Nonlinear electrodynamics of randomly inhomogeneous superconductors

We investigate the effect of macroscopic inhomogeneities on nonlinear transport properties of type-II superconductors and develop an effective medium theory to derive general relations between the global and local currents and electric fields. We show that even weak inhomogeneities with [delta J(c)(2)] << J(c)(2) can qualitatively change nonlinear transport characteristics (here delta J(c) denotes fluctuations of the critical current density J(c)), causing a nonmonotonic magnetic field dependence of the global averaged (J) over bar(c)(B), even if the local J(c)(B) decreases with B. We predict a superconducting Gunn effect, for which inhomogeneities can give rise to negative differential conductivity, bistability, and electric field domains.