Fractional conductivity in 2D and 3D crystals

Regular Article
  • 4 Downloads

Abstract.

In this work, we show that the phenomenon of fractional quantum Hall effect can be obtained for 2D and 3D crystal structures, using the noncommutative nature of spacetime and the Lambert W function. This fractional conductivity has been shown to be a consequence of the noncommutative geometry underlying the structure of graphene. Also, it has been shown, for graphene, that in the 3D case the conductivity is extremely small and depends on the self-energy that arises due to random fluctuations or zitterbewegung.

References

  1. 1.
    D.C. Tsui, H.L. Stormer, A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)ADSCrossRefGoogle Scholar
  2. 2.
    R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)ADSCrossRefGoogle Scholar
  3. 3.
    Michael Levin, Matthew P.A. Fisher, Phys. Rev. B 79, 235315 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    B.G. Sidharth, Abhishek Das, Chaos, Solitons Fractals 96, 85 (2017)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    B.G. Sidharth, Abhishek Das, Int. J. Mod. Phys. A 32, 1750117 (2017)ADSCrossRefGoogle Scholar
  6. 6.
    B.G. Sidharth, Int. J. Theor. Phys. 54, 2382 (2015)CrossRefGoogle Scholar
  7. 7.
    R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth, Adv. Comput. Math. 5, 329 (1996)MathSciNetCrossRefGoogle Scholar
  8. 8.
    S.R. Valluri, D.J. Jeffrey, R.M. Corless, Can. J. Phys. 78, 823 (2000)ADSGoogle Scholar
  9. 9.
    S.R. Valluri, M. Gil, D.J. Jeffrey, Shantanu Basu, J. Math. Phys. 50, 102103 (2009)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    B.G. Sidharth, S.R. Valluri, Int. J. Theor. Phys. 54, 2792 (2015)CrossRefGoogle Scholar
  11. 11.
    Ken Roberts, S.R. Valluri, Can. J. Phys. 95, 105 (2017)ADSCrossRefGoogle Scholar
  12. 12.
    Susanne Mertens, J. Phys.: Conf. Ser. 718, 022013 (2016)Google Scholar
  13. 13.
    J. Bellisard et al., J. Math. Phys. 35, 5373 (1994)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    K. Ziegler, Phys. Rev. B 75, 233407 (2007)ADSCrossRefGoogle Scholar
  15. 15.
    K. Ziegler, Phys. Rev. Lett. 97, 266802 (2006)ADSCrossRefGoogle Scholar
  16. 16.
    R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)ADSCrossRefGoogle Scholar
  17. 17.
    M.I. Katsnelson, Eur. Phys. J. B 51, 157 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    B.G. Sidharth, Int. J. Theor. Phys. 48, 497 (2009)CrossRefGoogle Scholar
  19. 19.
    B.G. Sidharth, Abhishek Das, Arka Roy, Int. J. Theor. Phys. 55, 801 (2016)CrossRefGoogle Scholar
  20. 20.
    P. Krekora, Q. Su, R. Grobe, Phys. Rev. Lett. 93, 043004 (2004)ADSCrossRefGoogle Scholar
  21. 21.
    R. Verma, A.N. Bose, Eur. Phys. J. Plus 132, 220 (2017)CrossRefGoogle Scholar
  22. 22.
    M. Eckstein, N. Franco, T. Miller, Phys. Rev. D 95, 061701(R) (2017)ADSCrossRefGoogle Scholar
  23. 23.
    B.G. Sidharth, Abhishek Das, Gravit. Cosmol. 22, 299 (2016)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.B.M. Birla Science CentreHyderabadIndia
  2. 2.Department of Physics and AstronomyUniversity of Western OntarioLondonCanada

Personalised recommendations