Correlation effects are investigated theoretically in the strongly Anderson-localized regime in the presence of spin-orbit (SO) interaction. Based on numerical studies on the Hubbard model with disordered on-site energies, we determine the magnetic-field dependence of the nearest-neighbor hopping conduction. In the absence of the SO interaction the magnetoconductance (MC) is positive. In the presence of the SO effect MC can be negative in low magnetic fields while it becomes positive in high magnetic fields. The multilevel Hubbard model, which has more than one level at each site, is also examined. The calculated results are qualitatively in good agreement with an experimental result of the nearest-neighbor hopping conduction in a Cu-particle film. We discuss the possibility of observing the proposed MC in other systems, e.g., an array of quantum dots.
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