The Local Larmor Clock, Partial Densities of States, and Mesoscopic Physics

  • Markus Büttiker
Part of the Lecture Notes in Physics book series (LNPMGR, volume 72)


The Larmor clock is one of the most widely discussed approaches to determine the time-scales of tunneling processes. The essential idea [1,2,3] of the Larmor clock is that the motion of the spin polarization in a narrow region of magnetic field can be exploited to provide information on the time carriers spend in this region. It is assumed that incident carriers are spin polarized and that they impinge on a region to which a small magnetic field is applied perpendicular to the spin polarization of the incident carriers (see Fig. 9.1). The spin polarization of the transmitted and reflected carriers can then be compared with the polarization of the incident carriers. Dividing the angle between the polarization of the exciting carriers and that of the incident carrier by the Larmor frequency ωl gives a time. Originally, only spin precession (the movement of the polarization in the plane perpendicular to the magnetic field) was considered. However, [3] pointed out, that especially if we deal with regions in which only evanescent waves exist (tunneling problems) the polarization executes not only a precession but also a rotation into the direction of the magnetic field. In fact in the presence of a tunneling barrier, the spin rotation, is the dominant effect. Reference [3] considered a rectangular barrier and considered a magnetic field of the same spatial extend as the barrier. In the local version of the Larmor clock, introduced by Leavens and Aers [4], we consider an arbitrary region in which the magnetic field is non-vanishing and investigate again the direction of the spin polarization and rotation of the transmitted and reflected carriers.


Spin Polarization Quantum Channel Optical Potential Transmission Probability Partial Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A.I. Baz’: Sov. J. Nuc. Phys. 4, 182 (1967); 5, 161 (1967)Google Scholar
  2. 2.
    V.F. Rybachenko: Sov. J. Nucl. Phys. 5, 635 (1967)Google Scholar
  3. 3.
    M. Büttiker: Phys. Rev. B 27, 6178 (1983)CrossRefADSGoogle Scholar
  4. 4.
    C.R. Leavens, G.C. Aers: Solid State Commun. 63, 1107 (1989)CrossRefADSGoogle Scholar
  5. 5.
    C.R. Leavens, G.C. Aers: Phys. Rev. B 40, 5387 (1989)CrossRefADSGoogle Scholar
  6. 6.
    M. Büttiker: J. Phys.: Condensed Matter 5, 9361 (1993)CrossRefADSGoogle Scholar
  7. 7.
    M. Büttiker, H. Thomas, A. Prêtre: Z. Phys. B 94, 133 (1994)CrossRefADSGoogle Scholar
  8. 8.
    M. Büttiker, A. Prêtre, H. Thomas: Phys. Rev. Lett. 70, 4114 (1993); M. Büttiker, H. Thomas, A. Prêtre: Phys. Lett. A 180, 364 (1993)CrossRefADSGoogle Scholar
  9. 9.
    V. Gasparian, T. Christen, M. Büttiker: Phys. Rev. A 54, 4022 (1996)CrossRefADSGoogle Scholar
  10. 10.
    T. Gramespacher, M. Buttiker: Phys. Rev. B 56, 13026 (1997); Phys. Rev. B 60, 2375 (1999); Phys. Rev. B 61, 8125 (2000)CrossRefADSGoogle Scholar
  11. 11.
    R. Dashen, S. Ma, H.J. Bernstein: Phys. Rev. 187, 345 (1969)zbMATHCrossRefADSGoogle Scholar
  12. 12.
    Y. Avishai, Y.B. Band: Phys. Rev. B 32, 2674 (1985)CrossRefADSGoogle Scholar
  13. 13.
    G. Iannaccone: Phys. Rev. B 51, 4727 (1995)CrossRefADSGoogle Scholar
  14. 14.
    G. Iannaccone, B. Pellegrini: Phys. Rev. B 53, 2020 (1996)CrossRefADSGoogle Scholar
  15. 15.
    M. Büttiker, R. Landauer: Phys. Rev. Lett. 49, 1739 (1982); Physica Scripta 32, 429 (1985)CrossRefADSGoogle Scholar
  16. 16.
    D. Sokolovski, L.M. Baskin: Phys. Rev. A 36, 4604 (1987); H.A. Fertig, Phys. Rev. B 47, 1346 (1993)CrossRefADSGoogle Scholar
  17. 17.
    V. Gasparian, M. Ortuno, J. Ruiz, E. Cuevas: Phys. Rev. Lett. 75, 2312 (1995); Y. Japha, G. Kurizki: Phys. Rev. A 60, 1811 (1999)CrossRefADSGoogle Scholar
  18. 18.
    A.M. Steinberg: Phys. Rev. Lett. 74, 2405 (1995)CrossRefADSGoogle Scholar
  19. 19.
    S. Brouard, R. Sala, J.G. Muga: Phys. Rev. A 49 4312 (1994)CrossRefADSGoogle Scholar
  20. 20.
    X. Zhao: J. Phys. Cond. Matter, 12, 4053 (2000)CrossRefADSGoogle Scholar
  21. 21.
    M. Büttiker: in Electronic Properties of Multilayers and low Dimensional Semiconductors, ed. by J. M. Chamberlain, L. Eaves, J. C. Portal, (Plenum, New York, 1990). pp. 297–315Google Scholar
  22. 22.
    S.A. Ramakrishna, N. Kumar: Phys. Rev. B 61, 3163 (2000)CrossRefADSGoogle Scholar
  23. 23.
    C.W.J. Beenakker: cond-mat/0009061Google Scholar
  24. 24.
    P.W. Brouwer, S.A. van Langen, K.M. Frahm, M. Büttiker, C.W.J. Beenakker: Phys. Rev. Lett. 79, 914 (1997)CrossRefADSGoogle Scholar
  25. 25.
    G. Binnig, H. Rohrer: Helv. Phys. Acta 55, 726 (1982); J. Tersoff, D.R. Hamann, Phys. Rev. B 31, 805 (1985)Google Scholar
  26. 26.
    M. Büttiker: IBM J. Res. Develop. 32, 63 (1988)CrossRefGoogle Scholar
  27. 27.
    P.W. Brouwer, C.W.J. Beenakker: Phys. Rev. B 55, 4695 (1997)CrossRefADSGoogle Scholar
  28. 28.
    T.P. Pareek, Sandeep Joshi, A.M. Jayannavar: Phys. Rev. B 57, 8809 (1998)CrossRefADSGoogle Scholar
  29. 29.
    M. Büttiker: in Analogies in Optics and Micro-Electronics, ed. by W. van Haeringen, D. Lenstra, Kluwer Academic Publishers, (Dordrecht-Boston-London, 1990) pp. 185–202Google Scholar
  30. 30.
    T. Christen, M. Büttiker: Phys. Rev. Lett. 77, 143 (1996)CrossRefADSGoogle Scholar
  31. 31.
    B.J. van Wees et al.: Phys. Rev. Lett. 60, 848 (1988); D.A. Wharam et al.: J. Phys. C: Solid State Phys. 21, L209 (1988)CrossRefADSGoogle Scholar
  32. 32.
    M. Büttiker, T. Christen: in Mesoscopic Electron Transport, NATO Advanced Study Institute, Series E: Applied Science, ed. by L. L. Sohn, L. P. Kouwenhoven, G. Schoen (Kluwer Academic Publishers, Dordrecht, 1997) Vol. 345. p. 259; cond-mat/9610025Google Scholar
  33. 33.
    Tiago De Jesus, Hong Guo, Jian Wang: Phys. Rev. B 62, 10774 (2000)CrossRefGoogle Scholar
  34. 34.
    J.P. Pieper, J.C. Price: Phys. Rev. Lett. 72, 3586 (1994)CrossRefADSGoogle Scholar
  35. 35.
    W. Desrat, D.K. Maude, L.B. Rigal, M. Potemski, J.C. Portal, L. Eaves, M. Henini, Z.R. Wasilewski, A. Toropov, G. Hill, M. A. Pate: Phys. Rev. B 62 12990 (2000)CrossRefADSGoogle Scholar
  36. 36.
    S.A. Mikhailov, V.A. Volkov: JETP Lett. 61, 524 (1995)ADSGoogle Scholar
  37. 37.
    M. Büttiker: J. Math. Phys., 37, 4793 (1996)zbMATHCrossRefADSMathSciNetGoogle Scholar
  38. 38.
    M. Büttiker: in Quantum Mesoscopic Phenomena and Mesoscopic Devices, ed. by I.O. Kulik, R. Ellialtioglu, (Kluwer, Academic Publishers, Dordrecht, 2000) Vol. 559, p. 211; cond-mat/9911188Google Scholar
  39. 39.
    F.T. Smith: Phys. Rev. 118 349 (1960)CrossRefADSMathSciNetGoogle Scholar
  40. 40.
    M.H. Pedersen, S.A. van Langen, M. Büttiker: Phys. Rev. B 57, 1838 (1998)CrossRefADSGoogle Scholar
  41. 41.
    M. Büttiker, A.M. Martin: Phys. Rev. B 61, 2737 (2000)CrossRefADSGoogle Scholar
  42. 42.
    Y.B. Levinson: Europhys. Lett. 39, 299 (1997); L. Stodolsky, Phys. Lett. B 459, 193 (1999)CrossRefADSGoogle Scholar
  43. 43.
    E. Buks, R. Schuster, M. Heiblum, D. Mahalu, V. Umansky: Nature 391, 871 (1998); D. Sprinzak, E. Buks, M. Heiblum, H. Shtrikman, Phys. Rev. Lett. 84, 5820 (2000)CrossRefADSGoogle Scholar
  44. 44.
    Y.V. Fyodorov, H.J. Sommers: Phys. Rev. Lett. 76, 4709 (1996); V.A. Gopar, P.A. Mello, M. Büttiker: Phys. Rev. Lett. 77, 3005 (1996); P.W. Brouwer, K.M. Frahm, C.W.J. Beenakker: Phys. Rev. Lett. 78, 4737 (1997); Texier, A. Comtet: ibid. 82, 4220 (1999)CrossRefADSGoogle Scholar
  45. 45.
    P.W. Brouwer: Phys. Rev. B 58, R10 135 (1998)CrossRefGoogle Scholar
  46. 46.
    J.E. Avron, A. Elgart, G.M. Graf, L. Sadun: Phys. Rev. B 62, R10618 (2000)CrossRefADSGoogle Scholar
  47. 47.
    T.A. Shutenko, I.L. Aleiner, B.L. Altshuler: Phys. Rev. B 61, 10366 (2000)CrossRefADSGoogle Scholar
  48. 48.
    M.L. Polianski, P.W. Brouwer: cond-mat/0102159Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Markus Büttiker
    • 1
  1. 1.Département de physique théoriqueUniversité de GenèveGenèveSwitzerland

Personalised recommendations