Temperature and magnetic-field dependence of the resistivity of carbon-black polymer composites

The dc electrical resistance of carbon-black polymer composites has been studied over a wide temperature range from 300 to 0.35 K and in high magnetic fields up to 20 T for different carbon concentrations above the percolation threshold. The temperature dependence of the resistivity of all samples follows a Mott variable-range-hopping dependence like In rho-T--n with n>1/2 over the whole temperature range. This temperature dependence with n>1/2 may be understood on the basis of the superlocalization of electronic states in the fractal structure of the carbon-black polymer. At high temperatures where the hopping distance is comparable to the localization length, the magnetoresistance is small and negative, which may be accounted for by the suppression of quantum interference effects. The large and positive magnetoresistance at low temperatures where the hopping distance is lar er than the localization length may be due to the shrinkage of impurity orbitals in the magnetic field.