Skip to main content
SpringerLink
Log in

Helical nuclear spin order in a strip of stripes in the quantum Hall regime

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

We investigate nuclear spin effects in a two-dimensional electron gas in the quantum Hall regime modeled by a weakly coupled array of interacting quantum wires. We show that the presence of hyperfine interaction between electron and nuclear spins in such wires can induce a phase transition, ordering electrons and nuclear spins into a helix in each wire. Electron-electron interaction effects, pronounced within the one-dimensional stripes, boost the transition temperature up to tens to hundreds of millikelvins in GaAs. We predict specific experimental signatures of the existence of nuclear spin order, for instance for the resistivity of the system at transitions between different quantum Hall plateaus.

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. T. Giamarchi, Quantum Physics in One Dimension (Oxford University Press, New York, 2003)

  2. V.J. Emery, E. Fradkin, S.A. Kivelson, T.C. Lubensky, Phys. Rev. Lett. 85, 2160 (2000)

    Article  ADS  Google Scholar 

  3. A. Vishwanath, D. Carpentier, Phys. Rev. Lett. 86, 676 (2001)

    Article  ADS  Google Scholar 

  4. R. Mukhopadhyay, C.L. Kane, T.C. Lubensky, Phys. Rev. B 64, 045120 (2001)

    Article  ADS  Google Scholar 

  5. S.L. Sondhi, K. Yang, Phys. Rev. B 63, 054430 (2001)

    Article  ADS  Google Scholar 

  6. C.L. Kane, R. Mukhopadhyay, T.C. Lubensky, Phys. Rev. Lett. 88, 036401 (2002)

    Article  ADS  Google Scholar 

  7. J.C.Y. Teo, C.L. Kane, Phys. Rev. B 89, 085101 (2014)

    Article  ADS  Google Scholar 

  8. J. Klinovaja, D. Loss, Phys. Rev. Lett. 111, 196401 (2013)

    Article  ADS  Google Scholar 

  9. J. Klinovaja, D. Loss, Eur. Phys. J. B 87, 171 (2014)

    Article  ADS  Google Scholar 

  10. A.A. Koulakov, M.M. Fogler, B.I. Shklovskii, Phys. Rev. Lett. 76, 499 (1996)

    Article  ADS  Google Scholar 

  11. M.M. Fogler, A.A. Koulakov, B.I. Shklovskii, Phys. Rev. B 54, 1853 (1996)

    Article  ADS  Google Scholar 

  12. R. Moessner, J.T. Chalker, Phys. Rev. B 54, 5006 (1996)

    Article  ADS  Google Scholar 

  13. E. Fradkin, S.A. Kivelson, Phys. Rev. B 59, 8065 (1999)

    Article  ADS  Google Scholar 

  14. A. McDonald, M.P.A. Fisher, Phys. Rev. B 61, 5724 (2000)

    Article  ADS  Google Scholar 

  15. M.P. Lilly, K.B. Cooper, J.P. Eisenstein, L.N. Pfeiffer, K.W. West, Phys. Rev. Lett. 82, 394 (1999)

    Article  ADS  Google Scholar 

  16. R.R. Du, D.C. Tsui, H.L. Stormer, L.N. Pfeiffer, K.W. Baldwin, K.W. West, Solid State Commun. 109, 389 (1999)

    Article  ADS  Google Scholar 

  17. M. Shayegan, H.C. Manoharan, S.J. Papadakis, E.P. De Poortere, Physica E 6, 40 (2000)

    Article  ADS  Google Scholar 

  18. I.V. Kukushkin, V. Umansky, K. von Klitzing, J.H. Smet, Phys. Rev. Lett. 106, 206804 (2011)

    Article  ADS  Google Scholar 

  19. A.G. Lebed, J. Exp. Theor. Phys. Lett. 43, 174 (1986)

    Google Scholar 

  20. D. Poilblanc, G. Montambaux, M. Heritier, P. Lederer, Phys. Rev. Lett. 58, 270 (1987)

    Article  ADS  Google Scholar 

  21. L.P. Gor’kov, A.G. Lebed, Phys. Rev. B 51, 3285 (1995)

    Article  ADS  Google Scholar 

  22. V.M. Yakovenko, Phys. Rev. B 43, 11353 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  23. D.-H. Lee, Phys. Rev. B 50, 10788 (1994)

    Article  ADS  Google Scholar 

  24. V.M. Yakovenko, in The Physics of Organic Superconductors and Conductors, edited by A.G. Lebed, Springer series in Material Sciences (Springer, Berlin, 2008), Vol. 110, p. 529

  25. K. Kobayashi, H. Satsukawa, J. Yamada, T. Terashima, S. Uji, Phys. Rev. Lett. 112, 116805 (2014)

    Article  ADS  Google Scholar 

  26. J. Klinovaja, D. Loss, Phys. Rev. Lett. 110, 126402 (2013)

    Article  ADS  Google Scholar 

  27. J. Klinovaja, D. Loss, Phys. Rev. Lett. 112, 246403 (2014)

    Article  ADS  Google Scholar 

  28. J. Klinovaja, D. Loss, Phys. Rev. B 90, 045118 (2014)

    Article  ADS  Google Scholar 

  29. T. Neupert, C. Chamon, C. Mudry, R. Thomale, arXiv:1403.0953 (2014)

  30. J. Klinovaja, Y. Tserkovnyak, arXiv:1405.4793 (2014)

  31. B. Braunecker, P. Simon, D. Loss, Phys. Rev. Lett. 102, 116403 (2009)

    Article  ADS  Google Scholar 

  32. B. Braunecker, P. Simon, D. Loss, Phys. Rev. B 80, 165119 (2009)

    Article  ADS  Google Scholar 

  33. T. Meng, D. Loss, Phys. Rev. B 87, 235427 (2013)

    Article  ADS  Google Scholar 

  34. C.P. Scheller, T.-M. Liu, G. Barak, A. Yacoby, L.N. Pfeiffer, K.W. West, D.M. Zumbühl, Phys. Rev. Lett. 112, 066801 (2014)

    Article  ADS  Google Scholar 

  35. M.A. Ruderman, C. Kittel, Phys. Rev. 96, 99 (1954)

    Article  ADS  Google Scholar 

  36. T. Kasuya, Prog. Theor. Phys. 16, 45 (1956)

    Article  ADS  MATH  Google Scholar 

  37. K. Yosida, Phys. Rev. 106, 893 (1956)

    Article  ADS  Google Scholar 

  38. M.R. Graber, W.A. Coish, C. Hoffmann, M. Weiss, J. Furer, S. Oberholzer, D. Loss, C. Schonenberger, Phys. Rev. B 74, 075427 (2006)

    Article  ADS  Google Scholar 

  39. M. Bockrath, D.H. Cobden, J. Lu, A.G. Rinzler, R.E. Smalley, L. Balents, P.L. McEuen, Nature 397, 598 (1999)

    Article  ADS  Google Scholar 

  40. H.O.H. Churchill, A.J. Bestwick, J.W. Harlow, F. Kuemmeth, D. Marcos, C.H. Stwertka, S.K. Watson, C.M. Marcus, Nat. Phys. 5, 321 (2009)

    Article  Google Scholar 

  41. J. Klinovaja, D. Loss, Phys. Rev. B 87, 045422 (2013)

    Article  ADS  Google Scholar 

  42. Y. Tserkovnyak, B.I. Halperin, O.M. Auslaender, A. Yacoby, Phys. Rev. Lett. 89, 136805 (2002)

    Article  ADS  Google Scholar 

  43. O. Auslaender, H. Steinberg, A. Yacoby, Y. Tserkovnyak, B.I. Halperin, K.W. Baldwin, L.N. Pfeiffer, K.W. West, Science 308, 88 (2005)

    Article  ADS  Google Scholar 

  44. P. Stano, J. Klinovaja, A. Yacoby, D. Loss, Phys. Rev. B 88, 045441 (2013)

    Article  ADS  Google Scholar 

  45. B. Braunecker, G.I. Japaridze, J. Klinovaja, D. Loss, Phys. Rev. B 82, 045127 (2010)

    Article  ADS  Google Scholar 

  46. P. Stano, J. Klinovaja, A. Yacoby, D. Loss, Phys. Rev. B 88, 045441 (2013)

    Article  ADS  Google Scholar 

  47. J. Klinovaja, D. Loss, Phys. Rev. B 87, 045422 (2013)

    Article  ADS  Google Scholar 

  48. J. Klinovaja, P. Stano, A. Yazdani, D. Loss, Phys. Rev. Lett. 111, 186805 (2013)

    Article  ADS  Google Scholar 

  49. B. Braunecker, P. Simon, Phys. Rev. Lett. 111, 147202 (2013)

    Article  ADS  Google Scholar 

  50. M.M. Vazifeh, M. Franz, Phys. Rev. Lett. 111, 206802 (2013)

    Article  ADS  Google Scholar 

  51. C. Kittel, Introduction to Solid State Physics (Wiley, New York, 2004)

  52. D. Loss, F.L. Pedrocchi, A.J. Legget, Phys. Rev. Lett. 107, 107201 (2011)

    Article  ADS  Google Scholar 

  53. D. Paget, G. Lampel, B. Sapoval, V.I. Safranov, Phys. Rev. B 15, 5780 (1977)

    Article  ADS  Google Scholar 

  54. M. Menzel, Y. Mokrousov, R. Wieser, J.E. Bickel, E. Vedmedenko, S. Bloegel, S. Heinze, K. von Bergmann, A. Kubetzka, R. Wiesendanger, Phys. Rev. Lett. 108, 197204 (2012)

    Article  ADS  Google Scholar 

  55. A. Yazdani, B.A. Jones, C.P. Lutz, M.F. Crommie, D.M. Eigler, Science 275, 1767 (1997)

    Article  Google Scholar 

  56. K. Hashimoto, K. Muraki, T. Saku, Y. Hirayama, Phys. Rev. Lett. 88, 176601 (2002)

    Article  ADS  Google Scholar 

  57. J.H. Smet, R.A. Deutschmann, F. Ertl, W. Wegscheider, G. Abstreiter, K. von Klitzing, Nature 415, 281 (2002)

    Article  ADS  Google Scholar 

  58. J.H. Smet, R.A. Deutschmann, W. Wegscheider, G. Abstreiter, K. von Klitzing, Phys. Rev. Lett. 86, 2412 (2000)

    Article  ADS  Google Scholar 

  59. S. Chesi, D. Loss, Phys. Rev. Lett. 101, 146803 (2008)

    Article  ADS  Google Scholar 

  60. P. Stano, D. Loss, arXiv:1408.2353 (2014)

  61. J.A. McNeil, W.G. Clark, Phys. Rev. B 13, 4705 (1976)

    Article  ADS  Google Scholar 

  62. K. Ono, S. Tarucha, Phys. Rev. Lett. 92, 256803 (2004)

    Article  ADS  Google Scholar 

  63. Y. Ren, W. Yu, S.M. Frolov, J.A. Folk, W. Wegscheider, Phys. Rev. B 81, 125330 (2010)

    Article  ADS  Google Scholar 

  64. D.C. Dixon et al., Phys. Rev. B 56, 4743 (1997)

    Article  ADS  Google Scholar 

  65. A. Kou, D.T. McClure, C.M. Marcus, L.N. Pfeiffer, K.W. West, Phys. Rev. Lett. 105, 056804 (2010)

    Article  ADS  Google Scholar 

  66. K.R. Wald, L.P. Kouwenhoven, P.L. McEuen, N.C. van der Vaart, C.T. Foxon, Phys. Rev. Lett. 73, 1011 (1994)

    Article  ADS  Google Scholar 

  67. T. Meng, L. Fritz, D. Schuricht, D. Loss, Phys. Rev. B 89, 045111 (2014)

    Article  ADS  Google Scholar 

  68. O.A. Starykh, D.L. Maslov, W. Häusler, L.I. Glazman, in Low-Dimensional Systems: Interactions and Transport Properties, Lecture Notes in Physics, edited by T. Brandes (Springer, New York, 2000), Part I, p. 37

  69. B. Braunecker, C. Bena, P. Simon, Phys. Rev. B 85, 035136 (2012)

    Article  ADS  Google Scholar 

  70. T. Meng, D. Loss, Phys. Rev. B 88, 035437 (2013)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, University of Basel, Klingelbergstrasse 82, 4056, Basel, Switzerland

    Tobias Meng & Daniel Loss

  2. Center for Emergent Matter Science, RIKEN, Wako, Saitama, 351-0198, Japan

    Peter Stano & Daniel Loss

  3. Institute of Physics, Slovak Academy of Sciences, 84511, Bratislava, Slovakia

    Peter Stano

  4. Department of Physics, Harvard University, Cambridge, Massachusetts, 02138, USA

    Jelena Klinovaja

Authors
  1. Tobias Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Peter Stano
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jelena Klinovaja
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Daniel Loss
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tobias Meng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meng, T., Stano, P., Klinovaja, J. et al. Helical nuclear spin order in a strip of stripes in the quantum Hall regime. Eur. Phys. J. B 87, 203 (2014). https://doi.org/10.1140/epjb/e2014-50445-1

Download citation

  • Received:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50445-1

Keywords

Search

Navigation