Quantum Interference Phenomena in Strong Localization

  • Mehran Kardar
  • Ernesto Medina
Chapter

Abstract

The role of quantum interference phenomena is examined for strongly localized, non-interacting electrons. We compute, both numerically and analytically, the probability distribution for tunneling between sites separated a distance t, by summing all forward scattering paths. We find a probability distribution that is approximately log-normal; its mean proportional to t, and its variance growing as t 2ω, with ω depending on the dimension d. Since the mean and variance are independent, two parameters are necessary to describe the tunneling probability. We also study the response of the system to a magnetic field B, with and without spin-orbit (SO) scattering. Without SO a magnetic field leads to an increase in the localization length scaling as B 1/2. With SO, there is still a positive magnetoconductance (initially scaling as B 2 t 3), but no change in the localization length. The universal characteristics of the probability distribution can be probed by examining its moments. These moments describe the world lines of n attracting bosons in d - 1 dimensions- a well known many body problem! Various results for this simple problem are then used to provide analytical information on the distribution for tunneling in strong localization.

Keywords

Exchange Attraction Localization Length Tunneling Probability Strong Localization Paired Path 
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.
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Mehran Kardar
    • 1
  • Ernesto Medina
    • 2
  1. 1.Department of PhysicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Intevep SACaracasVenezuela

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