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Quantum Coherence in Mesoscopic Systems pp 341–367Cite as

Resistance Fluctuations in Small Samples: Be Careful When Playing with Ohm’s Law

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Part of the book series: NATO ASI Series ((NSSB,volume 254))

Abstract

The discovery of random fluctuations [1,2] in the resistance of metal samples has wrought a small revolution in the understanding of electronic transport in samples with weak disorder (commonly known as metals). The fluctuations arise from quantum mechanical interference among the various trajectories that the electrons “follow” as they migrate from one end of the sample to the other. Obviously then the electrons must retain the coherence of their wavefunctions from one end to the other. By carefully summing up all the possible trajectories and interferences among them, Al’tshuler [3] and Lee et al. [4] have calculated the ensemble averaged variance of the conductance of wires of length L φ to be ((∆G)2) ≡ (G 2) -(G)2 ≡ (e 2/h)2. From an ensemble of classically identical samples (the theorists assume that the samples are carved from some mythical film where, on any scale larger than the mean free path length, the resistivity is utterly homogeneous, and the angular brackets refer to the average over this ensemble), one would find that the conductance fluctuates among the members by an amount characterized by a distribution of width ≃ e 2/h. Owing to a random Aharonov-Bohm (AB) effect, the conductance of a particular sample fluctuates by the same amount as a function of magnetic field [5], and the result of the sensitivity of the conductance to the impurity potential, it also fluctuates by ≃ e 2/h as a function of the Fermi energy [4] or when minute rearrangements occur in the impurity configuration [6]. In principle, this “universal” feature of the conductance of metal wires can be used as a measure of the phase coherence of the carriers and as a exquisitely sensitive probe of changes in the impurity potential [6].

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Authors and Affiliations

  1. IBM Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY, 10598, USA

    Sean Washburn

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  1. Physikalisch-Technische Bundesanstalt Braunschweig und Berlin, Braunschweig, Germany

    B. Kramer

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Washburn, S. (1991). Resistance Fluctuations in Small Samples: Be Careful When Playing with Ohm’s Law. In: Kramer, B. (eds) Quantum Coherence in Mesoscopic Systems. NATO ASI Series, vol 254. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-3698-1_23

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  • DOI: https://doi.org/10.1007/978-1-4899-3698-1_23

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