Magneto-Optical Spectroscopy

Chapter
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Abstract

The behaviour of electrons in (quasi-)two-dimensional systems in external magnetic fields is a fascinating area of physics. Classically, the Lorentz force caused by the magnetic field curves the trajectory of a charged particle. If such a particle is constrained to move only in one plane, in a strong enough field perpendicular to that plane, the trajectory of the particle becomes a closed orbit. However, quantum mechanically, due to wave nature of matter, only some of the orbits are stable. For a two-dimensional solid in low temperatures, this results in the electronic band structure turning into a discrete spectrum of Landau levels (LLs).

Keywords

Filling Factor Landau Level Bilayer Graphene Magnetic Field Curve Strong External Magnetic Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References

  1. 1.
    L. Landau, Diamagnetismus der Metalle. Zeitschrift für Physik 64, 629 (1930)ADSMATHCrossRefGoogle Scholar
  2. 2.
    L.J. Sham, in Electronic Properties in Semiconductor Heterostructures, ed. by P. Butcher, N.H. March, M.P. Tosi. Physics of Low-Dimensional Semiconductor Structures (Plenum Press, New York, 1993)Google Scholar
  3. 3.
    T. Chakraborty, P. Pietiläinen, The Quantum Hall Effects (Springer, Berlin, 1995)CrossRefGoogle Scholar
  4. 4.
    N. d’Ambrumenil, in Theory of the Quantum Hall Effect, ed. by P. Butcher, N.H. March, M.P. Tosi. Physics of Low-Dimensional Semiconductor Structures (Plenum Press, New York, 1993)Google Scholar
  5. 5.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Two-dimensional gas of massless dirac fermions in graphene. Nature 438, 197 (2005)ADSCrossRefGoogle Scholar
  6. 6.
    Y. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Experimental observation of quantum Hall effect and Berry’s phase in graphene. Nature 438, 201 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    K.S. Novoselov, E. McCann, S.V. Morozov, V.I. Fal’ko, M.I. Katsnelson, U. Zeitler, D. Jiang, F. Schedin, A.K. Geim, Unconventional quantum Hall effect and Berry’s phase of 2pi in bilayer graphene. Nat. Phys. 2, 177 (2006)CrossRefGoogle Scholar
  8. 8.
    Z. Jiang, Y. Zhang, Y.-W. Tan, H.L. Stormer, P. Kim, Quantum Hall effect in graphene. Solid State Commun. 143, 14 (2007)ADSCrossRefGoogle Scholar
  9. 9.
    J.C. Maan, in Magneto-Optical Properties of Semiconductor Heterostructures, ed. by P. Butcher, N.H. March, M.P. Tosi. Physics of Low-Dimensional Semiconductor Structures (Plenum Press, New York, 1993)Google Scholar
  10. 10.
    M.L. Sadowski, G. Martinez, M. Potemski, C. Berger, W.A. de Heer, Landau level spectroscopy of ultrathin graphite layers. Phys. Rev. Lett. 97, 266405 (2006)ADSCrossRefGoogle Scholar
  11. 11.
    Z. Jiang, E.A. Henriksen, L.C. Tung, Y.-J. Wang, M.E. Schwartz, M.Y. Han, P. Kim, H.L. Stormer, Infrared spectroscopy of Landau levels of graphene. Phys. Rev. Lett. 98, 197403 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    R.S. Deacon, K.-C. Chuang, R.J. Nicholas, K.S. Novoselov, A.K. Geim, Cyclotron resonance study of the electron and hole velocity in graphene monolayers. Phys. Rev. B 76, 081406(R) (2007)Google Scholar
  13. 13.
    M.L. Sadowski, G. Martinez, M. Potemski, C. Berger, W.A. de Heer, Magnetospectroscopy of epitaxial few-layer graphene. Solid State Commun. 143, 123 (2007)ADSCrossRefGoogle Scholar
  14. 14.
    E.A. Henriksen, Z. Jiang, L.-C. Tung, M.E. Schwartz, M. Takita, Y.-J. Wang, P. Kim, H.L. Stormer, Cyclotron resonance in bilayer graphene. Phys. Rev. Lett. 100, 087403 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    P. Płochocka, C. Faugeras, M. Orlita, M.L. Sadowski, G. Martinez, M. Potemski, M.O. Goerbig, J.-N. Fuchs, C. Berger, W.A. de Heer, High-energy limit of massless Dirac fermions in multilayer graphene using magneto-optical transmission spectroscopy. Phys. Rev. Lett. 100, 087401 (2008)ADSCrossRefGoogle Scholar
  16. 16.
    M. Orlita, C. Faugeras, P. Plochocka, P. Neugebauer, G. Martinez, D.K. Maude, A.-L. Barra, M. Sprinkle, C. Berger, W.A. de Heer, M. Potemski, Approaching the Dirac point in high mobility multi-layer epitaxial graphene. Phys. Rev. Lett. 101, 267601 (2008)ADSCrossRefGoogle Scholar
  17. 17.
    P. Neugebauer, M. Orlita, C. Faugeras, A.-L. Barra, M. Potemski, How perfect can graphene be? Phys. Rev. Lett. 103, 136403 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    E.A. Henriksen, P. Cadden-Zimansky, Z. Jiang, Z.Q. Li, L.-C. Tung, M.E. Schwartz, M. Takita, Y.-J. Wang, P. Kim, H.L. Stormer, Interaction-induced shift of the cyclotron resonance of graphene using infrared spectroscopy. Phys. Rev. Lett. 104, 067404 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    A.M. Witowski, M. Orlita, R. Stepniewski, A. Wysmolek, J.M. Baranowski, W. Strupinski, C. Faugeras, G. Martinez, M. Potemski, Quasi-classical cyclotron resonance of Dirac fermions in highly doped graphene. Phys. Rev. B 82, 165305, arXiv:1007.4153 (2010)Google Scholar
  20. 20.
    M. Orlita, M. Potemski, Dirac electronic states in graphene systems: optical spectroscopy studies. Semicond. Sci. Technol. 25, 063001 (2010)ADSCrossRefGoogle Scholar
  21. 21.
    W. Kohn, Cyclotron resonance and de Haas-van Alphen oscillations of an interacting electron gas. Phys. Rev. 123, 1242 (1961)ADSMATHCrossRefGoogle Scholar
  22. 22.
    D.S.L. Abergel, V.I. Fal’ko, Optical and magneto-optical far-infrared properties of bilayer graphene. Phys. Rev. B 75, 155430 (2007)ADSCrossRefGoogle Scholar
  23. 23.
    M. Inoue, Landau levels and cyclotron resonance in graphite. J. Phys. Soc. Jpn 17, 808 (1962)ADSCrossRefGoogle Scholar
  24. 24.
    O.P. Gupta, P.R. Wallace, Effect of trigonal warping on Landau-levels of graphite. Phys. Status Solidi B 54, 53 (1972)ADSCrossRefGoogle Scholar
  25. 25.
    K. Nakao, Landau-level structure and magnetic breakthrough in graphite. J. Phys. Soc. Jpn 40, 761 (1976)ADSCrossRefGoogle Scholar
  26. 26.
    E. McCann, V.I. Fal’ko, Landau level degeneracy and quantum hall effect in a graphite bilayer. Phys. Rev. Lett. 96, 086805 (2006)ADSCrossRefGoogle Scholar
  27. 27.
    D.S.L. Abergel, V. Apalkov, J. Berashevich, K. Ziegler, T. Chakraborty, Properties of graphene: a theoretical perspective. Adv. Phys. 59, 261 (2010)ADSCrossRefGoogle Scholar
  28. 28.
    M. Mucha-Kruczyński, D.S.L. Abergel, E. McCann, V.I. Fal’ko, On spectral properties of bilayer graphene: the effect of an SiC substrate and infrared magneto-spectroscopy. J. Phys. Condens. Matter 21, 344206 (2009)CrossRefGoogle Scholar
  29. 29.
    M. Mucha-Kruczyński, E. McCann, V.I. Fal’ko, Influence of interlayer asymmetry on magneto-spectroscopy of bilayer graphene. Solid State Commun. 149, 1111 (2009)ADSCrossRefGoogle Scholar
  30. 30.
    B.E. Feldman, J. Martin, A. Yacoby, Broken-symmetry states and divergent resistance in suspended bilayer graphene. Nat. Phys. 5, 889 (2009)CrossRefGoogle Scholar
  31. 31.
    E. McCann, Asymmetry gap in the electronic band structure of bilayer graphene. Phys. Rev. B 74, 161403(R) (2006)Google Scholar
  32. 32.
    E.V. Castro, K.S. Novoselov, S.V. Morozov, N.M.R. Peres, J.M.B. Lopes dos Santos, J. Nilsson, F. Guinea, A. Geim, A.H. Castro Neto, Biased bilayer graphene: semiconductor with a gap tunable by the electric field effect. Phys. Rev. Lett. 99, 216802 (2007)ADSCrossRefGoogle Scholar
  33. 33.
    H. Min, B. Sahu, S.K. Banerjee, A.H. MacDonald, Ab initio theory of gate induced gaps in graphene bilayers. Phys. Rev. B 75, 155115 (2007)ADSCrossRefGoogle Scholar
  34. 34.
    F. Guinea, A.H. Castro Neto, N.M.R. Peres, Electronic states and landau levels in graphene stacks. Phys. Rev. B 73, 245426 (2006)ADSCrossRefGoogle Scholar
  35. 35.
    J.M. Pereira Jr, F.M. Peeters, P. Vasilopoulos, Landau levels and oscillator strength in a biased bilayer of graphene. Phys. Rev. B 76, 115419 (2007)ADSCrossRefGoogle Scholar
  36. 36.
    T. Misumi, K. Shizuya, Electromagnetic response and pseudo-zero-mode landau levels of bilayer graphene in a magnetic field. Phys. Rev. B 77, 195423 (2008)ADSCrossRefGoogle Scholar
  37. 37.
    E.V. Castro, K.S. Novoselov, S.V. Morozov, N.M.R. Peres, J.M.B. Lopes dos Santos, J. Nilsson, F. Guinea, A. Geim, A.H. Castro Neto, Electronic properties of a biased graphene bilayer. J. Phys. Condens. Matter 22, 175503 (2010)ADSCrossRefGoogle Scholar
  38. 38.
    S.V. Kusminskiy, D.K. Campbell, A.H. Castro Neto, Electron-electron interactions in graphene bilayers. Europhys. Lett. 85, 58005 (2009)ADSCrossRefGoogle Scholar
  39. 39.
    D.S.L. Abergel, T. Chakraborty, Long-range Coulomb interaction in bilayer graphene. Phys. Rev. Lett. 102, 056807 (2009)ADSCrossRefGoogle Scholar
  40. 40.
    K. Shizuya, Many-body corrections to cyclotron resonance in monolayer and bilayer graphene. Phys. Rev. B 81, 075407 (2010)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of PhysicsLancaster UniversityLancasterUK

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