Hall effect in hopping conduction in an ensemble of quantum dots

The Hall effect in heterostructures with a two-dimensional array of tunneling-coupled Ge quantum dots grown by molecular-beam epitaxy on Si is investigated. The conductivity of these structures in zero magnetic field at $4.2$ K varies in the range of $10^{-4}-10^{-12}\Omega^{-1}$, which includes both the diffusive transport under weak localization conditions and hopping conduction. It is shown that the Hall effect can be discerned against the magnetoresistance-related background in both high- and low-conductivity structures. The Hall coefficient in the hopping regime exhibits a nonmonotonic dependence on the occupancy of quantum dots by holes. This behavior correlates with that of the localization length of the hole wavefunctions.