Tunneling-percolation origin of nonuniversality: Theory and experiments

Abstract

A vast class of disordered conducting-insulating compounds close to the percolation threshold is characterized by nonuniversal values of transport critical exponent $t$, in disagreement with the standard theory of percolation which predicts $t\ensuremath{\simeq}2.0$ for all three-dimensional systems. Various models have been proposed in order to explain the origin of such universality breakdown. Among them, the tunneling-percolation model calls into play tunneling processes between conducting particles which, under some general circumstances, could lead to transport exponents dependent of the mean tunneling distance $a$. The validity of such theory could be tested by changing the parameter $a$ by means of an applied mechanical strain. We have applied this idea to universal and nonuniversal $\mathrm{Ru}{\mathrm{O}}_{2}$-glass composites. We show that when $t>2$ the measured piezoresistive response $\mathrm{\ensuremath{\Gamma}}$, i.e., the relative change of resistivity under applied strain, diverges logarithmically at the percolation threshold, while for $t\ensuremath{\simeq}2$, $\mathrm{\ensuremath{\Gamma}}$ does not show an appreciable dependence upon the $\mathrm{Ru}{\mathrm{O}}_{2}$ volume fraction. These results are consistent with a mean tunneling dependence of the nonuniversal transport exponent as predicted by the tunneling-percolation model. The experimental results are compared with analytical and numerical calculations on a random-resistor network model of tunneling percolation.