Relativistic Brownian motion on a graphene chip

  • A. Pototsky
  • F. Marchesoni
  • F. V. Kusmartsev
  • P. Hänggi
  • S. E. Savel’ev
Regular Article

Abstract

Relativistic Brownian motion can be inexpensively demonstrated on a graphene chip. The interplay of stochastic and relativistic dynamics, governing the transport of charge carrier in graphene, induces noise-controlled effects such as (i) a stochastic effective mass, detectable as a suppression of the particle mobility with increasing the temperature; (ii) transverse harmonic mixing, whereby electron transport can be controlled by two orthogonal, commensurate ac drives; (iii) a transverse ratchet effect, measurable as a net current orthogonal to an ac drive on an asymmetric substrate, and (iv) chaotic stochastic resonance. Such properties can be of practical applications in the emerging graphene technology.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    J. Dunkel, P. Hänggi, S. Hilbert, Nat. Phys. 5, 741 (2009)CrossRefGoogle Scholar
  2. 2.
    J. Dunkel, P. Hänggi, Phys. Rev. 471, 1 (2009)Google Scholar
  3. 3.
    P.K.F. Rieder, Cosmic Rays at Earth (Elsevier Science, New York, 2001)Google Scholar
  4. 4.
    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
  5. 5.
    A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)ADSCrossRefGoogle Scholar
  6. 6.
    A.V. Rozhkov, G. Giavaras, Y.P. Bliokh, V. Freilikher, F. Nori, Phys. Rep. 503, 77 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    S.A. Mikhailov, Phys. Rev. B 79, 241309(R) (2009)ADSCrossRefGoogle Scholar
  8. 8.
    Z. Jiang, E.A. Henriksen, L.C. Tung, Y.-J. Wang, M.E. Schwartz, M.Y. Han, P. Kim, H.L. Stormer, Phys. Rev. Lett. 98, 197403 (2007).ADSCrossRefGoogle Scholar
  9. 9.
    R.S. Deacon, K.C. Chuang, R.J. Nicholas, K.S. Novoselov, A.K. Geim, Phys. Rev. B 76, 081406 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    M. Müller, L. Fritz, S. Sachdev, B 78, 115406 (2008)Google Scholar
  11. 11.
    M. Müller, L. Fritz, S. Sachdev, J. Schmalian, AIP Conf. Proc. 1134, 170 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    A.F. Young, P. Kim, Nat. Phys. 5, 222 (2009)CrossRefGoogle Scholar
  13. 13.
    F. Wang, Y. Zhang, C. Tian, C. Girit, A. Zettl, M. Crommie, Y.R. Shen, Science 320, 206 (2008)ADSCrossRefGoogle Scholar
  14. 14.
    D. Cubero, J. Casado-Pascual, J. Dunkel, P. Talkner, P. Hänggi, Phys. Rev. Lett. 99, 170601 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nat. Phys. 2, 620 (2006)CrossRefGoogle Scholar
  16. 16.
    P.G. Silvestrov, K.B. Efetov, Phys. Rev. Lett. 98, 016802 (2007)ADSCrossRefGoogle Scholar
  17. 17.
    M.V. Fistul, K.B. Efetov, Phys. Rev. Lett. 98, 256803 (2007)ADSCrossRefGoogle Scholar
  18. 18.
    S.E. Savel’ev, A.S. Alexandrov, Phys. Rev. B 84, 035428 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    S. Savel’ev, F. Marchesoni, F. Nori, Phys. Rev. Lett. 91, 010601 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    S. Savel’ev, F. Marchesoni, F. Nori, Phys. Rev. Lett. 92, 160602 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    F.V. Kusmartsev, A.M. Tsvelick, JETP Lett. 42, 257 (1986)ADSGoogle Scholar
  22. 22.
    F. Debbasch, K. Mallick, J.P. Rivet, J. Stat. Phys. 88, 945 (1998)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    M. Müller, J. Schmalian, L. Fritz, Phys. Rev. Lett. 103, 025301 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    Z. Sun, C.L. Pint, D.C. Marcano, C. Zhang, J. Yao, G. Ruan, Zh. Yan, Yu Zhu, R.H. Hauge, J.M. Tour, Nature Commun. 2, 559 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)ADSCrossRefGoogle Scholar
  26. 26.
    F. Marchesoni, Phys. Lett. A 119, 221 (1986)MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    S. Savel’ev, F. Marchesoni, P. Hänggi, F. Nori, Europhys. Lett. 67, 179 (2004)ADSCrossRefGoogle Scholar
  28. 28.
    S. Savel’ev, F. Marchesoni, P. Hänggi, F. Nori, Europhys. J. B 40, 403 (2004)ADSGoogle Scholar
  29. 29.
    P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)ADSCrossRefGoogle Scholar
  30. 30.
    A.K. Geim, K.S. Novoselov, Nat. Mater. 6, 183 (2007)ADSCrossRefGoogle Scholar
  31. 31.
    A.K. Geim, Science 324, 1530 (2009)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • A. Pototsky
    • 1
  • F. Marchesoni
    • 2
  • F. V. Kusmartsev
    • 3
  • P. Hänggi
    • 4
  • S. E. Savel’ev
    • 3
  1. 1.Department of MathematicsUniversity of Cape TownRondeboschSouth Africa
  2. 2.Dipartimento di FisicaUniversità di CamerinoCamerinoItaly
  3. 3.Department of PhysicsLoughborough UniversityLoughboroughUK
  4. 4.Institut für PhysikUniversität AugsburgAugsburgGermany

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