Possible Explanation of Nonlinear Conductivity in Thin-Film Metal Wires

We introduce the idea of an incoherence length ${L}_{2}$ at which inelastic collision broadening equals electronic energy-level separation. The two-dimensional conductance crosses over at ${L}_{2}$ from a $\mathrm{ln}L$ dependence suggested recently by Abrahams et al. to Ohmic behavior. These ideas and plausible relaxation and heating models are used to explain the nonlinear conductivity observations of Dolan and Osheroff.