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Transmission, Reflection and the Resistance of Small Conductors

  • M. Büttiker
Part of the NATO ASI Series book series (NSSB, volume 231)

Abstract

In this paper we present a simple discussion of the resistance of multi-probe conductors formulated in terms of transmission and reflection probabilities for carriers incident on the sample (Büttiker, 1986a; 1988a). It is transport in open conductors with current probes and voltage probes which is addressed. The formulation of resistances in terms of transmission of carriers through a conducting structure and reflection at the conductor stressing equilibrium electron reservoirs as carrier sources and sinks has been successfully applied to explain a number of transport phenomena in small conductors. These phenomena include the observed symmetries of the magneto-resistances at low fields in Aharonov-Bohm experiments (Büttiker, 1986a; Benoit et al. 1986), and in ballistic electron focusing experiments (van Houten et al. 1989) as well as in a number of other experiments both on macroscopic and microscopic conductors. This approach has also been applied to the phenomena of huge conductance fluctuations in multi-probe conductors (Büttiker, 1987; Baranger et al. 1988, Kane et al. 1989), and to low field magnetic anomalies in ballistic conductors (Roukes et al. 1987; Timp et al. 1988; Takagaki et al. 1988; Ford et al. 1989a; Avishai and Band, 1989; Kirczenow, 1989a; Ravenhall et al. 1989, Baranger and Stone, 1989a; Beenakker and van Houten, 1989a). Most important, the same formulae provide an especially clear discussion of the quantum Hall effect and lead to the prediction (Büttiker, 1988b) and experimental confirmation of quantized four-terminal resistances at values which differ from the bulk quantization (Washburn et al. 1988, Haug et al. 1988; van Wees et al. 1989a, Komiyama et al. 1989a). This approach and experiments for the first time shed light on the important role of contacts in the quantization at high magnetic fields, and thus have permitted a clearer understanding of the quantum Hall effect.

Keywords

Quantum Channel Edge State Transmission Probability Quantum Hall Effect Hall Resistance 
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

© Plenum Press, New York 1990

Authors and Affiliations

  • M. Büttiker
    • 1
  1. 1.IBM Research DivisionThomas J. Watson Research CenterYorktown HeightsUSA

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