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Fractional conductivity in 2D and 3D crystals

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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.

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References

  1. D.C. Tsui, H.L. Stormer, A.C. Gossard, Phys. Rev. Lett. 48, 1559 (1982)

    Article  ADS  Google Scholar 

  2. R.B. Laughlin, Phys. Rev. Lett. 50, 1395 (1983)

    Article  ADS  Google Scholar 

  3. Michael Levin, Matthew P.A. Fisher, Phys. Rev. B 79, 235315 (2009)

    Article  ADS  Google Scholar 

  4. B.G. Sidharth, Abhishek Das, Chaos, Solitons Fractals 96, 85 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  5. B.G. Sidharth, Abhishek Das, Int. J. Mod. Phys. A 32, 1750117 (2017)

    Article  ADS  Google Scholar 

  6. B.G. Sidharth, Int. J. Theor. Phys. 54, 2382 (2015)

    Article  Google Scholar 

  7. R.M. Corless, G.H. Gonnet, D.E.G. Hare, D.J. Jeffrey, D.E. Knuth, Adv. Comput. Math. 5, 329 (1996)

    Article  MathSciNet  Google Scholar 

  8. S.R. Valluri, D.J. Jeffrey, R.M. Corless, Can. J. Phys. 78, 823 (2000)

    ADS  Google Scholar 

  9. S.R. Valluri, M. Gil, D.J. Jeffrey, Shantanu Basu, J. Math. Phys. 50, 102103 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  10. B.G. Sidharth, S.R. Valluri, Int. J. Theor. Phys. 54, 2792 (2015)

    Article  Google Scholar 

  11. Ken Roberts, S.R. Valluri, Can. J. Phys. 95, 105 (2017)

    Article  ADS  Google Scholar 

  12. Susanne Mertens, J. Phys.: Conf. Ser. 718, 022013 (2016)

    Google Scholar 

  13. J. Bellisard et al., J. Math. Phys. 35, 5373 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  14. K. Ziegler, Phys. Rev. B 75, 233407 (2007)

    Article  ADS  Google Scholar 

  15. K. Ziegler, Phys. Rev. Lett. 97, 266802 (2006)

    Article  ADS  Google Scholar 

  16. R. Kubo, J. Phys. Soc. Jpn. 12, 570 (1957)

    Article  ADS  Google Scholar 

  17. M.I. Katsnelson, Eur. Phys. J. B 51, 157 (2006)

    Article  ADS  Google Scholar 

  18. B.G. Sidharth, Int. J. Theor. Phys. 48, 497 (2009)

    Article  Google Scholar 

  19. B.G. Sidharth, Abhishek Das, Arka Roy, Int. J. Theor. Phys. 55, 801 (2016)

    Article  Google Scholar 

  20. P. Krekora, Q. Su, R. Grobe, Phys. Rev. Lett. 93, 043004 (2004)

    Article  ADS  Google Scholar 

  21. R. Verma, A.N. Bose, Eur. Phys. J. Plus 132, 220 (2017)

    Article  Google Scholar 

  22. M. Eckstein, N. Franco, T. Miller, Phys. Rev. D 95, 061701(R) (2017)

    Article  ADS  Google Scholar 

  23. B.G. Sidharth, Abhishek Das, Gravit. Cosmol. 22, 299 (2016)

    Article  ADS  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. B.M. Birla Science Centre, Adarsh Nagar, 500063, Hyderabad, India

    B. G. Sidharth & Abhishek Das

  2. Department of Physics and Astronomy, University of Western Ontario, N6A3K7, London, Canada

    S. R. Valluri

Authors
  1. B. G. Sidharth
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  2. Abhishek Das
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  3. S. R. Valluri
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Corresponding author

Correspondence to B. G. Sidharth.

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Sidharth, B.G., Das, A. & Valluri, S.R. Fractional conductivity in 2D and 3D crystals. Eur. Phys. J. Plus 133, 145 (2018). https://doi.org/10.1140/epjp/i2018-11965-4

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  • DOI: https://doi.org/10.1140/epjp/i2018-11965-4

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