Single-electron transport through quantum point contact

Regular Article


Here, we employ a numerical approach to investigate the transport and conductance characteristics of a quantum point contact. A quantum point contact is a narrow constriction of a width comparable to the electron wavelength defined in a two-dimensional electron gas (2DEG) by means of split-gate or etching technique. Their properties have been widely investigated in the experiments. In our study, we define a quantum Hall based split-gate quantum point contact with standard gate geometry. Firstly, we obtain the spatial distribution of incompressible strips (current channels) by applying a self consistent Thomas-Fermi method to a realistic heterostructure under quantized Hall conditions. Later, time-dependent Schrödinger equation is solved for electrons injected in the current channels. The transport characteristics and time-evolutions are analyzed in the integer filling factor regime (ν = 1) with the single electron density. The results confirm that the current direction in a realistic quantum point contact can be controllable with the external interventions.


Mesoscopic and Nanoscale Systems 


  1. 1.
    B.J. van Wees, H. van Houten, C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel, C.T. Foxon, Phys. Rev. Lett. 60, 848 (1988)ADSCrossRefGoogle Scholar
  2. 2.
    D.A. Wharam, T.J. Thornton, R. Newbury, M. Pepper, H. Ahmed, J.E.F. Frost, D.G. Hasko, D.C. Peacockt, D.A. Ritchie, G.A.C. Jones, J. Phys. C 21, 209 (1988)ADSCrossRefGoogle Scholar
  3. 3.
    Y. Ji, Y. Chung, D. Sprinzak, M. Heiblum, D. Mahalu, H. Shtrikman, Nature 422, 415 (2003)ADSCrossRefGoogle Scholar
  4. 4.
    I. Neder, M. Heiblum, Y. Levinson, D. Mahalu, V. Umansky, Phys. Rev. Lett. 96, 016804 (2006)ADSCrossRefGoogle Scholar
  5. 5.
    M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986)ADSCrossRefGoogle Scholar
  6. 6.
    B.I. Halperin, Phys. Rev. B 25, 2185 (1982)ADSCrossRefGoogle Scholar
  7. 7.
    K.J. Thomas, J.T. Nicholls, M.Y. Simmons, M. Pepper, D.R. Mace, D.A. Ritchie, Phys. Rev. Lett. 77, 135 (1996)ADSCrossRefGoogle Scholar
  8. 8.
    A. Kristensen et al., Physica B 249, 180 (1998)ADSCrossRefGoogle Scholar
  9. 9.
    A. Siddiki, F. Marquardt, Phys. Rev. B 75, 045325 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    D.B. Chklovskii, B.I. Shklovskii, L.I. Glazman, Phys. Rev. B 46, 4026 (1992)ADSCrossRefGoogle Scholar
  11. 11.
    A. Siddiki, R.R. Gerhardts, Phys. Rev. B 68, 125315 (2003)ADSCrossRefGoogle Scholar
  12. 12.
    A.Siddiki, R.R. Gerhardts, Phys. Rev. B 70, 195335 (2004)ADSCrossRefGoogle Scholar
  13. 13.
    A. Weichselbaum, S.E. Ulloa, Phys. Rev. E 68, 056707 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    S. Arslan, E. Cicek, D. Eksi, S. Aktas, A. Weichselbaum, A. Siddiki, Phys. Rev. B 78, 125423 (2008)ADSCrossRefGoogle Scholar
  15. 15.
    V. Kotimaki, E. Cicek, A. Siddiki, E. Rasanen, New Phys. 14, 053024 (2012)CrossRefGoogle Scholar
  16. 16.
    E. Ahlswede, P. Weitz, J. Weis, K. von Klitzing, K. Eberl, Physica B 298, 562 (2001)ADSCrossRefGoogle Scholar
  17. 17.
    E. Ahlswede, J. Weis, K. von Klitzing, K. Eberl, Physica E 12, 165 (2002)ADSCrossRefGoogle Scholar
  18. 18.
    V. Kotimaki, E. Rasanen, Phys. Rev. B 81, 245316 (2010)ADSCrossRefGoogle Scholar
  19. 19.
    M.A.L. Marques, A. Castro, G.F. Bertsch, A. Rubio, Comput. Phys. Commun. 151, 60 (2003)ADSCrossRefGoogle Scholar
  20. 20.
    A. Castro, H. Appel, M. Oliveira, C.A. Rozzi, X. Andrade, F. Lorenzen, M.A.L. Marques, E.K.U. Gross, A. Rubio, Phys. Stat. Sol. B 243, 2465 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    A. Siddiki, J. Horas, D. Kupidura, W. Wegscheider, S. Ludwig, New J. Phys. 12, 113011 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    K. Guven, R.R. Gerhardts, Phys. Rev. B 67, 115327 (2003)ADSCrossRefGoogle Scholar
  23. 23.
    F. Dahlem, E. Ahlswede, J. Weis, K. von Klitzing, Phys. Rev. B 82, 121305 (2010)ADSCrossRefGoogle Scholar
  24. 24.
    A. Salman, V. Kotimaki, A. Siddiki, E. Rasanen, Eur. Phys. J. B 86, 155 (2013)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Adnan Menderes University, Faculty of Arts and Sciences, Physics DepartmentAydınTurkey
  2. 2.Mimar Sinan Fine Arts University, Faculty of Science and Letters, Physics DepartmentİstanbulTurkey

Personalised recommendations