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Quantum kinetic equations of the system “graphene + dimensionally quantized film”

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Abstract

We consider the problem of epitaxial graphene formed on a dimensionally quantized film. We give a microscopic derivation of the quantum kinetic equations for the system “graphene + dimensionally quantized film.” Based on the obtained equations, we investigate the features of electron states of the system under consideration and obtain analytic expressions for the transferred charge in this system.

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References

  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Science, 306, 666–669 (2004); arXiv:cond-mat/0410550v1 (2004).

    Article  ADS  Google Scholar 

  2. K. S. Novoselov, D. Jiang, F. Schedin, T. J. Booth, V. V. Khotkevich, S. V. Morozov, and A. K. Geim, Proc. Natl. Acad. Sci. USA, 102, 10451–10453 (2005); arXiv:cond-mat/0503533v1 (2005).

    Article  ADS  Google Scholar 

  3. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Nature, 438, 197–200 (2005).

    Article  ADS  Google Scholar 

  4. A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Modern Phys., 81, 109–162 (2009); arXiv:0709.1163v2 [cond-mat.other] (2007).

    Article  ADS  Google Scholar 

  5. Yu. E. Lozovik, S. P. Merkulova, and A. A. Sokolik, Phys. Usp., 51, 727–744 (2008).

    ADS  Google Scholar 

  6. M. Hongki, R. Bistritzer, J-J. Su, and A. H. MacDonald, Phys. Rev. B, 78, 121401(R) (2008); arXiv:0802.3462v2 [cond-mat.mes-hall] (2008).

    ADS  Google Scholar 

  7. M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Nature Phys., 2, 620–625 (2006); arXiv:cond-mat/0604323v2 (2006).

    Article  ADS  Google Scholar 

  8. C. W. J. Beenakker, Rev. Modern Phys., 80, 1337–1354 (2008); arXiv:0710.3848v2 [cond-mat.mes-hall] (2007).

    Article  ADS  Google Scholar 

  9. G. Giovannetti, P. A. Khomyakov, G. Brocks, V. M. Karpan, J. van den Brink, and P. J. Kelly, Phys. Rev. Lett., 101, 026803 (2008); arXiv:0802.2267v3 [cond-mat.mtrl-sci] (2008).

    Article  ADS  Google Scholar 

  10. P. A. Khomyakov, G. Giovannetti, P. C. Rusu, J. van den Brink, and P. J. Kelly, Phys. Rev. B., 79, 195425 (2009); arXiv:0902.1203v1 [cond-mat.mtrl-sci] (2009).

    Article  ADS  Google Scholar 

  11. P. A. Khomyakov, A. A. Starikov, G. Brocks, and P. J. Kelly, Phys. Rev. B, 82, 115437 (2010); arXiv: 0911.2027v3 [cond-mat.mtrl-sci] (2009).

    Article  ADS  Google Scholar 

  12. M. Vanin, J. J. Mortensen, A. K. Kelkkanen, J. M. Garcia-Lastra, K. S. Thygesen, and K. W. Jacobsen, “Graphene on metals: A Van der Waals density functional study,” arXiv:0912.3078v1 [cond-mat.mes-hall] (2009).

  13. S. Yu. Davydov, Tech. Phys. Lett., 37, 476–477.

  14. S. Yu. Davydov, Semiconductors, 45, 618–622.

  15. S. Yu. Davydov, Semiconductors, 45, 1070–1076.

  16. P. W. Anderson, Phys. Rev., 124, 41–53 (1961).

    Article  MathSciNet  ADS  Google Scholar 

  17. D. M. Newns, Phys. Rev., 178, 1123–1135 (1969).

    Article  ADS  Google Scholar 

  18. F. D. M. Haldane and P. W. Anderson, Phys. Rev. B., 13, 2553–2559 (1976).

    Article  ADS  Google Scholar 

  19. R. P. Meilanov, B. A. Abramova, M. M. Gadzhialiev, and V. V. Dzhabrailov, Phys. Solid State, 44, 2196–2199 (2002).

    Article  ADS  Google Scholar 

  20. R. P. Meilanov, B. A. Abramova, G. M. Musaev, and M. M. Gadzhialiev, Phys. Solid State, 46, 1107–1109 (2004); R. P. Meilanov and B. A. Abramova, Phys. Solid State, 50, 133–138 (2008).

    Article  ADS  Google Scholar 

  21. Yu. E. Lozovik and S. Yu. Volkov, Phys. Solid State, 45, 364–368 (2003).

    Article  ADS  Google Scholar 

  22. R. Z. Vitlina and A. V. Chaplik, JETP Lett., 78, 651–653 (2003).

    Article  ADS  Google Scholar 

  23. Z. Z. Alisultanov and R. P. Meilanov, Phys. Solid State, 54, 1486–1493 (2012).

    Article  ADS  Google Scholar 

  24. L. P. Kadanoff and G. Baym, Quantum Statistical Mechanics: Green’s Function Methods in Equilibrium and Nonequilibrium Problems, Benhamin, New York (1962).

    Google Scholar 

  25. R. P. Meilanov, Poverkhnost’ Fiz. Khim. Mekh., 3, 52 (1999).

    Google Scholar 

  26. D. C. Langreth and P. Nordlander, Phys. Rev. B, 43, 2541–2557 (1991).

    Article  ADS  Google Scholar 

  27. A. S. Kondrat’ev and A. E. Kuchma, Electron Fermi Liquid of Normal Metals [in Russian], Leningrad State Univ. Press, Leningrad (1980).

    Google Scholar 

  28. L. Kong et al., J. Phys. Chem. C, 114, 21618–21524 (2010).

    Article  Google Scholar 

  29. J. González, F. Guinea, and M. A. H. Vozmediano, Nucl. Phys. B, 424, 595–618 (1994).

    Article  ADS  Google Scholar 

  30. J. González, F. Guinea, and M. A. H. Vozmediano, Phys. Rev. B, 59, R2474–R2477 (1999); arXiv:cond-mat/9807130v1 (1998).

    Article  ADS  Google Scholar 

  31. D. C. Elias, R. V. Gorbachev, A. S. Mayorov, S. V. Morozov, A. A. Zhukov, P. Blake, L. A. Ponomarenko, I. V. Grigorieva, K. S. Novoselov, F. Guinea, and A. K. Geim, Nature Physics, 7, 701–704 (2011); arXiv: 1104.1396v2 [cond-mat.mes-hall] (2011).

    Article  ADS  Google Scholar 

  32. N. Garcia, P. Esquinazi, and A. A. Pasa, “Comment on “Dirac cones reshaped by interaction effects in suspended graphene” by Elias et al., Nature Physics 7, 701 (2011),” arXiv:1110.2601v2 [cond-mat.str-el] (2011).

    Google Scholar 

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Authors and Affiliations

  1. Prokhorov General Physics Institute, RAS, Moscow, Russia

    Z. Z. Alisultanov

  2. Institute for Geothermal Problems, Daghestan Science Center, RAS, Makhachkala, Russia

    R. P. Meilanov

Authors
  1. Z. Z. Alisultanov
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  2. R. P. Meilanov
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Correspondence to Z. Z. Alisultanov.

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__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 172, No. 3, pp. 454–467, September, 2012.

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Alisultanov, Z.Z., Meilanov, R.P. Quantum kinetic equations of the system “graphene + dimensionally quantized film”. Theor Math Phys 172, 1278–1288 (2012). https://doi.org/10.1007/s11232-012-0113-7

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  • DOI: https://doi.org/10.1007/s11232-012-0113-7

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