Abstract
The logarithmic temperature dependence of resistivity, commonly observed in disordered films, has generally been interpreted as evidence for electron weak localization, with its slope indicative of the inelastic scattering mechanism. In this work, we show that the two-dimensional (2D) quantum percolation (QP) model, pertaining to disordered metallic films, predicts a sample-size-dependent $\mathrm{ln}L$ conductance correction that is three times larger than that for the Anderson model. Moreover, when the film has a finite thickness, the coefficient of $\mathrm{ln}L$ decreases to about $\frac{2}{3}$ of its 2D value for both the QP and the Anderson models. These results have direct implications for the interpretation of experimental data.
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