Granular Effect on Electron Conduction in Discontinuous Metal Films

We reanalyze the seminal work by Dolan and Osheroff [Phys. Rev. Lett. $\mathbf{\text{43}}$, 721 (1979)] which reported anomalous low-temperature conduction of high-resistivity thin-film metal strips. We argue that the observed logarithmic increase of resistance with decreasing temperature in their 3-nm-thick Au-Pd strips be ascribed to the granularity effect on electron conduction in discontinuous metal films. This reanalysis is further supported by our measurements on conducting Pb${}_x$(SiO${}_2$)${}_{1-x}$ nanogranular films, where $x$ is the volume fraction of Pb.