Tunneling-percolation origin of nonuniversality: theory and experiments

TL;DR

This paper investigates the tunneling-percolation model as an explanation for nonuniversal transport exponents in disordered materials, supported by experiments on RuO2-glass composites showing divergence in piezoresistive response near the percolation threshold.

Contribution

It provides experimental validation for the tunneling-percolation model explaining nonuniversality in transport exponents through strain-dependent measurements.

Findings

Divergence of piezoresistive response at the percolation threshold for t > 2

No significant change in response for t = 2

Results align with tunneling-percolation theory predictions

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 = 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 RuO2-glass composites. We show that when t > 2 the measured piezoresistive response \Gamma, i. e., the relative change of resistivity under applied strain, diverges logarithmically at the percolation threshold, while for t = 2, \Gamma does not show an appreciable dependence upon the RuO2 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.