Weak and Strong Localization in Three-Dimensional Granular Bismuth Films

For various kinds of thick granular Bi films, conductivity and magnetoresistance (MR) have been measured at low temperatures down to 0.05 K in magnetic fields up to 84 kOe. Corresponding to the degree of disorder in a sample, systematic results have been obtained at low temperatures. For samples of low resistivity, conductivity with dependence and anomalous positive MR appear. These are well explained by the three-dimensional weak localization theory taking account of spin-orbit interaction. The inelastic scattering time shows dependence. For samples of high resistivity, large change of conductivity with log T-3/2 dependence and large positive MR with log H dependence are observed. For the sample of the highest resistivity, the conductivity changes more rapidly than log T. The MR is positive and rather large. This saturates and slightly decreases in high magnetic fields at very low temperatures.