Skip to main content
SpringerLink
Log in

Size quantization in planar graphene-based heterostructures: Pseudospin splitting, interface states, and excitons

  • Electronic Properties of Solid
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

A planar quantum-well device made of a gapless graphene nanoribbon with edges in contact with gapped graphene sheets is examined. The size-quantization spectrum of charge carriers in an asymmetric quantum well is shown to exhibit a pseudospin splitting. Interface states of a new type arise from the crossing of dispersion curves of gapless and gapped graphene materials. The exciton spectrum is calculated for a planar graphene quantum well. The effect of an external electric field on the exciton spectrum is analyzed.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. Dubonos, I. Grogorieva, and A. Firsov, Science (Washington) 306, 666 (2004).

    Article  ADS  Google Scholar 

  2. 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 (London) 438, 197 (2005).

    Article  ADS  Google Scholar 

  3. Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Nature (London) 438, 201 (2005).

    Article  ADS  Google Scholar 

  4. S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, Phys. Rev. Lett. 100, 016602 (2008).

    Article  ADS  Google Scholar 

  5. X. Du, I. Skachko, A. Barker, and E. Y. Andrei, Nat. Nanotechnol. 3, 491 (2008).

    Article  ADS  Google Scholar 

  6. L. Brey and H. A. Fertig, Phys. Rev. B: Condens. Matter 73, 235411 (2006).

    Article  ADS  Google Scholar 

  7. L. Brey and H. A. Fertig, Phys. Rev. B: Condens. Matter 75, 125434 (2007).

    Article  ADS  Google Scholar 

  8. Y.-W. Son, M. L. Cohen, and S. G. Louie, Phys. Rev. Lett. 97, 216803 (2006).

    Article  ADS  Google Scholar 

  9. R. Saito, G. Dresselhaus, and M. S. Dresselhaus, Physical Properties of Carbon Nanotubes (Imperial College Press, London, 1998).

    Book  Google Scholar 

  10. T. Ando, J. Phys. Soc. Jpn. 74, 777 (2005).

    Article  ADS  MATH  Google Scholar 

  11. X. Wang, Y. Ouyang, X. Li, H. Wang, J. Guo, and H. Dai, Phys. Rev. Lett. 100, 206803 (2008).

    Article  ADS  Google Scholar 

  12. L. A. Ponomarenko, F. Schedin, M. I. Katsnelson, R. Yang, E. W. Hill, K. S. Novoselov, and A. K. Geim, Science (Washington) 320, 356 (2008).

    Article  ADS  Google Scholar 

  13. G. Giovannetti, P. A. Khomyakov, G. Brocks, P. J. Kelly, and J. van den Brink, Phys. Rev. B: Condens. Matter 76, 073103 (2007).

    Article  ADS  Google Scholar 

  14. A. Mattausch and O. Pankratov, Phys. Rev. Lett. 99, 076802 (2007).

    Article  ADS  Google Scholar 

  15. S. Y. Zhou, G.-H. Gweon, A. V. Fedorov, P. N. First, W. A. de Heer, D.-H. Lee, F. Guinea, A. H. Castro Neto, and A. Lanzara, Nat. Mater. 6, 770 (2007).

    Article  ADS  Google Scholar 

  16. D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim, and K. S. Novoselov, Science (Washington) 323, 610 (2009).

    Article  ADS  Google Scholar 

  17. S. Lebegue, M. Klintenberg, O. Eriksson, and M. I. Katsnelson, Phys. Rev. B: Condens. Matter 79, 245117 (2009).

    Article  ADS  Google Scholar 

  18. I. Zanella, S. Guerini, S. B. Fagan, J. M. Filho, and A. G. S. Filho, Phys. Rev. B: Condens. Matter 77, 073404 (2008).

    Article  ADS  Google Scholar 

  19. S. Marchini, S. Günther, and J. Witterlin, Phys. Rev. B: Condens. Matter 76, 075429 (2007).

    Article  ADS  Google Scholar 

  20. D. Martoccia, P. R. Willmon, T. Brugger, M. Björck, S. Günther, C. M. Schlepütz, A. Cervellino, S. A. Pauli, B. D. Patterson, S. Marchini, J. Wintterlin, W. Moritz, and T. Greber, Phys. Rev. Lett. 101, 126102 (2008).

    Article  ADS  Google Scholar 

  21. I. Pletikosić, M. Kralj, P. Pervan, R. Brako, J. Coraux, A. T. N’Diaye, C. Busse, and T. Michely, Phys. Rev. Lett. 102, 056808 (2009).

    Article  ADS  Google Scholar 

  22. M. Y. Han, B. Özyilmaz, Y. Zhang, and P. Kim, Phys. Rev. Lett. 98, 206805 (2007).

    Article  ADS  Google Scholar 

  23. L. E. Vorob’ev, E. L. Ivchenko, D. A. Firsov, and V. A. Shalygin, Optical Properties of Nanostructures (Nauka, St. Petersburg, 2001) [in Russian].

    Google Scholar 

  24. P. V. Ratnikov and A. P. Silin, Kratk. Soobshch. Fiz., No. 2, 11 (2009).

  25. B. G. Idlis and M. Sh. Usmanov, Sov. Phys. Semicond. 26(2), 186 (1992).

    Google Scholar 

  26. A. I. Akhiezer and V. B. Berestetskii, Quantum Electrodynamics (Wiley, New York, 1965; Nauka, Moscow, 1969).

    Google Scholar 

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

    Article  ADS  Google Scholar 

  28. Yu. E. Lozovik, S. P. Merkulova, and A. A. Sokolik, Phys.—Usp. 51(7), 727 (2008).

    ADS  Google Scholar 

  29. S. S. Schweber, An Introduction to Relativistic Quantum Field Theory (Harper and Row, New York, 1961; Inostrannaya Literatura, Moscow, 1963).

    Google Scholar 

  30. A. M. Tsvelik, Quantum Field Theory in Condensed Matter Physics (Fizmatlit, Moscow, 2002; Cambridge University Press, Cambridge, 2007).

    Google Scholar 

  31. T. W. Appelquist, M. Bowick, D. Karabali, and L. C. R. Wijewardhana, Phys. Rev. D: Part. Fields 33, 3704 (1986).

    Article  ADS  Google Scholar 

  32. B. A. Volkov, B. G. Idlis, and M. Sh. Usmanov, Phys.—Usp. 38(7), 761 (1995).

    Article  ADS  Google Scholar 

  33. A. V. Kolesnikov and A. P. Silin, JETP 82(6), 1145 (1996).

    ADS  Google Scholar 

  34. A. V. Kolesnikov and A. P. Silin, J. Phys.: Condens. Matter 9, 10929 (1997).

    Article  ADS  Google Scholar 

  35. A. P. Silin and S. V. Shubenkov, Phys. Solid State 40(7), 1223 (1998).

    Article  ADS  Google Scholar 

  36. E. A. Andryushin, Sh. U. Nutsalov, and A. P. Silin, Phys. Low-Dimens. Struct. 7/8, 85 (1999).

    Google Scholar 

  37. E. A. Andryushin, S. A. Vereshchagin, and A. P. Silin, Kratk. Soobshch. Fiz., No. 6, 21 (1999).

  38. E. A. Andryushin, A. P. Silin, and S. A. Vereshchagin, Phys. Low-Dimens. Struct. 3/4, 85 (2000).

    Google Scholar 

  39. E. A. Andryushin, Sh. U. Nutsalov, and A. P. Silin, Kratk. Soobshch. Fiz., No. 3, 3 (2001).

  40. P. V. Ratnikov and A. P. Silin, Kratk. Soobshch. Fiz., No. 11, 22 (2005).

  41. A. Rycerz, J. Tworzydło, and C. W. J. Beenakker, Nat. Phys. 3, 172 (2007).

    Article  Google Scholar 

  42. J. Tworzydo, I. Snyman, A. R. Akhmerov, and C. W. J. Beenakker, Phys. Rev. B: Condens. Matter 76, 035411 (2007).

    Article  ADS  Google Scholar 

  43. A. R. Akhmerov and C. W. J. Beenakker, Phys. Rev. Lett. 98, 157003 (2007).

    Article  ADS  Google Scholar 

  44. D. Xiao, W. Yao, and Q. Niu, Phys. Rev. Lett. 93, 236809 (2007).

    Article  ADS  Google Scholar 

  45. Z. Z. Zhang, K. Chang, and K. S. Chan, Appl. Phys. Lett. 93, 062106 (2008).

    Article  ADS  Google Scholar 

  46. J. L. Carcia-Pomar, A. Cortijo, and M. Nieto-Vesperinas, Phys. Rev. Lett. 100, 236801 (2008).

    Article  ADS  Google Scholar 

  47. J. M. Pereira, Jr., F. M. Peeters, R. N. Costa Filho, and G. A. Farias, J. Phys.: Condens. Matter 21, 045301 (2009).

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  49. D. A. Abanin, P. A. Lee, and L. S. Levitov, Phys. Rev. Lett. 96, 176803 (2006).

    Article  ADS  Google Scholar 

  50. T. M. Rice, J. C. Hensel, T. G. Phillips, and G. A. Thomas, The Electron-Hole Liquid in Semiconductors: Theoretical Aspects (Academic, New York, 1977; Mir, Moscow, 1980).

    Google Scholar 

  51. I. E. Tamm, Phys. Z. Sowjetunion 1, 733 (1932).

    MATH  Google Scholar 

  52. S. G. Tikhodeev, JETP Lett. 53(3), 171 (1991).

    ADS  Google Scholar 

  53. S. G. Tikhodeev, Solid State Commun. 78, 339 (1991).

    Article  ADS  Google Scholar 

  54. A. V. Kolesnikov, R. Lipperheide, A. P. Silin, and U. Wille, Europhys. Lett. 43, 331 (1998).

    Article  ADS  Google Scholar 

  55. E. A. Andryushin, A. P. Silin, and S. A. Vereshchagin, Phys. Low-Dimens. Struct. 3/4, 79 (2000).

    Google Scholar 

  56. P. V. Ratnikov and A. P. Silin, Phys. Solid State 52(8), 1763 (2010).

    Article  ADS  Google Scholar 

  57. A. A. Abrikosov, J. Low Temp. Phys. 2, 37 (1970).

    Article  ADS  Google Scholar 

  58. S. A. Brazovskii, Sov. Phys. JETP 35, 433 (1972).

    ADS  Google Scholar 

  59. T. Ando, J. Phys. Soc. Jpn. 66, 1066 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  60. V. S. Babichenko, L. V. Keldysh, and A. P. Silin, Sov. Phys. Solid State 22(4), 723 (1980).

    Google Scholar 

  61. Yu. E. Lozovik and V. I. Yudson, Phys. Lett. A 56, 393 (1976).

    Article  ADS  Google Scholar 

  62. L. V. Keldysh, JETP Lett. 29(11), 658 (1979).

    ADS  Google Scholar 

  63. R. Loudon, Am. J. Phys. 27, 649 (1959).

    Article  ADS  Google Scholar 

  64. A. Dalgarno and J. T. Lewis, Proc. R. Soc. London, Ser. A 233, 70 (1955).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. D. A. B. Miller, D. C. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, Phys. Rev. Lett. 53, 2173 (1984).

    Article  ADS  Google Scholar 

  66. D. Graf, F. Molitor, K. Ensslin, C. Stampfer, A. Jungen, C. Hierold, and L. Wirtz, Nano Lett. 7, 238 (2007).

    Article  ADS  Google Scholar 

  67. Z. H. Ni, W. Chen, X. F. Fan, J. L. Kuo, T. Yu, A. T. S. Wee, and Z. X. Shen, Phys. Rev. B: Condens. Matter 77, 115416 (2008).

    Article  ADS  Google Scholar 

  68. A. C. Ferrari, J. C. Meyer, V. Scardaci, C. Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim, Phys. Rev. Lett. 97, 187401 (2006).

    Article  ADS  Google Scholar 

  69. I. Calizo, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, Nano Lett. 7, 2645 (2007).

    Article  ADS  Google Scholar 

  70. A. P. Silin and S. A. Vereshchagin, Phys. Low-Dimens. Struct. 9/10, 115 (2001).

    Google Scholar 

  71. Yu. A. Bychkov and E. I. Rashba, JETP Lett. 39(2), 78 (1984).

    ADS  Google Scholar 

  72. Yu. A. Bychkov and E. I. Rashba, J. Phys. C: Solid State Phys. 17, 6039 (1984).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991, Russia

    P. V. Ratnikov & A. P. Silin

Authors
  1. P. V. Ratnikov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. P. Silin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to P. V. Ratnikov.

Additional information

Original Russian Text © P.V. Ratnikov, A.P. Silin, 2012, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2012, Vol. 141, No. 3, pp. 582–601.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ratnikov, P.V., Silin, A.P. Size quantization in planar graphene-based heterostructures: Pseudospin splitting, interface states, and excitons. J. Exp. Theor. Phys. 114, 512–528 (2012). https://doi.org/10.1134/S1063776112020094

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776112020094

Keywords

Search

Navigation