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Effects of spatial dispersion on the Casimir force between graphene sheets

  • D. Drosdoff
  • A. D. Phan
  • L. M. WoodsEmail author
  • I. V. Bondarev
  • J. F. Dobson
Regular Article

Abstract

The asymptotic dispersion force F between two graphene sheets at a separation d is unusual: at T = 0 K, FC d p , where p = 4, unlike the 2D insulating (p = 5) or metallic (p = 7/2) cases. Here it is shown that these anomalous low-temperature properties of p are retained even when spatial dispersion (nonlocality) is included in the optical response properties of graphene. Furthermore, it is shown that the prefactor C is only weakly decreased (by <20%) upon spatial dispersion inclusion. For larger temperatures and nonzero chemical potential, such dispersion has even a lesser effect on the graphene/graphene force. The opening of a band gap in the graphene electronic structure, however, can cause larger sensitivity to spatial dispersion at elevated temperatures.

Keywords

Mesoscopic and Nanoscale Systems 

References

  1. 1.
    H.B.G. Casimir, Proc. K. Ned. Akad. Wet. 51, 793 (1948)zbMATHGoogle Scholar
  2. 2.
    F. London, Z. Phys. 63, 245 (1930)ADSzbMATHCrossRefGoogle Scholar
  3. 3.
    A.A. Abrikosov, L.P. Gorkov, I.E. Dzyaloshinski,Methods of Quantum Field Theory in Statistical Physics (Dover Publications, Inc., New York, 1975)Google Scholar
  4. 4.
    A.W. Rodriguez, F. Capasso, S.G. Johnson, Nature photonics 5, 211 (2011)ADSCrossRefGoogle Scholar
  5. 5.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 360, 666 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.V. Morozov, A.K. Geim, Proc. Natl. Acd. Sci. 102, 10451 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    Y.M. Lin, C. Dimitrakopoulos, K.A. Jenkins, D.B. Farmer, H.Y. Chiu, Science 327, 662 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    M.D. Stoller, S. Park, Y. Zhu, J. An, R.S. Ruoff, Nano Lett. 8, 3498 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    J.F. Dobson, Surf. Sci. 605, 1621 (2011)ADSCrossRefGoogle Scholar
  10. 10.
    D. Drosdoff, L.M. Woods, Phys. Rev. A 84, 062501 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    J.L. Sarabadani, A. Naji, R. Asgari, R. Podgornik, Phys. Rev. B 84, 155407 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    V. Svetovoy, Z. Moktdadir, M. Elwenspoek, H. Mizuta, Europhys. 96, 14006 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    M. Bordag, I.V. Fialkovsky, D.M. Gitman, D.V. Vassilevich, Phys. Rev. B 80, 245406 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    I.V. Fialkovsky, V.N. Marachevsky, D.V. Vassilevich, Phys. Rev B 84, 035446 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    B.E. Sernelius, Europhys. Lett. 95, 57003 (2011)ADSCrossRefGoogle Scholar
  16. 16.
    D. Drosdoff, L.M. Woods, Phys. Rev. B 82, 155459 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    G. Gómez-Santos, Phys. Rev. B 80, 245424 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    J.F. Dobson, A. White, A. Rubio, Phys. Rev. Lett. 96, 073201 (2006)ADSCrossRefGoogle Scholar
  19. 19.
    B.E. Sernelius, J. Phys. A: Math. Gen. 39, 6741 (2006)MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    R. Esquivel-Sirvent, C. Villarreal, W.L. Mochán, A.M. Contreras-Reyes, V.B. Svetovoy, J. Phys. A: Math. Gen. 39, 6323 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    K. Brenner, Y. Yang, R. Murali, Carbon 50, 637 (2012)CrossRefGoogle Scholar
  22. 22.
    Z. Lin, M. Song, D. Ding, Y. Liu, M. Liu, C. Wong, Phys. Chem. Chem. Phys. 14, 3381 (2012)CrossRefGoogle Scholar
  23. 23.
    S.Y. Zhou, G.-H. Gweon, A.V. Fedorov, P.N. First, W.A. De Heer, D.-H. Lee, F. Guinea, A.H. Castro Neto, A. Lanzara, Nat. Mater. 6, 770 (2007)ADSCrossRefGoogle Scholar
  24. 24.
    F. Yavari, C. Kritzinger, C. Gaire, L. Song, H. Gullapalli, T. Borca-Tasciuc, P.M. Ajayan, N. Koratkar, Small 6, 2535 (2010)CrossRefGoogle Scholar
  25. 25.
    D. Haberer, D.V. Vyalikh, S. Taioli, B. Dora, M. Farjam, J. Fink, D. Marchenko, T. Pichler, K. Ziegler, S. Simonucci, M.S. Dresselhaus, M. Knupfer, B. Büchner, A. Grüneis, Nano Lett. 10, 3360 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    L.A. Falkovsky, A.A. Varlamov, Eur. Phys. J. B 56, 281 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    R. Kubo, J. Phys. Soc. Jpn 12, 570 (1957)MathSciNetADSCrossRefGoogle Scholar
  28. 28.
    J. Blinowski, N. Hy Hau, C. Rigaux, J.P. Vieren, R. Le Toullec, G. Furdin, A. Hérold, J. Melin, J. Phys. 41, 47 (1980)CrossRefGoogle Scholar
  29. 29.
    V.M. Marachevsky, J. Phys. A: Math. Theor. 45, 374021 (2012)CrossRefGoogle Scholar
  30. 30.
    F.S.S. Rosa, D.A.R. Dalvit, P.W. Milonni, Phys. Rev. A 78, 03117 (2008)Google Scholar
  31. 31.
    T. Ando, J. Phys. Soc. Jpn 75, 074716 (2006)ADSCrossRefGoogle Scholar
  32. 32.
    Y.V. Churkin, A.B. Fedortsov, G.L. Klimchitskaya, V.A. Yurova, Phys. Rev. B 82, 165433 (2010)ADSCrossRefGoogle Scholar
  33. 33.
    A.O. Caride, G.L. Klimchitskaya, V.M. Mostepanenko, S.I. Zanette, Phys. Rev. A 71, 042901 (2005)ADSCrossRefGoogle Scholar
  34. 34.
    L.P. Pitaevskii, Phys. Rev. Lett. 101, 163202 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    V.B. Svetovoy, Phys. Rev. Lett. 101, 163603 (2008)ADSCrossRefGoogle Scholar
  36. 36.
    H. Ehrenreich, M.H. Cohen, Phys. Rev. 115, 786 (1959)MathSciNetADSzbMATHCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • D. Drosdoff
    • 1
  • A. D. Phan
    • 1
  • L. M. Woods
    • 1
    Email author
  • I. V. Bondarev
    • 2
  • J. F. Dobson
    • 3
  1. 1.Department of PhysicsUniversity of South FloridaTampaUSA
  2. 2.Department of PhysicsNorth Carolina Central UniversityDurhamUSA
  3. 3.Micro and Nanotechnology CentreGriffith UniversityNathanAustralia

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