini, Phys. Lett. B 453, 17 (1999)ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    J. González, F. Guinea, M.A.H. Vozmediano, Phys. Rev. Lett. 69, 172 (1992)ADSCrossRefGoogle Scholar
  38. 38.
    D. Kolesnikov, V. Osipov, Eur. Phys. J. B 49, 465 (2006)ADSCrossRefGoogle Scholar
  39. 39.
    D.-H. Lee, Phys. Rev. Lett. 103, 196804 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    J. Gonzalez, F. Guinea, M.A.H. Vozmediano, Nucl. Phys. B 406, 771 (1993)ADSCrossRefGoogle Scholar
  41. 41.
    J. González, F. Guinea, M.A. Vozmediano, Int. J. Mod. Phys. B 7, 4331 (1993)ADSCrossRefGoogle Scholar
  42. 42.
    V. Osipov, D. Kolesnikov, Rom. J. Phys. 50, 457 (2005)Google Scholar
  43. 43.
    A. Morpurgo, F. Guinea, Phys. Rev. Lett. 97, 196804 (2006)ADSCrossRefGoogle Scholar
  44. 44.
    M.E. Peskin, D.V. Schroeder, An Introduction to quantum field theory (Addison-Wesley, Reading, USA, 1995)Google Scholar
  45. 45.
    R. D’Auria, M. Trigiante, From Special Relativity to Feynman Diagrams (Springer International, 2011)Google Scholar
  46. 46.
    R. D’Auria, P. Fre, Nucl. Phys. B 201, 101 (1982)ADSCrossRefGoogle Scholar
  47. 47.
    L. Castellani, R. D’Auria, P. Fre, Supergravity and Superstrings: A Geometric Perspective, Vols. 1-2-3 (World Scientific, 1991)Google Scholar
  48. 48.
    M. Green, J. Schwarz, E. Witten, Superstring Theory (Cambridge University Press, Cambridge, 1987)Google Scholar
  49. 49.
    R. Kubo, Can. J. Phys. 34, 1274 (1956)ADSCrossRefGoogle Scholar
  50. 50.
    R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)ADSCrossRefGoogle Scholar
  51. 51.
    G.D. Mahan, Many-Particle Physics (Springer Science & Business Media, 2013)Google Scholar
  52. 52.
    A. Chaves, T. Frederico, O. Oliveira, W. De Paula, M. Santos, J. Phys.: Condens. Matter 26, 185301 (2014)Google Scholar
  53. 53.
    G.W. Hanson, J. Appl. Phys. 103, 064302 (2008)ADSCrossRefGoogle Scholar
  54. 54.
    F. Hipolito, A. Chaves, R. Ribeiro, M. Vasilevskiy, V.M. Pereira, N. Peres, Phys. Rev. B 86, 115430 (2012)ADSCrossRefGoogle Scholar
  55. 55.
    L. Falkovsky, S. Pershoguba, Phys. Rev. B 76, 153410 (2007)ADSCrossRefGoogle Scholar
  56. 56.
    C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles (John Wiley & Sons, 2008)Google Scholar
  57. 57.
    X. Xie, L. Ju, X. Feng, Y. Sun, R. Zhou, K. Liu, S. Fan, Q. Li, K. Jiang, Nano Lett. 9, 2565 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Politecnico di Torino, Dipartimento DISATTorinoItaly
  2. 2.Istituto Nazionale di Fisica Nucleare (INFN) - Sezione di TorinoTorinoItaly

Personalised recommendations