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 T 1/2 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 T -3/2 dependence. For samples of high resistivity, large change of conductivity with log T 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.