Universal behavior of magnetoresistance in quantum dot arrays with different degrees of disorder

The magnetoresistance in a two-dimensional array of Ge/Si quantum dots was studied in a wide range of zero magnetic field conductances, where the transport regime changes from a hopping to a diffusive one. The behavior of the magnetoresistance is found to be similar for all samples--it is negative in weak fields and becomes positive with increasing magnetic field. The result apparently contradicts existing theories. To explain experimental data we suggest that clusters of overlapping quantum dots are formed. These clusters are assumed to have metal-like conductance, the charge transfer taking place via hopping between the clusters. Relatively strong magnetic field shrinks electron wavefunctions, decreasing inter-cluster hopping and, therefore, leading to a positive magnetoresistance. Weak magnetic field acts on 'metallic' clusters, destroying the interference of the electron wavefunctions corresponding to different paths (weak localization) inside clusters. The interference may be restricted either by inelastic processes, or by the cluster size. Taking into account weak localization inside clusters and hopping between them within the effective medium approximation, we extract effective parameters characterizing charge (magneto-) transport.