Universal Distribution of Resistance Fluctuations in Highly Disordered Granular Materials
Cecilia Pennetta
Abstract
We study the distribution of resistance fluctuations in conducting thin films with granular structure. A film is modeled as a resistor network in a non-equilibrium steady state determined by the competition between two biased stochastic processes consisting in the breaking and recovery of elementary resistors. The distribution of resistance fluctuations is found to exhibit relevant deviations from Gaussianity when the values of the external bias approach the threshold of electrical breakdown. The magnitude of these deviations increases strongly at increasing the degree of internal disorder. We show that this non-Gaussianity is in general related to the finite size of the system, thus vanishing in the thermodynamic limit. However, in highly disordered materials, close to the critical point of the conductor-insulator transition, the non-Gaussianity persists in the large size limit. Remarkably, in this case we have found that the distribution of the resistance fluctuations follows the universal Bramwell-Holdsworth-Pinton distribution within numerical uncertainty.
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