NonlinearI-Vcharacteristics near the percolation threshold

Abstract

The I-V characteristics of a carbon-wax mixture slightly above the percolation threshold are found to be nonlinear. Generally for low (linear) -resistance samples, the I-V curves are smooth. The leading nonlinear term is quadratic, rather than cubic. For high-resistance samples, the onset of nonlinearity is marked by the appearance of resonance like structures in the R-V curves. The current ${\mathit{I}}_{\mathit{c}}$ at which nonlinearity starts scales with the linear conductance ${\mathrm{\Sigma }}_1$ as ${\mathit{I}}_{\mathit{c}}$∼${\mathrm{\Sigma }}_1^{\mathit{x}}$, with x≊1.4 in both cases. The second-order conductance, ${\mathrm{\Sigma }}_2$, in the case of smooth curves, also scales with ${\mathrm{\Sigma }}_1$ as ${\mathrm{\Sigma }}_2$∼${\mathrm{\Sigma }}_1^{\mathit{y}}$, with y≊0.59. Results are discussed within the framework of two previously suggested models. It is shown that none of these models can explain fully results obtained with the carbon-wax system.