Abstract
We calculate the electrical resistivity (ER) \ensuremath{\rho} 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${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{\mathit{f}}$, and characteristic length ${\mathit{l}}_{\mathit{c}}$, for different-order interactions and different Euclidean dimensionalities d. As to the first interaction, \ensuremath{\rho} is proportional to T at the high-T limit, as known, and \ensuremath{\rho}\ensuremath{\sim}aT+${\mathit{bT}}_{\mathit{f}}^{3\mathit{d}\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}$/${\mathit{d}}_{\mathit{f}}$+d${\mathrm{\ifmmode \tilde{}\else \~{}\fi{}}}_{\mathit{f}}$-1 at some low-T ranges. In the second-order case, \ensuremath{\rho} 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 \ensuremath{\rho}-T curve, while after it \ensuremath{\rho} is a monotonically increasing function of T. The form of the \ensuremath{\rho}-${\mathit{d}}_{\mathit{f}}$ 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.
Published Version
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