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Graphene Quantum Dots pp 91–110Cite as

Electron–Electron Interactions in Graphene Quantum Dots

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Part of the book series: NanoScience and Technology ((NANO))

Abstract

This chapter introduces the problem of electron–electron interactions, briefly describes several methods and their application to graphene quantum dots. The Hubbard model, the mean-field Hartree-Fock method, the Density Functional Theory and the configuration interaction (CI) method are introduced and applied to graphene quantum dots.

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References

  1. G.D. Mahan, Many-Particle Physics (Plenum Press, New York, 1990)

    Book  Google Scholar 

  2. J.J. Quinn, K.-S. Yi, Solid State Physics: Principles and Modern Applications (Springer, Heidelberg, 2009)

    Google Scholar 

  3. G. Giuliani, G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2008)

    Google Scholar 

  4. P. Hawrylak, Phys. Rev. Lett. 59, 485 (1987)

    Article  ADS  Google Scholar 

  5. P. Hawrylak, S. Das Sarma, Advances in studies of electrons in low dimensional structures. Solid State Commun. 127, 753 (2003)

    Article  ADS  Google Scholar 

  6. P. Hawrylak, M. Korkusinski, Electronic and optical properties of self-assembled quantum dots, in Single Quantum Dots: Fundamentals, Applications, and New Concepts, vol. 90, Topics in Applied Physics, ed. by P. Michler (Springer, Heidelberg, 2003), pp. 25–92

    Chapter  Google Scholar 

  7. C.-Y. Hsieh, Y.P. Shim, M. Korkusinski, P. Hawrylak, Physics of triple quantum dot molecule with controlled electron numbers. Rep. Prog. Phys. 75, 114501 (2012)

    Article  Google Scholar 

  8. G. Dresselhaus, M.S. Dresselhaus, Adv. Phys. 30(2), 139–326 (1981)

    Article  ADS  Google Scholar 

  9. K. Shung, Phys. Rev. B 34, 979993 (1986)

    Google Scholar 

  10. P. Hawrylak, Solid State Commun. 63, 241 (1987)

    Article  ADS  Google Scholar 

  11. 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 

  12. S. Das Sarma, S. Adam, E.H. Hwang, E. Rossi, Rev. Mod. Phys. 83, 407 (2011)

    Article  ADS  Google Scholar 

  13. V.N. Kotov, B. Uchoa, V.M. Pereira, F. Guinea, A.H. Castro Neto, Rev. Mod. Phys. 84, 10671125 (2012)

    Article  Google Scholar 

  14. M.A.H. Vozmediano, F. Guinea, Phys. Scr. T146, 014015 (2012)

    Article  ADS  Google Scholar 

  15. M.I. Katsnelson, Graphene: Carbon in Two Dimensions (Cambridge University Press, Cambridge, 2012)

    Book  Google Scholar 

  16. A.H. MacDonald, J. Jung, F. Zhang, Phys. Scr. T146, 014012 (2012)

    Article  ADS  Google Scholar 

  17. A. Hideo, D. Mildred (eds.), Physics of Graphene (Springer, Heidelberg, 2014)

    Google Scholar 

  18. L.E.F. Foa Torres, S. Roche, J.C. Charlier, Introduction to Graphene Based Nanomaterials: From Electronic Structure to Quantum Transport (Cambridge University Press, Cambridge, 2014)

    Google Scholar 

  19. C. Wang, D. Wong, A.V. Shytov, V.W. Brar, S. Choi, Q. Wu, H.-Z. Tsai, W. Regan, A. Zettl, R.K. Kawakami, S.G. Louie, L.S. Levitov, M.F. Crommie, Science 340, 734 (2013)

    Article  ADS  Google Scholar 

  20. C. Toke, P.E. Lammert, V.H. Crespi, J.K. Jain, Phys. Rev. B 74, 235417 (2006)

    Article  ADS  Google Scholar 

  21. V.M. Apalkov, T. Chakraborty, Phys. Rev. Lett. 97, 126801 (2006)

    Article  ADS  Google Scholar 

  22. N. Shibata, K. Nomura, J. Phys. Soc. Jpn. 78, 104708 (2009)

    Article  ADS  Google Scholar 

  23. L. Yang, M.L. Cohen, S.G. Louie, Nano Lett. 7, 3112 (2007)

    Article  ADS  Google Scholar 

  24. T. Wassmann, A.P. Seitsonen, A.M. Saitta, M. Lazzeri, F. Mauri, Phys. Rev. Lett. 101, 096402 (2008)

    Article  ADS  Google Scholar 

  25. P. Koskinen, S. Malola, H. Häkkinen, Phys. Rev. Lett. 101, 115502 (2008)

    Article  ADS  Google Scholar 

  26. K.T. Chan, J.B. Neaton, M.L. Cohen, Phys. Rev. B 77, 235430 (2008)

    Article  ADS  Google Scholar 

  27. H. Sevincli, M. Topsakal, E. Durgun, S. Ciraci, Phys. Rev. B 77, 195434 (2008)

    Article  ADS  Google Scholar 

  28. I. Ozfidan, M. Korkusinski, A.D. Güçlü, J. McGuire P. Hawrylak, Phys. Rev. B 89, 085310 (2014)

    Google Scholar 

  29. S. Sorella, E. Tosatti, Europhys. Lett. 19, 699 (1992)

    Article  ADS  Google Scholar 

  30. T.O. Wehling, E. Sasioglu, C. Friedrich, A.I. Lichtenstein, M.I. Katsnelson, S. Blügel, Phys. Rev. Lett. 106, 236805 (2011)

    Article  ADS  Google Scholar 

  31. E.K.U. Gross, E. Runge, O. Heinonen, Many-Particle Physics (Adam Hilger, New York, 1991)

    Google Scholar 

  32. B.J. Ransil, Rev. Mod. Phys. 32, 245 (1960)

    Article  ADS  Google Scholar 

  33. A.D. Güçlü, P. Potasz, O. Voznyy, M. Korkusinski, P. Hawrylak, Phys. Rev. Lett. 103, 246805 (2009)

    Article  ADS  Google Scholar 

  34. P. Potasz, A.D. Güçlü, P. Hawrylak, Phys. Rev. B 82, 075425 (2010)

    Article  ADS  Google Scholar 

  35. P.R. Wallace, Phys. Rev. 71, 622 (1947)

    Article  MATH  ADS  Google Scholar 

  36. J. Hubbard, Proc. R. Soc. Lond. Ser. A 276, 238 (1963)

    Article  ADS  Google Scholar 

  37. K.A. Chao, J. Spałek, A.M. Oleś, J. Phys. C: Solid State Phys. 10, L271 (1977)

    Article  ADS  Google Scholar 

  38. K.A. Chao, J. Spałek, A.M. Oleś, Phys. Rev. B 18, 3453 (1978)

    Article  ADS  Google Scholar 

  39. M. Ezawa, Phys. Rev. B 76, 245415 (2007)

    Article  ADS  Google Scholar 

  40. J. Fernandez-Rossier, J.J. Palacios, Phys. Rev. Lett. 99, 177204 (2007)

    Article  ADS  Google Scholar 

  41. O.V. Yazyev, Phys. Rev. Lett. 101, 037203 (2008)

    Article  ADS  Google Scholar 

  42. P. Hohenberg, W. Kohn, Phys. Rev. 136, B864 (1964)

    Article  MathSciNet  ADS  Google Scholar 

  43. W. Kohn, L.J. Sham, Phys. Rev. 140, A1133–A1138 (1965)

    Article  MathSciNet  ADS  Google Scholar 

  44. O. Voznyy, A.D. Güçlü, P. Potasz, P. Hawrylak, Phys. Rev. B 83, 165417 (2011)

    Article  ADS  Google Scholar 

  45. A. Wensauer, M. Korkusiński, P. Hawrylak, Solid State Commun. 130, 115 (2004)

    Article  ADS  Google Scholar 

  46. C. Lanczos, J. Natl. Bureau Standards 45, 255 (1950)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Physics, Izmir Institute of Technology, Izmir, Turkey

    Alev Devrim Güçlü

  2. Institute of Physics, Wrocław University of Technology, Wrocław, Poland

    Pawel Potasz

  3. Emerging Technologies Division, Quantum Theory Group, National Research Council of Canada, Ottawa, ON, Canada

    Marek Korkusinski

  4. Department of Physics, University of Ottawa, Ottawa, ON, Canada

    Pawel Hawrylak

Authors
  1. Alev Devrim Güçlü
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  2. Pawel Potasz
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  3. Marek Korkusinski
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  4. Pawel Hawrylak
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Corresponding author

Correspondence to Alev Devrim Güçlü .

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Güçlü, A.D., Potasz, P., Korkusinski, M., Hawrylak, P. (2014). Electron–Electron Interactions in Graphene Quantum Dots. In: Graphene Quantum Dots. NanoScience and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44611-9_5

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