Anomalous hopping exponents of ultrathin metal films

Abstract

Under the above title Markovic et al. [Phys. Rev. B 62, 2195 (2000)] summarized their and others' low-temperature data that show that a consistent underlying conduction mechanism is needed to explain thermally activated resistivities, with an exponent $x=0.75(5),$ on films of Ag, Bi, Pb, and Pd, with thicknesses of 5--15 \AA{}. While this x cannot be explained by any kind of conventional continuum hopping model, with or without Coulomb interactions, here it is shown that the exponent $x=\frac{3}{4}$ is the direct result of a filamentary vibron quantum percolation model appropriate to a granular network film. The concepts used in this model were recently used to derive finite-size scaling exponents and/or phase diagrams in many other contexts, including network glasses, the impurity band metal-insulator transition, high-temperature superconductors, and evolutionary biology.