Frequency-Dependent Transport in Quantum Wires

  • Bernhard Kramer
  • Jan Mašek
Part of the NATO ASI Series book series (NSSB, volume 214)


Coherent quantum transport phenomena have been the subject of many theoretical and experimental studies since the discovery of quantum interference oscillations in the magnetoresistance of thin metallic cylinders (Altshuler et al., 1981; Sharvin and Sharvin, 1981). Universal reproducible stochastic fluctuations in the magnetoresistance of small metallic systems (Washburn and Webb, 1986) have been attributed to the interference of elastically scattered electrons at randomly distributed impurities. In quasi one-dimensional inversion layers in Mosfets, similar fluctuations have been observed when changing the gate voltage at low temperatures (Fowler et al., 1982). They are due to localisation of electron states. Most recently, a new quantisation phenomenon was discovered in the conductance of geometrically constricted inversion layers of high-quality GaA1As heterostructures (van Wees et al, 1988; Wharam et al., 1988). It is believed that in these systems, at very low temperatures (< 1K) the electrons behave coherently and are not scattered elastically within distances of several p.m, due to the absence of phase-randomising scattering events and of impurities. The quantisation of the conductance can then be interpreted as a consequence of the size quantisation of the electronic energy levels (Imry, 1986; Sharvin, 1965; Johnston and Schweitzer, 1988; Kramer and Masek, 1988; Isawa, 1988; Kawabata, 1989).


JETP Letter Random Potential Linear Response Theory Channel Contribution Dimensionless Conductance 
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  1. Abramowitz, M., Stegun, I.A., 965, Handbook of Mathematical Functions (Dover Publications, New York)Google Scholar
  2. Albers, R.C., Gubernatis, J.E., 1978, Phys. Rev. B, 17, 4487ADSCrossRefGoogle Scholar
  3. Altshuler, B.L., Kravtsov, V.E., Lerner, Z.V., 1986, Soy. Phys.Google Scholar
  4. Altshuler, B.L., Kravtsov, V.E., Lerner, Z.V., JETP Letters 43, 441;ADSGoogle Scholar
  5. Altshuler, B.L., Kravtsov, V.E., Lerner, Z.V., Zh. Eksp. Teor. Fiz. 91, 2276Google Scholar
  6. Altshuler, B.L., Kravtsov, V.E., Lerner, I.V., 1987, Zh. Eksp. Teor. Fiz. 94, 258Google Scholar
  7. Altshuler, B.L., Kravtsov, V.E., Lerner, I.V., 1988, Springer Proc. Phys. 28, 300CrossRefGoogle Scholar
  8. Altshuler, B.L., Aronov, A., Spivak, B.Z., 1981, Soy. Phys. JETP Letters 33, 94ADSGoogle Scholar
  9. Altshuler, B.L., Aronov, A., 1985, in: “Electron-Electron Interactions in Disordered Systems”, A.L. Efros, M. Pollak, eds., Elsevier, New YorkGoogle Scholar
  10. Anderson, P.W., Abrahams, E., Ramakrishnan, T.V., 1979, Phys. Rev. Letters 43, 718ADSCrossRefGoogle Scholar
  11. Fisher, D.S., Lee, P.A., 1981, Phys. Rev. B 23, 6851MathSciNetADSCrossRefGoogle Scholar
  12. Fowler, A.B., Hartstein, A., Webb, R.A., 1982, Phys. Rev. Letters 48, 196ADSCrossRefGoogle Scholar
  13. Imry, Y., 1986, Physics of Mesoscopic Systems, in: “Directions in Condensed Matter Physics”, G. Grinstein and G. Mazenko, eds., 101, World Scientific, Singapore Isawa, Y., 1988, J. Phys. Soc. Japan 57, 3457Google Scholar
  14. Johnston, R., Schweitzer, L., 1988, J. Phys. C 21, L861ADSGoogle Scholar
  15. Kawabata, A., preprint, to be publishedGoogle Scholar
  16. Kramer, B., Masek, J., 1988, J. Phys. C 21, L1147ADSGoogle Scholar
  17. Kramer, B., Masek, J., 1989, to be publishedGoogle Scholar
  18. Lee, P.A., Ramakrishnan, T.V., 1985, Rev. Mod. Phys. 57, 287ADSCrossRefGoogle Scholar
  19. Lee, P.A., Stone, D., Fukuyama, H., 1987, Phys. Rev. B 35, 1039Google Scholar
  20. Luttinger, J.M., 1951, Phys. Rev. B 4, 814Google Scholar
  21. MacKinnon, A., 1985, Z. Phys. B 59, 385Google Scholar
  22. Masek, J., Kramer, B., 1988, Sol. St. Commun. 68, 611ADSCrossRefGoogle Scholar
  23. Masek, J., Kramer, B., 1989, Z. Phys. B75, 37CrossRefGoogle Scholar
  24. Masek, J., Kramer, B., 1989, Z. Phys. B75, 37CrossRefGoogle Scholar
  25. Schmid, A., 1985, Springer Ser. Sol. St. Sci. 61, 212ADSGoogle Scholar
  26. Sharvin, Y.V., 1965, Zh. Eksp. Teor. Fiz. 48, 984Google Scholar
  27. Sharvin, D.Yu., Sharvin, V.Yu., 1981, Soy. Phys. JETP Letters 34, 272ADSGoogle Scholar
  28. Szafer, A., Stone, A.D., 1989, Phys. Rev. Letters 62, 300ADSCrossRefGoogle Scholar
  29. Velicky, B., Masek, J., Kramer, B., 1989, to be publishedGoogle Scholar
  30. Washburn, S., Webb, R.A., 1986, Adv. Phys. 35, 375ADSCrossRefGoogle Scholar
  31. Wees, van, B.J., Houten, van, H., Beenakker, C.W.J., Williamson, J.G., Kouwenhoven, L.P., Marel, van der, D., and Foxon, C.T., 1988, Phys. Rev. Letters 60, 848ADSCrossRefGoogle Scholar
  32. Wharam, D.A., Thornton, T.J., Newbury, R., Pepper, M., Ahmed, H., Frost, J.E.F., Hasko, D.G., Peacock, D.C., Ritchie, D.A., and Jones, G.A.C., 1988, J. Phys. C 21, L209ADSGoogle Scholar

Copyright information

© Plenum Press, New York 1990

Authors and Affiliations

  • Bernhard Kramer
    • 1
  • Jan Mašek
    • 2
  1. 1.Physikalisch-Technische BundesanstaltBraunschweigF.R. Germany
  2. 2.Institute of PhysicsAcademy of SciencePrague 8CSSR

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