Disorder in a resistor network and the influence of disorder on the occurrence of superconductivity in thin granular metal films
Richard A. Ferrell
DOI 10.1103/PhysRevB.43.2726 · Physical Review B
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Abstract
A new computational method, based on a stationary property of the total dissipated power, is employed for determining the effect of disorder on the sheet resistance of a regular two-dimensional resistor network of coordination number z. It is found that a fractional variance of δ2 in the conductances raises the sheet resistance by the factor 1+2δ2/z. Applying this result to a thin granular metal film, where the conduction is by tunneling, and combining it with a separate study of quantum fluctuations, increases the maximum normal-state sheet resistance for global phase coherence and superconductivity by the factor 1+5δ2/2z. Two appendixes discuss in detail the computational method and compare it with the more familiar effective-medium theory.
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