Anomalous hopping exponents of ultrathin metal films

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 the thickness of 5-15 Angstrom. 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=3/4 is the direct result of a filamentary vibron quantum percolation model appropriate to a granular network film. The concepts used int his 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.