Logarithmic temperature dependence of Hall transport in granular metals

We have measured the Hall coefficient $R_H$ and the electrical conductivity $\sigma$ of a series of ultrathin indium tin oxide films between 2 and 300 K. A robust $R_H$\,$\propto$\,ln$T$ law is observed in a considerably wide temperature range of 2 and $\sim$120 K. This ln$T$ dependence is explained as originated from the electron-electron interaction effect in the presence of granularity, as newly theoretically predicted. Furthermore, we observed a $\sigma$\,$\propto$\,ln$T$ law from 3 K up to several tens K, which also arose from the Coulomb interaction effect in inhomogeneous systems. These results provide strong experimental supports for the current theoretical concepts for charge transport in granular metals with intergrain tunneling conductivity $g_T$$\gg$1.