Snaking states on a cylindrical surface in a perpendicular magnetic field

  • Andrei ManolescuEmail author
  • Tomas Orn Rosdahl
  • Sigurdur I. Erlingsson
  • Llorens Serra
  • Vidar Gudmundsson
Regular Article


We calculate electronic states on a closed cylindrical surface as a model of a core-shell nanowire. The length of the cylinder can be infinite or finite. We define cardinal points on the circumference of the cylinder and consider a spatially uniform magnetic field perpendicular to the cylinder axis, in the direction South-North. The orbital motion of the electrons depends on the radial component of the field which is nonuniform around the circumference: it is equal to the total field at North and South, but vanishes at the West and East sides. For a strong field, when the magnetic length is comparable to the radius of the cylinder, the electronic states at North and South become localized cyclotron orbits, whereas at East and West the states become long and narrow snaking orbits propagating along the cylinder. The energy of the cyclotron states increases with the magnetic field whereas the energy of the snaking states is stable. Consequently, at high magnetic fields the electron density vanishes at North and South and concentrates at East and West. We include spin-orbit interaction with linear Rashba and Dresselhaus models. For a cylinder of finite length the Dresselhaus interaction produces an axial twist of the charge density relative to the center of the wire, which may be amplified in the presence of the Rashba interaction.


Mesoscopic and Nanoscale Systems 


  1. 1.
    M.A. McCord, D.D. Awschalom, Appl. Phys. Lett. 57, 2153 (1990)ADSCrossRefGoogle Scholar
  2. 2.
    F.M. Peeters, A. Matulis, Phys. Rev. B 48, 15166 (1993)ADSCrossRefGoogle Scholar
  3. 3.
    A.A. Matulis, F.M. Peeters, P. Vasilopoulos, Phys. Rev. Lett. 72, 1518 (1994)ADSCrossRefGoogle Scholar
  4. 4.
    M. Cerchez, S. Hugger, T. Heinzel, N. Schulz, Phys. Rev. B 75, 035341 (2007)ADSCrossRefGoogle Scholar
  5. 5.
    A. Tarasov, S. Hugger, H. Xu, M. Cerchez, T. Heinzel, I.V. Zozoulenko, U. Gasser-Szerer, D. Reuter, A.D. Wieck, Phys. Rev. Lett. 104, 186801 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    H.A. Carmona, A.K. Geim, A. Nogaret, P.C. Main, J.T. Foster, M. Henini, S.P. Beaumont, M.G. Blamire, Phys. Rev. Lett. 74, 3009 (1995)ADSCrossRefGoogle Scholar
  7. 7.
    P.D. Ye, D. Weiss, R.R. Gerhardts, M. Seeger, M.K. von Klitzing, K. Eberl, H. Nickel, Phys. Rev. Lett. 74, 3013 (1995)ADSCrossRefGoogle Scholar
  8. 8.
    J.E. Müller, Phys. Rev. Lett. 68, 385 (1992)ADSCrossRefGoogle Scholar
  9. 9.
    S.I. Ibrahim, F.M. Peeters, Phys. Rev. B 52, 17321 (1995)ADSCrossRefGoogle Scholar
  10. 10.
    S.D.M. Zwerschke, A. Manolescu, R.R. Gerhardts, Phys. Rev. B 60, 5536 (1999)ADSCrossRefGoogle Scholar
  11. 11.
    A. Cho, Science 313, 164 (2006)CrossRefGoogle Scholar
  12. 12.
    K.-J. Friedland, R. Hey, H. Kostial, A. Riedel, K.H. Ploog, Phys. Rev. B 75, 045347 (2007)ADSCrossRefGoogle Scholar
  13. 13.
    K.-J. Friedland, A. Siddiki, R. Hey, H. Kostial, A. Riedel, Phys. Rev. B 79, 125320 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    X.X. Gayer, DPG Meeting, Berlin, March 2012Google Scholar
  15. 15.
    K.-J. Friedland, R. Hey, H. Kostial, A. Riedel, Phys. Stat. Sol. (c) 5, 2850 (2008)CrossRefGoogle Scholar
  16. 16.
    C. Thelander, P. Agarwal, S. Brongersma, J. Eymery, L. Feiner, A. Forchel, M. Scheffler, W. Riess, B. Ohlsson, U. Gösele, L. Samuelson, Materials Today 9, 28 (2006)CrossRefGoogle Scholar
  17. 17.
    T. Bryllert, L.E. Wernersson, L.E. Froberg, L. Samuelson, IEEE Electron Device Lett. 27, 323 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    T. Richter, C. Blömers, H. Lüth, R. Callarco, M. Indlekoffer, M. Marso, T Schäpers, Nano Lett. 8, 2834 (2008)Google Scholar
  19. 19.
    C. Blömers, T. Schäpers, T. Richter, R. Callarco, H. Lüth, M. Marso, Phys. Rev. B 77, 201301(R) (2008)ADSCrossRefGoogle Scholar
  20. 20.
    S. Wirths, K. Weis, A. Winden, K. Sladek, C. Volk, S. Alagha, T.E. Weirich, M. von der Ahe, H. Hardtdegen, H. Lüth, N. Demarina, D. Grützmacher, T. Schäpers, J. Appl. Phys. 110, 053709 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    C. Blömers, M.I. Lepsa, M. Luysberg, D. Grützmacher, H. Lüth, H.T. Schäpers, Nano Lett. 11, 3550 (2011)ADSCrossRefGoogle Scholar
  22. 22.
    C. Blömers, T. Rieger, P. Zellekens, F. Haas, M.I. Lepsa, H. Hardtdegen, Ö. Gül, N. Demarina, D. Grützmacher, H. Lüth, T. Schäpers, Nanotechnology 24, 035203 (2013)ADSCrossRefGoogle Scholar
  23. 23.
    C. Blömers, T. Grap, M.I. Lepsa, J. Moers, S. Trellenkamp, D. Grützmacher, H. Lüth, T. Schäpers, Appl. Phys. Lett. 101, 152106 (2012)ADSCrossRefGoogle Scholar
  24. 24.
    Y. Tserkovnyak, B.I. Halperin, Phys. Rev. B 74, 245327 (2006)ADSCrossRefGoogle Scholar
  25. 25.
    V.N. Gladilin, J. Tempere, J.T. Devreese, P.M. Koenraad, Phys. Rev. B 87, 165424 (2013)ADSCrossRefGoogle Scholar
  26. 26.
    G. Ferrari, A. Bertoni, G. Goldoni, E. Molinari, Phys. Rev. B 78, 115326 (2008)ADSCrossRefGoogle Scholar
  27. 27.
    G. Ferrari, G. Cuoghi, A. Bertoni, G. Goldoni, E. Molinari, J. Phys.: Conf. Ser. 193, 012027 (2009)ADSCrossRefGoogle Scholar
  28. 28.
    G. Ferrari, G. Goldoni, A. Bertoni, G. Cuoghi, E. Molinari, Nano Lett. 9, 1631 (2009)ADSCrossRefGoogle Scholar
  29. 29.
    M. Royo, A. Bertoni, G. Goldoni, Phys. Rev. B 87, 115316 (2013)ADSCrossRefGoogle Scholar
  30. 30.
    B.M. Wong, F. Léonard, Q. Li, T. Wang, Nano Lett. 11, 3074 (2011)ADSCrossRefGoogle Scholar
  31. 31.
    T. Rieger, M. Luysberg, T. Schäpers, D. Grützmacher, M.I. Lepsa, Nano Lett. 12, 5559 (2012)ADSCrossRefGoogle Scholar
  32. 32.
    F. Haas, K. Sladek, A. Winden, M. von der Ahe, T.E. Weirich, T. Rieger, H. Lüth, D. Grützmacher, T. Schäpers, H. Hardtdegen, Nanotechnology 24, 085603 (2013)ADSCrossRefGoogle Scholar
  33. 33.
    S. Bellucci, P. Onorato, Phys. Rev. B 82, 205305 (2010)ADSCrossRefGoogle Scholar
  34. 34.
    A. Bringer, T. Schäpers, Phys. Rev. B 83, 115305 (2011)ADSCrossRefGoogle Scholar
  35. 35.
    R. Winkler, Spin orbit coupling effects in two-dimensional electron and hole systems (Springer-Verlag, Berlin, Heidelberg, New York, 2003)Google Scholar
  36. 36.
    T. Ihn, Semiconductor nanostructures. Quantum states and electronic transport (Oxford University Press, 2010)Google Scholar
  37. 37.
    C. Fasth, A. Fuhrer, L. Samuelson, V.N. Golovach, D. Loss, Phys. Rev. Lett. 98, 266801 (2007)ADSCrossRefGoogle Scholar
  38. 38.
    H.J. Joyce, J. Wong-Leung, Q. Gao, H.H. Tan, C. Jagadish, Nano Lett. 10, 908 (2010)ADSCrossRefGoogle Scholar
  39. 39.
    J.H. van Vleck, The theory of Electric and Magnetic Susceptibilities (Oxford University Press, London, 1932)Google Scholar
  40. 40.
    A.V. Moroz, C.H.W. Barnes, Phys. Rev. B 61, R2464 (2000)ADSCrossRefGoogle Scholar
  41. 41.
    A.V. Moroz, C.H.W. Barnes, Phys. Rev. B 60, 14272 (1999)ADSCrossRefGoogle Scholar
  42. 42.
    L. Serra, D. Sanchez, R. Lopez, Phys. Rev. B 76, 045339 (2007)ADSCrossRefGoogle Scholar
  43. 43.
    J.S. Sheng, K. Chang, Phys. Rev. B 74, 235315 (2006)ADSCrossRefGoogle Scholar
  44. 44.
    J.S. Nowak, B. Szafran, Phys. Rev. B 80, 195319 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    C. Daday, A. Manolescu, D.C. Marinescu, V. Gudmundsson, Phys. Rev. B 84, 115311 (2011)ADSCrossRefGoogle Scholar
  46. 46.
    S. Bellucci, P. Onorato, Phys. Rev. B 68, 245322 (2003)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Andrei Manolescu
    • 1
    Email author
  • Tomas Orn Rosdahl
    • 2
  • Sigurdur I. Erlingsson
    • 1
  • Llorens Serra
    • 3
  • Vidar Gudmundsson
    • 2
  1. 1.School of Science and EngineeringReykjavik UniversityReykjavikIceland
  2. 2.Science InstituteUniversity of IcelandReykjavikIceland
  3. 3.IFISC (CSIC-UIB) and Department of PhysicsUniversity of the Balearic IslandsPalma de MallorcaSpain

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