Selective Population of Modes in Electron Waveguides: Bend Resistances and Quenching of the Hall Resistance

  • Harold U. Baranger
  • A. Douglas Stone
Part of the NATO ASI Series book series (NSSB, volume 214)


In determining the salient characteristics of transport in small structures, the size of the sample compared to the important length scales in the material— the fermi wavelength, the elastic mean-free-path, the phase coherence length, and the localization length— defines several different regimes. In the last five years a great deal of attention has been devoted to studying the conductance fluctuations present in the coherent diffusive regime for which the system size is of the order of the phase-breaking length and much larger than the elastic scattering length.[1] More recent work has established that in certain materials electrons can travel without significant scattering or dephasing over a surprisingly large distance. The material of choice in this regard is the two-dimensional electron gas which is created at the GaAs/GaAlAs interface in modulation-doped heterostructures for which the elastic mean-free-path can be greater than 1 μm and the phase-breaking length can be greater than 10 μm. Furthermore, one can define wires in this material with a width of order the fermi wavelength.[2] Studies of transport in these “quasi-onedimensional ballistic microstructures” have revealed many novel features.


Fermi Energy Selective Population Hall Resistance Cross Structure Forward Transmission 
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  1. 1.
    For a review see H. Heimrich, G. Bauer, and F. Kuchar, eds., Physics and Technology of Submicron Structures ( Springer-Verlag, New York, 1988 ).Google Scholar
  2. 2.
    G. Timp, A. M. Chang, P. Mankiewich, R. Behringer, J. E. Cunningham, T. Y. Chang, and R. E. Howard, Phys. Rev. Lett. 59, 732 (1987).ADSCrossRefGoogle Scholar
  3. 3.
    M. Büttiker, Phys. Rev. Lett. 57, 1761 (1986).ADSCrossRefGoogle Scholar
  4. 4.
    R. Landauer, IBM J. Res. Develop. 1, 233 (1957)MathSciNetCrossRefGoogle Scholar
  5. R. Landauer, Z. Phys. B 68, 217 (1987).ADSCrossRefGoogle Scholar
  6. 5.
    A. D. Stone and A. Szafer, IBM J. Res. Develop. 32, 384 (1988).CrossRefGoogle Scholar
  7. 6.
    H. U. Baranger and A. D. Stone, submitted to Phys. Rev. B.Google Scholar
  8. 7.
    P. A. Lee and D. S. Fisher, Phys. Rev. Lett. 47, 882 (1981)MathSciNetADSCrossRefGoogle Scholar
  9. H. U. Baranger, A. D. Stone, and D. P. DiVincenzo, Phys. Rev. B 37, 6521 (1988).ADSCrossRefGoogle Scholar
  10. 8.
    G. Timp, H. U. Baranger, P. deVegvar, J. E. Cunningham, R. E. Howard, R. Behringer, and P. M. Mankiewich, Phys. Rev. Lett. 60, 2081 (1988).ADSCrossRefGoogle Scholar
  11. 9.
    M. L. Roukes, A. Scherer, S. J. Allen Jr., H. G. Craighead, R. M. Ruthen, E. D. Beebe and J. P. Harbison, Phys. Rev. Lett. 59, 3011 (1987).ADSCrossRefGoogle Scholar
  12. 10.
    H. U. Baranger and A. D. Stone, submitted to Phys. Rev. Lett.Google Scholar
  13. 11.
    The width in all of the straight wire cases, both with and without a magnetic field, is 21 sites. A hardwall boundary consists of simply truncating the lattice; for a harmonic cross-section, the single-site energies are varied within a structure of width 41. The graded-width wire varies from 21 to 41. To grade, we introduce a linear potential in the shaded region in the inset to Fig. 5b whose slope starts large and becomes zero near the junction. The B field is zero far from the junction and graded to the desired value within W of the junction; the non-uniformity of B does not affect the low field properties.Google Scholar
  14. 12.
    Y. Takagaki, K. Gamo, S. Namba, S. Ishida, S. Takaoka, K. Murase, K. Ishibashi, and Y. Aoyagi, Solid State Commun. 68, 1051 (1988).ADSCrossRefGoogle Scholar
  15. 13.
    F. Lenz, J. T. Londergan, E. J. Moniz, R. Rosenfelder, M. Stingl, and K. Yazaki, Ann. Phys. 170, 65 (1986).ADSCrossRefGoogle Scholar
  16. 14.
    F. M. Peeters, to be published in Superlattices and Microstructures and this proceedings.Google Scholar
  17. 15.
    R. L. Schult, D. G. Ravenhall, and H. W. Wyld, Phys. Rev. B 39, 5476 (1989).ADSCrossRefGoogle Scholar
  18. 16.
    S. Das Sarma and F. Stem, Phys. Rev. B 32, 8442 (1985).ADSCrossRefGoogle Scholar
  19. F. F. Fang, T. P. Smith, and S. L. Wright, Surf. Sci. 196, 1988 (1988).CrossRefGoogle Scholar
  20. 17.
    C. J. B. Ford, T. J. Thornton, R. Newbury, M. Pepper, H. Ahmed D. C. Peacock, D. A. Ritchie, J. E. F. Frost, and G. A. C. Jones, Phys. Rev. B 38, 8518 (1988).ADSCrossRefGoogle Scholar
  21. 18.
    A. M. Chang and T. Y. Chang, submitted to Phys. Rev. Lett..Google Scholar
  22. 19.
    C. J. B. Ford, S. Washburn, M. Büttiker, C. M. Knoedler, and J. M. Hong, submitted to Phys. Rev. Lett.Google Scholar
  23. 20.
    M. L. Roukes, private communication.Google Scholar
  24. 21.
    C. W. J. Beenakker and H. van Houten, Phys. Rev. Lett. 60, 2406 (1988).ADSCrossRefGoogle Scholar
  25. 22.
    F. M. Peeters, Phys. Rev. Lett. 61, 589 (1988).ADSCrossRefGoogle Scholar
  26. 23.
    D. G. Ravenhall, H. W. Wyld, and R. L. Schult, Phys. Rev. Lett. 62, 1780 (1989).ADSCrossRefGoogle Scholar
  27. 24.
    G. Kirczenow, Phys. Rev. Lett. 62, 1920 (1989) and submitted to Phys. Rev. B.Google Scholar
  28. 25.
    A. Kumar, S. E. Laux, and F. Stern, Appi. Phys. Lett. 54, 1270 (1989).ADSCrossRefGoogle Scholar
  29. 26.
    J. H. Davies, Bull. Am. Phys. Soc. 34, 589 (1989).Google Scholar
  30. A. Kumar, S. E. Laux, and F. Stem, Bull. Am. Phys. Soc. 34, 589 (1989).Google Scholar
  31. 27.
    C. W. J. Beenakker and H. van Houten, to be published in Phys. Rev. B.Google Scholar
  32. 28.
    A. Szafer and A. D. Stone, Phys. Rev. Lett. 62, 300 (1989).ADSCrossRefGoogle Scholar
  33. 29.
    H. van Houten and C. W. J. Beenakker, to be published in Nanostructure Physics and Fabrication, edited by M. Reed (Academic Press, 1989 ).Google Scholar
  34. 30.
    Within the adiabatic approximation and in the absence of a magnetic field, paths involving multiple reflections from the confining potential contribute substantially to the transmission around a bend, thus making a simple estimate of the effect of the B field difficult. Such multiple-scattering paths contribute a much smaller fractional amount to the forward transmission.Google Scholar
  35. 31.
    A. Chang has pointed out that once the magnetic field is large enough to turn the collimated beam into one of the leads, the Hall resistance will be particularly large.Google Scholar
  36. 32.
    B. J. van Wees, E. M. M. Willems, C. J. P. M. Harmans, C. W. J. Beenakker, H. van Houten, J. G. Williamson, C. T. Foxon, and J. J. Harris, Phys. Rev. Lett. 62, 1181 (1989).ADSCrossRefGoogle Scholar
  37. 33.
    B. J. van Wees, E. M. M. Willems, L. P. Kouwenhoven, C. J. P. M. Harmans, J. G. Williamson, C. T. Foxon, and J. J. Harris, Phys. Rev. B 39, 8066 (1989).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Harold U. Baranger
    • 1
  • A. Douglas Stone
    • 2
  1. 1.AT&T Bell Laboratories 4G-314HolmdelUSA
  2. 2.Applied PhysicsYale UniversityNew HavenUSA

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