Electrical resistance of disordered one-dimensional lattices

Rolf Landauer

doi:10.1080/14786437008238472

April 1, 1970Philosophical magazine

Electrical resistance of disordered one-dimensional lattices

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Key Points

Investigate the theoretical mechanism governing electrical resistance and wave transmission across disordered one-dimensional atomic lattices.
Formulated a one-dimensional quantum transport framework evaluating electron scattering through multiple localized potential barriers.
Calculated electrical resistance as a function of barrier transmission and reflection coefficients across disordered chains.
Demonstrated that electrical resistance scales non-linearly with length due to the coherent superposition of backscattered electron waves.
Identified that structural disorder causes exponential wave localization along one-dimensional lattices, suppressing standard diffusive conduction.

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Implication

Theoretical analysis reveals how transmission and reflection govern electrical resistance in disordered one-dimensional lattices, indicating that disorder induces exponential electron localization.

Abstract

(1970). Electrical resistance of disordered one-dimensional lattices. The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics: Vol. 21, No. 172, pp. 863-867.

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Rolf Landauer (1970) studied this question.

synapsesocial.com/papers/6a1b768c664f78119642e394 https://doi.org/10.1080/14786437008238472

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Electrical resistance of disordered one-dimensional lattices

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Electrical resistance of disordered one-dimensional lattices

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