Skip to main content

Quantum Hall Conductivity in Degenerate Electron Gas in Graphene-Like System

  • Conference paper
  • First Online:
Proceedings of 28th National Conference on Condensed Matter Physics

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 269))

  • 271 Accesses

Abstract

Hall electrical conductivity is studied with relaxation time approximation based kinetic theory framework for metallic and graphene-like cases within a strong magnetic field-limit. A simple inversely proportional dependence on magnetic field in classical case is transformed to a complex field-dependent counterpart due to Landau quantization for quantum case. The order of magnitude of normalized conductivity is compared with the corresponding experimental values of graphene systems, which can be reduced to the order of \({e}^{2}/h\) due to quantum Hall effect.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. E. Hall, On a new action of the magnet on electric currents. Am. J. Math. 2(3), 287–292 (1879)

    Article  MathSciNet  Google Scholar 

  2. K. v Klitzing, G. Dorda, M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized hall resistance. Phys. Rev. Lett. 45, 494 (1980)

    Google Scholar 

  3. 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, 197–200 (2005)

    Article  ADS  Google Scholar 

  4. K.S. Novoselov et al., Science 315, 1379 (2007)

    Article  ADS  Google Scholar 

  5. B.N. Narozhny, Electronic hydrodynamics in graphene, Ann. Phys. 411, 167979 (2019)

    Google Scholar 

  6. B.N. Narozhny, I.V. Gornyi, M. Titov, M. Schutt, A.D. Mirlin, Hydrodynamics in graphene: linear-response transport. Phys. Rev. B 91, 035414 (2015)

    Google Scholar 

  7. A. Lucas, K. Chung Fong, Hydrodynamics of electrons in grapheme. J. Phys.: Condens. Matter 30, 053001 (2018)

    Google Scholar 

  8. B.N. Narozhny, M. Schutt, Magnetohydrodynamics in graphene: shear and Hall viscosities. Phys. Rev. B 100, 035125 (2019)

    Google Scholar 

  9. M. Muller, L. Fritz, S. Sachdev, Quantum-critical relativistic magnetotransport in grapheme. Phys. Rev. B 78, 115406 (2008).

    Google Scholar 

  10. A. Bandyopadhyay, S. Ghosh, R.L.S. Farias, J. Dey, G. Krein, Anisotropic electrical conductivity of magnetized hot quark matter. Phys. Rev. D 102, 114015 (2020)

    Google Scholar 

  11. S. Samanta, J. Dey, S. Satapathy, S. Ghosh, Quantum expression of electrical conductivity from massless quark matter to hadron resonance gas in presence of magnetic field (2020), arXiv:2002.04434

    Google Scholar 

  12. D. Tong, Lectures on the quantum hall effect, arXiv:1606.06687 [hep-th]

  13. C. Hwang, D. Siegel, SK. Mo, Fermi velocity engineering in graphene by substrate modification. Sci Rep. 2, 590 (2012)

    Google Scholar 

  14. S. Stankovich et al., Graphene-based composite materials. Nature 442, 282–286 (2006)

    Article  ADS  Google Scholar 

  15. M.A. Worsley et al., Synthesis of graphene aerogel with high electrical conductivity. J. Am. Chem. Soc. 132(40), 14067–14069 (2010)

    Article  Google Scholar 

  16. Z.H. Tang et al., Chem. Int. Ed. 49, 4603 (2010)

    Google Scholar 

  17. Y. Xu, K. Sheng, C. Li, G. Shi, ACS Nano 4, 4324 (2010)

    Article  Google Scholar 

  18. Z.S. Wu et al., ACS Nano 3, 411 (2009)

    Article  Google Scholar 

  19. J. Xi, M. Long, L. Tang, D. Wanga, Z. Shuai, First-principles prediction of charge mobility in carbon and organic nanomaterials. Nanoscale 4, 4348–4369 (2012)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Authors T.D and J.D acknowledge MHRD for PhD fellowships.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Debakeenandan Pradhan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Pradhan, D., Das, T., Tamang, A., Dey, J., Ghosh, S., Vempati, S. (2021). Quantum Hall Conductivity in Degenerate Electron Gas in Graphene-Like System. In: Nair, R.G., Seban, L., Ningthoukhongjam, P. (eds) Proceedings of 28th National Conference on Condensed Matter Physics. Springer Proceedings in Physics, vol 269. Springer, Singapore. https://doi.org/10.1007/978-981-16-5407-7_24

Download citation

  • DOI: https://doi.org/10.1007/978-981-16-5407-7_24

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-5406-0

  • Online ISBN: 978-981-16-5407-7

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics