Electronic Properties of Multilayer Graphene

Chapter
Part of the NanoScience and Technology book series (NANO)

Abstract

In this chapter, we study the electronic structure of arbitrarily stacked multilayer graphene in the absence or presence of magnetic field. The energy band structure and the Landau-level spectrum are obtained using a π-orbital continuum model with nearest-neighbor intralayer and interlayer tunneling terms. Using degenerate state perturbation theory, we analyze the low-energy effective theory and show that the low-energy electronic structure of arbitrarily stacked graphene multilayers consists of chiral pseudospin doublets with a conserved chirality sum. We discuss the implications of this for the quantum Hall effect, optical conductivity, and electrical conductivity.

References

  1. 1.
    A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)ADSCrossRefGoogle Scholar
  2. 2.
    A.K. Geim, A.H. MacDonald, Phys. Today 60(8), 35 (2007)CrossRefGoogle Scholar
  3. 3.
    M.I. Katsnelson, Mater. Today 10, 20 (2007)CrossRefGoogle Scholar
  4. 4.
    A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    N.M.R. Peres, Rev. Mod. Phys. 82, 2673 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    S. Das Sarma, S. Adam, E.H. Hwang, E. Rossi, Rev. Mod. Phys. 83, 407 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    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
  8. 8.
    C. Berger, Z. Song, T. Li, X. Li, A.Y. Ogbazghi, R. Feng, Z. Dai, A.N. Marchenkov, E.H. Conrad, P.N. First, W.A. de Heer, J. Phys. Chem. B 108, 19912 (2004)CrossRefGoogle Scholar
  9. 9.
    T. Ohta, A. Bostwick, T. Seyller, K. Horn, E. Rotenberg, Science 313, 951 (2006)ADSCrossRefGoogle Scholar
  10. 10.
    A. Rycerz, J. Tworzydl, C.W.J. Beenakker, Nat. Phys. 3, 172 (2007)CrossRefGoogle Scholar
  11. 11.
    V.V. Cheianov, V. Fal’ko, B.L. Altshuler, Science 315, 1252 (2007)Google Scholar
  12. 12.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438, 197 (2005)ADSCrossRefGoogle Scholar
  13. 13.
    Y. Zhang, Y.-W. Tan, H.L. Stormer, P. Kim, Nature 438, 201 (2005)ADSCrossRefGoogle Scholar
  14. 14.
    S. Latil, L. Henrard, Phys. Rev. Lett. 97, 036803 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    F. Guinea, A.H. Castro Neto, N.M.R. Peres, Phys. Rev. B 73, 245426 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    B. Partoens, F.M. Peeters, Phys. Rev. B 74, 075404 (2006)ADSCrossRefGoogle Scholar
  17. 17.
    B. Partoens, F.M. Peeters, Phys. Rev. B 75, 193402 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    M. Koshino, T. Ando, Phys. Rev. B 76, 085425 (2007)ADSCrossRefGoogle Scholar
  19. 19.
    M. Koshino, T. Ando, Phys. Rev. B 77, 115313 (2008)ADSCrossRefGoogle Scholar
  20. 20.
    H. Min, A.H. MacDonald, Phys. Rev. B 77, 155416 (2008)ADSCrossRefGoogle Scholar
  21. 21.
    H. Min, A.H. MacDonald, Prog. Theor. Phys. Suppl. 176, 227 (2008)MATHCrossRefGoogle Scholar
  22. 22.
    M. Aoki, H. Amawashi, Solid State Commun. 142, 123 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    F. Zhang, B. Sahu, H. Min, A.H. MacDonald, Phys. Rev. B 82, 035409 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    K.F. Mak, J. Shan, T.F. Heinz, Phys. Rev. Lett. 104, 176404 (2010)ADSCrossRefGoogle Scholar
  25. 25.
    C.L. Lu, C.P. Chang, Y.C. Huang, R.B. Chen, M.L. Lin, Phys. Rev. B 73, 144427 (2006)ADSCrossRefGoogle Scholar
  26. 26.
    C.-L. Lu, H.-C. Lin, C.-C. Hwang, J. Wang, M.-F. Lin, C.-P. Chang, Appl. Phys. Lett. 89, 221910 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    M. Koshino, T. Ando, Solid State Commun. 149, 1123 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    H. Min, A.H. MacDonald, Phys. Rev. Lett. 103, 067402 (2009)ADSCrossRefGoogle Scholar
  29. 29.
    J. Nilsson, A.H. Neto, F. Guinea, N.M. Peres, Phys. Rev. Lett. 97, 266801 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    J. Nilsson, A.H. Castro Neto, Phys. Rev. Lett. 98, 126801 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    J. Nilsson, A.H. Castro Neto, F. Guinea, N.M.R. Peres, Phys. Rev. B 78, 045405 (2008)ADSCrossRefGoogle Scholar
  32. 32.
    H. Min, P. Jain, S. Adam, M.D. Stiles, Phys. Rev. B 83, 195117 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    H. Min, E.H. Hwang, S. Das Sarma, Phys. Rev. B 83, 161404(R) (2011)Google Scholar
  34. 34.
    J.M.B. Lopes dos Santos, N.M.R. Peres, A.H. Castro Neto, Phys. Rev. Lett. 99, 256802 (2007)ADSCrossRefGoogle Scholar
  35. 35.
    J. Hass, F. Varchon, J.E. Milla̋n-Otoya, M. Sprinkle, N. Sharma, W.A. de Heer, C. Berger, P.N. First, L. Magaud, E.H. Conrad, Phys. Rev. Lett. 100, 125504 (2008)Google Scholar
  36. 36.
    E.J. Mele, Phys. Rev. B 81, 161405(R) (2010)Google Scholar
  37. 37.
    P.D. Ritger, N.J. Rose, Equations with Applications (McGraw-Hill Book Company, New York, 1968)MATHGoogle Scholar
  38. 38.
    R. Saito, G. Dresselhaus, M.S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998)CrossRefGoogle Scholar
  39. 39.
    E. McCann, V.I. Falko, Phys. Rev. Lett. 96, 086805 (2006)ADSCrossRefGoogle Scholar
  40. 40.
    J.C. Charlier, J.P. Michenaud, X. Gonze, Phys. Rev. B 46, 4531 (1992)ADSCrossRefGoogle Scholar
  41. 41.
    J.J. Sakurai, Modern Quantum Mechanics (Addison Wesley, Reading, 1994)Google Scholar
  42. 42.
    R.R. Nair, P. Blake, A.N. Grigorenko, K.S. Novoselov, T.J. Booth, T. Stauber, N.M.R. Peres, A.K. Geim, Science 320, 1308 (2008)ADSCrossRefGoogle Scholar
  43. 43.
    F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, Y.R. Shen, Science 320, 206 (2008)ADSCrossRefGoogle Scholar
  44. 44.
    Z.Q. Li, E.A. Henriksen, Z. Jiang, Z. Hao, M.C. Martin, P. Kim, H.L. Stormer, D.N. Basov, Nat. Phy. 4, 532 (2008)CrossRefGoogle Scholar
  45. 45.
    K.F. Mak, M.Y. Sfeir, Y. Wu, C.H. Lui, J.A. Misewich, T.F. Heinz, Phys. Rev. Lett. 101, 196405 (2008)ADSCrossRefGoogle Scholar
  46. 46.
    P.E. Gaskell, C. Rodenchuk, H.S. Skulason, T. Szkope, Appl. Phys. Lett. 94, 143101 (2009)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Center for Nanoscale Science and TechnologyNational Institute of Standards and TechnologyGaithersburgUSA
  2. 2.Maryland NanoCenterUniversity of MarylandCollege ParkUSA
  3. 3.Department of Physics and AstronomySeoul National UniversitySeoulKorea

Personalised recommendations