Published online by Cambridge University Press: 28 February 2011
We review the origins of the magnetoresistance in granular metals with emphasis on the quantum coherence effects arising from the interference of electrons traveling by different paths. We discuss the maximum in the magnetoresistance expected from scaling arguments and observed in granular aluminum. Two theories of the magnetoresistance in the variable range hopping regime, one based on the magnetic-field induced shift of the mobility edge and the other dealing with ‘directed’ hopping, are compared with experiments.