Abstract
The characteristic length scales for the transport in disordered metals are discussed. Based on a phenomenological model of phase randomising scattering processes, the influence of the phase coherence length on the conductance of ballistic systems is studied. It is argued that the frequency dependence of the conductance of quasi-one dimensional systems can be used in order to determine not only the statistical average but the whole distribution function of the phase coherence length. Various cases of distributions, the δ-function, the exponential, and the Gamma distribution, are discussed. It is shown that due to quantum coherence effects deviations from the classical (Drude) behavior of the conductance exist. For independent scattering processes the probability distribution function is given by the Poisson distribution function. In this case an expression for the conductance can be derived which contains the ballistic transport, and the result for the exponential distribution.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bergmann, G.: Phys. Rep.107, 2 (1984)
Al'tshuler, B.L., Aronov, A.G., Khmel'niskii, D.E., Larkin, A.I.: In: Quantum theory of solids. Lifshits, I.M. (ed.). Moscow: MIR 1982
Aronov, A.G., Sharvin, Yu.V.: Rev. Mod. Phys.59, 755 (1987)
Washburn, S., Webb, R.A.: Adv. Phys.35 375 (1986)
Lee, P.A., Stone, A.D., Fukuyama, H.: Phys. Rev. B35, 1039 (1987)
Thouless, D.J.: Phys. Rev. Letters39, 1167 (1977)
Schmid, A.: In: Localisation, interaction, and transport phenomena. Kramer, B., Bergmann, G., Bruynseraede, Y. (eds.). Berlin, Heidelberg, New York: Springer 1985
Anderson, P.W., Abrahams, E., Ramakrishnan, T.V.: Phys. Rev. Letters43, 718 (1979)
Hikami, S., Larkin, A.I., Nagaoka, Y.: Progr. Theor. Phys.63, 707 (1980)
van Wees, B.J., Kouwenhoven, L.P., van Houten, H., Beenacker, C.W.J., Mooij, J.E., Foxon, C.T., Harris, J.J.: Phys. Rev. B38, 3625 (1988); van Wees, B.J., van Houten, H., Beenakker, C.W.J., Williamson, J.G., Kouwenhoven, L.P., van der Marel, D., Foxon, C.T.: Phys. Rev. Letters60, 848 (1988)
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., Jones, G.A.C.: J. Phys. C21, L209 (1988)
Mašek, J., Kramer B.: Sol. State Commun.68, 611 (1988)
In connection with transport in amorphous semiconductors, a different version of a random phase model has been discussed by Hindley, N.K.: J. Non-Cryst. Solids5, 17; 31 (1970)
Jacoboni, C., Reggiani, L.: Rev. Mod. Phys.55, 645 (1983)
Handbook of mathematical functions. Abramowitz, M., Stegun I.A. (eds.). Washington: National Bureau of Standard 1964
Alfano, R.R.: Semiconductors probed by ultrafast laser spectroscopy, Vol. II. London: Academic Press 1984
Kramer, B., Mašek, J.: (in preparation)
Mašek, J., Kramer, B.: Z. Phys. B-Condensed Matter75, 37 (1989)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kramer, B., Mašek, J. Influence of the phase coherence length on ballistic transport. Z. Physik B - Condensed Matter 76, 457–462 (1989). https://doi.org/10.1007/BF01307895
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01307895