Hall effect in the dielectric regime of granular metal films

The Hall effect is considered in the dielectric regime of granular metal films, where the charge-transport mechanism is quantum-mechanical tunneling between isolated metallic grains. The dominant temperature dependence of the Hall mobility is found to be ${\mu }_H\sim \exp [-{\left(\frac{T}{T_{0H}}\right)}^{\frac{1}{2}}]$, where $T_{0H}<<T_0$, the characteristic temperature in the exponent of the electrical conductivity. The sign of the Hall effect is found to alternate with the orbital-quantum number of the highest occupied level at the grain Fermi energy, giving rise to cancellation effects which reduce the magnitude of ${\mu }_H$ by a temperature-dependent prefactor. These arise from finite temperature effects and the inherent spread in grain diameters.