Nonlinear Effects on the Conductivity of a Superconductor above Its Transition Temperature

We study the conductivity $\sigma$ of a metal for temperatures slightly greater than its transition temperature $T_c$. In this region, the conductivity can reach very high values, because of the fluctuations of the order parameter. But, as we increase the electric field, the velocity of the accelerated electrons increases, the lifetime of the fluctuations decreases, and the conductivity decreases. For sufficiently high fields, the conductivity is thus found to vary as $E^{\frac{(\nu -4)}{3}}$, $\nu$ being the dimension of the sample.