We calculate the electrical resistivity (ER) ρ of a fractal network from the view of the scattering of extended electronic states with both phonons and fractons and obtain different dependences of ER on the fractal dimensionality ${\mathit{d}}_{\mathit{f}}$, temperature T, fracton dimensionality d${\mathrm{̃}}_{\mathit{f}}$, and characteristic length ${\mathit{l}}_{\mathit{c}}$, for different-order interactions and different Euclidean dimensionalities d. As to the first interaction, ρ is proportional to T at the high-T limit, as known, and ρ∼aT+${\mathit{bT}}_{\mathit{f}}^{3\mathit{d}\mathrm{̃}}$/${\mathit{d}}_{\mathit{f}}$+d${\mathrm{̃}}_{\mathit{f}}$-1 at some low-T ranges. In the second-order case, ρ is a constant at the high-T limit, which is consistent with some recent experiments. In particular, we find that before a special fractal dimensionality ${\mathit{d}}_{\mathit{f}}^0$, there exists a minimum in the ρ-T curve, while after it ρ is a monotonically increasing function of T. The form of the ρ-${\mathit{d}}_{\mathit{f}}$ curve also shows different characteristics when d changes from 2 to 3. Finally, we discuss the percolating network and obtain scalar laws and scalar exponents.

• Received 13 April 1994

DOI:https://doi.org/10.1103/PhysRevB.51.883