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Scattering in graphene with impurities: A low energy effective theory

  • Mesoscopic and Nanoscale Systems
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Abstract

We analyze the scattering sector of the Hamiltonians for both gapless and gapped graphene in the presence of a charge impurity using the 2D Dirac equation, which is applicable in the long wavelength limit. We show that for certain range of the system parameters, the combined effect of the short range interactions due to the charge impurity can be modelled using a single real parameter appearing in the boundary conditions. The phase shifts and the scattering matrix depend explicitly on this parameter. We argue that this parameter for graphene can be fixed empirically, through measurements of observables that depend on the scattering data.

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References

  1. K.S. Novoselov, D. Jiang, F. Schedin, T.J. Booth, V.V. Khotkevich, S.M. Morozov, A.K. Geim, PNAS 102, 10451 (2005)

    Article  ADS  Google Scholar 

  2. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)

    Article  ADS  Google Scholar 

  3. G.W. Semenoff, Phys. Rev. Lett. 53, 2449 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  4. V.M. Pereira, J. Nilsson, A.H. Castro Neto, Phys. Rev. Lett. 99, 166802 (2007)

    Article  ADS  Google Scholar 

  5. A.V. Shytov, M.I. Katsnelson, L.S. Levitov, Phys. Rev. Lett. 99, 236801 (2007)

    Article  ADS  Google Scholar 

  6. A.V. Shytov, M.I. Katsnelson, L.S. Levitov, Phys. Rev. Lett. 99, 246802 (2007)

    Article  ADS  Google Scholar 

  7. Kumar S. Gupta, Siddhartha Sen, Mod. Phys. Lett. A 24, 99 (2009)

    Article  MATH  ADS  Google Scholar 

  8. V.R. Khalilov, C.L. Ho, Mod. Phys. Lett. A 13, 615 (1998)

    Article  ADS  Google Scholar 

  9. D.S. Novikov, Phys. Rev. B 76, 245435 (2007)

    Article  ADS  Google Scholar 

  10. V.M. Pereira, V.N. Kotov, A.H. Castro Neto, Phys. Rev. B 78, 085101 (2008)

    Article  ADS  Google Scholar 

  11. V.N. Kotov, V.M. Pereira, B. Uchoa, Phys. Rev. B 78, 075433 (2008)

    Article  ADS  Google Scholar 

  12. Kumar S. Gupta, Siddhartha Sen, Phys. Rev. B 78, 205429 (2008)

    Article  ADS  Google Scholar 

  13. R. Jackiw, Diverse Topics in Theoretical and Mathematical Physics, Beg Memorial Volume, p. 35–53

  14. P. de Sousa Gerbert, Phys. Rev. D 40, 1346 (1989)

    Article  Google Scholar 

  15. P. de Sousa Gerbert, R. Jackiw, Commun. Math. Phys. 124, 229 (1989)

    Article  MATH  ADS  Google Scholar 

  16. H. Falomir, P.A.G. Pisani, J. Phys. A 34, 4143 (2001)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. S.P. Gavrilov, D.M. Gitman, A.A. Smirnov, Eur. Phys. J. direct C 30, 009 (2003)

    Google Scholar 

  18. B.L. Voronov, D.M. Gitman, I.V. Tyutin, Theor. Math. Phys. 150, 34 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  19. C. Manuel, R. Tarrach, Phys. Lett. B 328, 113 (1994)

    Article  ADS  Google Scholar 

  20. Giovanni Amelino-Camelia, Dongsu Bak, Phys. Lett. B 343, 231 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  21. Pulak Ranjan Giri, Kumar S. Gupta, S. Meljanac, A. Samsarov, Phys. Lett. A 372, 2967 (2008)

    Article  ADS  Google Scholar 

  22. B. Basu-Mallick, Pijush K. Ghosh, Kumar S. Gupta, Nucl. Phys. B 659, 437 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  23. B. Basu-Mallick, Pijush K. Ghosh, Kumar S. Gupta, Phys. Lett. A 311, 87 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  24. S. Meljanac, A. Samsarov, B. Basu-Mallick, Kumar S. Gupta, Eur. Phys. J. C 49, 875 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  25. B. Basu-Mallick, Kumar S. Gupta, S. Meljanac, A. Samsarov, Eur. Phys. J. C 58, 159 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  26. Y.A. Sitenko, N.D. Vlasii, Nucl. Phys. B 787 [FS], 241 (2007)

    Article  MATH  ADS  Google Scholar 

  27. Y.A. Sitenko, N.D. Vlasii, arXiv:0808.1676 [cond-mat.str-el]

  28. M.I. Katsnelson, K.S. Novoselov, Solid State Commun. 143, 3 (2007)

    Article  ADS  Google Scholar 

  29. M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Table (Dover Publications, New York, 1974)

    Google Scholar 

  30. M. Reed, B. Simon, Methods of Modern Mathematical Physics (Academic Press, New York, 1972), Vol. 2

    MATH  Google Scholar 

  31. T.O. Wehling, M.I. Katsnelson, A.I. Lichtenstein, Chem. Phys. Lett. 476, 125 (2009)

    Article  ADS  Google Scholar 

  32. A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)

    Article  ADS  Google Scholar 

  33. A. Moroz, Phys. Lett. B 358, 305 (1995)

    Article  MathSciNet  ADS  Google Scholar 

  34. D.-H. Lin, Jour. Math. Phys. 47, 042302 (2006)

    Article  ADS  Google Scholar 

  35. J. Gonzalez, F. Guinea, M.A.H. Vozmediano, Phys. Rev. B 59, R2474 (1999)

    Article  ADS  Google Scholar 

  36. M.I. Katsnelson, Phys. Rev. B 74, 201401(R) (2006)

    Article  ADS  Google Scholar 

  37. R.R. Biswas, S. Sachdev, D.T. Son, Phys. Rev. B 76, 205122 (2007)

    Article  ADS  Google Scholar 

  38. M.M. Fogler, D.S. Novikov, B.I. Shklovskii, Phys. Rev. B 76, 233402 (2007)

    Article  ADS  Google Scholar 

  39. I.S. Terekhov, A.I. Milstein, V.N. Kotov, O.P. Sushkov, Phys. Rev. Lett. 100, 076803 (2008)

    Article  ADS  Google Scholar 

  40. H.P. Dahal, A.V. Balatsky, J.-X. Zhu, Phys. Rev. B 77, 115114 (2008)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta, 700064, India

    K. S. Gupta

  2. Rudjer Bošković Institute, Bijenička c.54, HR-10002, Zagreb, Croatia

    A. Samsarov

  3. School of Mathematical Sciences, UCD, Belfield, Dublin 4, Dublin, Ireland

    S. Sen

  4. Department of Theoretical Physics, Indian Association for the Cultivation of Science, 700032, Calcutta, India

    S. Sen

Authors
  1. K. S. Gupta
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  2. A. Samsarov
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  3. S. Sen
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Correspondence to A. Samsarov.

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Gupta, K., Samsarov, A. & Sen, S. Scattering in graphene with impurities: A low energy effective theory. Eur. Phys. J. B 73, 389–404 (2010). https://doi.org/10.1140/epjb/e2010-00001-2

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  • DOI: https://doi.org/10.1140/epjb/e2010-00001-2

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